PROCESS OF CHANGE AND THE FACTORS INVOLVED IN THEM, …

BOLCSESZDOKTORI DISSZERTACIO

PROCESS OF CHANGE AND THE FACTORS

INVOLVED IN THEM, AS GOING OVER STUDENTS

WHO SPECIALIZE IN CORRECTIVE TEACHING OF

MATHEMATICS.

Liora Givon

2003

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EOTVOS LORAND UNIVERSITY, FACULTY OF ART

Ph.D. SCHOOL OF EDUCATION

PROCESS OF CHANGE AND THE FACTORS

INVOLVED IN THEM, AS GOING OVER STUDENTS

WHO SPECIALIZE IN CORRECTIVE TEACHING OF

MATHEMATICS

Liora Givon

Tutor: Dr. Istvan Nahalka

2003

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Declaration

I, Liora Givon, Israeli I.D. Number 05409630-0, hereby declare that this

dissertation was not submitted to any other university for the Ph.D.

degree.

Signed by

_______________

Liora Givon

15 Moran St.

Herzlia, 46414

Israel

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CONTENTS

Acknowledgments 5 Preface 6 Introduction 9 Chapter 1 Layout of The Study 11 1.1 Definition of Research Program 11 1.2 Purposes and Hypothesis 14 1.3 Methodology 15 1.4 Tools 19 1.5 Procedures 27 Chapter 2 Theoretical Fundaments 32 2.1 Reflection in Teaching 32 2.2 Developing Reflection in the Process of

Teachers’ Training 47

2.3 The Connection Between Reflection Evaluation and Building of Knowledge in a Constructive Environment

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Chapter 3 Results and Analysis 94 3.1 Strengthening the Sense of Confidence 98 3.2 The Change in the Sense of Efficacy 115 3.3 Controlling Teaching Methods of Mathematics 128 3.4 The Change in the Degree of Reflection 140 Chapter 4 Discussion 159 Chapter 5 Conclusion 169 Chapter 6 Recommendations Based on the Findings 176 Chapter 7 Summary 179 Chapter 8 Literature (References) 184 Appendices 200

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ACKNOWLEDGMENTS I would like to express special thanks to my scientific advisor, Dr. Istvan Nahalka, for his highly professional guidance and help. My gratitude goes to Dr. Yafa Bar-Ziv my colleague from the Kibbutzim College of Education for her enthusiastic and friendly support in the process of planning and editing my work. A special thanks goes also to my students for their positive cooperation while conducting this research. And last but not least, my thankfulness to my husband, Ehud, my children Yael, Yuval, Na'ama and Eyal, who supported me with love along the way and tolerated my long days and nights hours of work on this research.

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Preface The need for this study resulted from my interest, following a personal process I had gone through as a teacher for children with special needs, as an instructor for regular and special education teachers, and my work at the teachers training college. When I started to work, as a young teacher, I underwent a process of “entry shock”, in spite of my studies and training. Most of the time I was busy surviving, in front of my class, rather than learning and understanding my pupils. My work was characterized by lack of confidence, confusion and perplexity. The first training sessions I had as a teacher focused on basic problems I faced. Later they were some sort of pause from work, a chance to re-thinking and self-control. They evoked the need for change and diversity, released me from a load of negative emotions (anger, insult, frustration and disappointment) I had gathered in my work. They also allowed me re-consider – from a different perspective – the present, my future steps, as well as develop discretion and ability to prioritize my tasks. Years later, serving as teachers’ instructor, I could see in them the same processes I had gone through, but could not put my finger on them. I noticed that young teachers demonstrate enthusiasm and freshness, combined with a sense of vocation and a will to innovate (as well as implement and use the new theoretical knowledge), on one hand. On the other hand, adapting to the system often causes them to give up on clear elements of their self. The sense of enthusiasm is pushed aside, and the teachers adapt features, which the system thinks to be positive and welcome, resulting from thinking “what is right” rather than ”what should be done”. In my efforts to survive I realized that the teachers many times give up their own uniqueness. Another feature I experienced as a teacher, and then noticed as an instructor, was the lack of confidence in applying theoretical knowledge. In my case I dealt with it by acquired experience and accompanying training. Training if vital for new teachers, who are still feeling their way in the tangled framework of school, parents, pupils and supervision. As an instructor I discovered the need to give teachers taking their first steps a “platform” to express their needs, emphasizing their unique, independent thinking. In the training sessions I discussed with them every problem, both in groups and individually, with the purpose of directing, supporting, giving a shoulder – without causing dependency. Through training the

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teachers could authentically express their distress. They were overt and flexible, and were ready for self-criticism and change, if needed. Though the training was intended to impart knowledge in various subjects, including teaching skills (in the aspect of methodics and knowledge of various teaching methods) – it is an action intended to cope with the meanings of the profession. I.e., The teacher, as I see it, is not a pupil learning “specific subjects”. Training is a tool with which the teacher can clarify the meaning of teaching and the subject taught, trying to connect these two pivots. By discussing the subject with another person of knowledge in teaching and training, and with colleagues, the teacher can consolidate his professional identity, acquire new insights, improve his teaching methods and express his perceptions about teaching. Training, very often, is intended to contribute to clarifying the link between teacher and pupil, pinpointing the pupil’s needs and finding the way to balance them, are an indirect message of training - but basically, it deals with the teacher’s needs. Training attempts to help the teacher grow from the stage of dealing with his own problems (survival) to the next stage, focusing on the pupil and his needs. Following my personal experience as teacher and instructor, as well as many talks I had with colleagues, I concluded that it is possible, and advisable, to deal with the problems of teachers at the beginning of their way – already during their training. Correct professional training may contribute to the teacher’s confidence, to his sense of efficacy, improving his teaching methods and reaching high levels of reflection. Of all the courses I am teaching, I was interested especially in this one – dealing with students’ experience in math teaching to children with special educational needs. This course is unique and of great interest because it is experimental, and due to the fact that it is related to previous fears and failures in math experienced by the participating students. This course is unique also because of it being new and original for the students. For them, it was the first time they have experienced procedural individual work with a pupil. (Usually they experienced working in classes, small as they were). The process of change they underwent happened due to a process of socialization with the profession, but also due to the reflective training they received. As instructor of the course, I had the privilege of significant sharing of this primary experience. I assume that in this course, of all courses, the training would be more significant than in any other training course.

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After teaching several times in this course, realizing the importance of training – in relation to my past as a teacher and instructor – I decided to go more deeply into the matter. The present study describes and characterizes the process of change undergone by students during the course. By this study I wish to examine the meaning of my intervention and unique contribution to the change and growth process of the students, i.e., how does my intervention induce a change, in addition to the more familiar changes the teachers go through at the beginning of their way. Following the results of this study, its conclusions and recommendations, we could elaborate and improve the work and training model, to assist teachers in teaching this, and other subjects – which will be its contribution.

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Introduction The cognitive area is considered one of the most important intervention means for any educational and didactic process. It is used in a variety of ways, both for cultural transfer, and for the gathering and transferring of information, for education to values, personal shaping, etc’. The procedures of teaching have also gone a long way through human history. The process of learning is thought of as a passive process of receiving messages, whereas the process of teaching is a process of transferring these messages. This approach has been characteristic of teaching-learning processes, including the teacher training academies. During the recent decades there has been a tremendous progress in understanding the process of learning in humans. It is related to the fast economic, social and cultural changes around us. In our world, the emphasis has been of nurturing the ability of pupils for life long education. In a sophisticated, hi-tech technological environment, those who wish to perform efficiently, as per Darling–Hammond (1996), will only be the pupils, who know how to find, and select – out of the flood of information – the details necessary to create data bases. Among others - Non-cognitive factors, such as personal involvement of the learner, have received increased importance. The issue of the pupil’s personal involvement is now one of the cornerstones of the teaching doctrine. The learner is not perceived as just an object, but rather as both an object and subject. For that purpose he has to control his own learning process. I.e., In order to achieve the efficiency required for the success of teaching process, the teacher cannot ignore himself as one of the active factors in this process. He should be able to deal at the same time with both “objects” he acts on, but no less has he to be able to activate on himself procedures of meta-cognitive control. By these procedures he can direct his work properly and do it with efficiency, and high levels of efficiency in achieving his educational and didactic purposes. Multi-directional reference as such, is definitely a problem. But this problem is even more acute due to the necessity to activate it immediately, during the teacher’s work, when he cannot settle for the delayed one, after a while. With all the importance of reflection on action, it requires completion of reflection in action (Schon, 1987).

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The present study examines the process of change and the factors involved, undergone by students training in corrective math teaching. During the course, the students were exposed to various teaching situations, at the same time developing and nurturing situations of reflection. The study discusses various aspects of reflective teaching, and the place of reflection in the professional training process of the trainees. The course creates a reflective culture by experiencing individual work with pupils having problems in math, dialogues, training sessions and feedback, written reports and feedback following each lesson. All these components are an integral part of a process intended to train a teacher with full control of his own learning process. These processes include, in addition to knowledge of teaching methods, intensifying procedures and changing of knowledge base, reflection-linked procedures, evaluation and building of knowledge in a constructivist environment.

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1Chapter Layout of the Study

1.1 Definition of the Research Program The purpose of this study is to examine the process of change undergone by students in the course for corrective teaching of mathematics, as part of their training in special education. Within the framework of their studies in special education, at their last year, the students are required to choose one subject of specialization of the following two: Teaching of reading and writing, or mathematics to children with special educational needs. One of the groups, specializing in math, is managed and instructed by myself, in a course, which is based on experience and accompanied by reflective guidance. At the beginning of the year, personal interviews were held with the students who had chosen this course of corrective teaching of math (to children with special needs). Most of them reported that the reasons they had chosen this specialization were: Personal problems, fear and apprehension, lack of knowledge in the teaching of math in general and especially to children with special needs, lack of tools and aversion of the subject. They all hoped that during the course they could broaden their knowledge, acquire a variety of tools, as well as having some sort of corrective experience during the year. At the end of school year, in the personal interviews, summing up sessions and written feedback from the students, a different picture can be noticed. The barrier of the subject has been removed, motivation to teach has increased and significant changes have occurred in their attitude to the subject and the teaching thereof. (of course, there are differences in the type of change and its intensity between them). Professional literature describes the process of change undergone by teachers, and during the course the students experience work with children. Ina Fuchs (1995) defines the process of professional development of a teacher as the process he/she undergoes from the beginning of training and starting to work, until their retirement. She argues that the professional development of a teacher is expressed in his educational approach, his cognitive level and his professional knowledge, his teaching skills, personal confidence, the ability to perform in the organization in which he works and the satisfaction he derives from work.

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Professional focus, as per Fuchs (1995) relates to the professional development, taking place following the process of learning. Such process is characterized by the acquisition of knowledge and insight, a clear standpoint toward education and the professional group, and control of the behavioral repertoire needed by the teacher in everyday doing in his professional environment. The emphasis in this focus is on a process enabling both personal and professional specialization, at a high standard of teaching. To be more specific, this approach focuses on the changes taking place in the quality of teaching during the various phased:

• The acquisition of knowledge related to learning environment. • Gradation starting with the very socialization until it becomes

extreme commitment to work, increasing control of teaching skills. • An open attitude toward curriculum. • A richer repertoire of teaching methods, feeding on experience and

time. • Changes in the teacher’s image and standpoints. • The direction of his personal concepts. • Greater flexibility, and increased relaxation, following the increase

in confidence and the wish to experiment new methods and ideas. Ina Fuchs (1995) presents a model comprised of four stages. As she sees it the model is related to age, but more than that it is related to the experience in teaching. This approach reads that though some teachers may reach a high level of professionalism very fast, other will never get there. According to this model, there are four phases of professional development: Survival, or becoming – a phase of vast possibilities for coping with basic problems of teaching, thus it is accompanied with stress and anxiety. Growing – an interim phase, characterized by processes of building, acquisition of knowledge and a better perception of the learners and the teacher himself – by the teacher. Curriculum and other materials are better understood, teachers find more satisfaction in their work, as well as looking for ways to improve it. Maturity – a phase characterized by both personal and professional confidence, involvement in professional life, ability to focus on the learner and his needs, as well as relaxation and an open mind for new ideas.

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Full professional functioning – the phase in which the teacher is all absorbed in the educational process, makes the most of his potential, is capable of responding to all the pupil’s needs, and has an integrative perception of teaching (Katz, 1972; Unruh & Turnerm 1970, Burden, 1982; Watts, 1980; Gregorc, 1973). According to professional literature, all teachers go through several phases and changes of professional development. In a pioneering study I did previously (being an instructor at the course) I found out that student undergo many significant changes during the course, some of which are mentioned in literature. They also report that this course had the most meaning for them. No doubt these changes take place due to the nature of the course, which includes experiencing, as well as being related to mathematics. It is mathematics - usually known to arouse frustrations, stress and experience of failure and anxiety – that my intervention as instructor is more significant. The process of experience in the course is accompanied by reflective teaching and guidance. I assumed that, in addition to the natural process, as mentioned by Fuchs (1995) my intervention makes all the change. Following the findings, I wish to set up some sort of intervention model that will serve teachers training students: Specializing in corrective teaching within the framework of training process. This model shall be based on material accumulated during the course. The choice of qualitative study was made in order to examine a field process. In order to study this process, I found it extremely important to be on site, see all the details, observe the participants and understand their thoughts, talk to them and understand their behavior. To do all that I had to collect evidence and information, regarding their feelings, standpoints and work. The tools I chose for that purpose were as follows: Personal interviews, observations, training and feedback sessions, as well as pedagogic diaries (to be detailed in “tools”). Part of these tools served me previously in my work, though I had to improve them for this study. My assumption is that the study tools can render a great amount of information regarding process of change undergone by the student during the course.

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1.2 Purposes and Hypothesis 1.2.1 Purpose of the Study The purposes of this study are as follows: To identify, record, expose, characterize and analyze processes of change undergone by students of special education, who chose to specialize in corrective teaching of math to children with learning disorders. To examine the involved factors which create these processes of change. 1.2.2 Questions of the Study The questions raised by this study are:

• What process of change do the students (teaching trainees) go through in their special education course (4th year): Specializing in corrective teaching of mathematics?

• What are the factors effecting the process of change? 1.2.3 Hypothesis of the Study The present study examines the process of change undergone by students specializing in corrective teaching of math. Since the performer of this study (instructor of the course) deals with teachers’ training in corrective teaching of math to children experiencing difficulties, and having done a previous pioneer study, she raises several assumptions regarding the processes expected to take place among these students during the course. We can assume that students will undergo a process of socialization, every beginning teacher goes through. But, with regard to math, there is another factor of stress due to anxiety, frustration and a feeling of insecurity resulting from previous personal failure (as reported by teacher at the beginning of the year). Thus, we may assume that following individual work with children with difficulties in math, twice a week, plus tutoring sessions including a dialogue and consultation, and both oral and written feedback from the instructor – many changes are bound to happen. These changes will be in the students’ sensation of capability regarding the teaching of math, in coping with didactic and emotional feelings of their pupils, in their own professional identity and personal and professional growth. These changes will express themselves in several plains:

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Learning of new contents in math, teaching and improving of teaching methods of math. Improving the feeling of confidence in learning and teaching of math. Improving the ability to plan a lesson and adapt it to the pupil’s needs; writing lesson layouts and translating the targets into applied work. Understanding the pupil’s emotional difficulties, coping with them and understanding the link between them and learning achievements. Making changes during lesson, and coping with unexpected situations. 1.3 Methodology 1.3.1 Study Population The sample of this study consists of fifteen female students, at the Kibbutzim Teachers’ College, all specializing in special education. They are all in the fourth year – their last, and all of them chose to major in teaching mathematics to children with learning disorders or difficulties in math. (Students majoring in special education are required to choose one of two options: Teaching of reading or math to children with learning disorders or difficulties). All the students have graduated high school, they all have basic knowledge of math, and all have passed the threshold exam for basic skills. They live in various places in Israel and are of average socio-economic level. The age of fourteen students ranges between the age of 26-28 years, and one is 35 years old (studying to be a teacher following a decision to change her profession). Two of them have children. The pupils who arrived to work at the seminar were fourth graders at one of the regular schools in the southern part of Tel Aviv. 1.3.2.Structure of the course: A workshop specializing in corrective teaching of children with special needs: Purposes of the Course (as presented in the curriculum given to students): Developing a professional approach, which includes reflective teaching and examination of the link between tasks and the learner’s needs. Getting to know the rubric and experiencing thereof as a tool in teaching-learning process. Experiencing alternative assessment in constructivistic learning.

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Performing didactic diagnosis in math and preparing an individual program as per the findings. Choosing activities and tasks to challenge and promote the pupil. Intensifying the understanding of learning difficulties in math. Developing learning strategies to overcome difficulties and gaps. Practicing Treatment methods for corrective math teaching. Experiencing planning and performing of individual structured treatment according to the following detail: Subjects of the course: Experiencing diagnostic analysis of pupils with difficulties in mathematics:

• Acquaintance and info gathering. • Choosing tasks appropriate for the pupil. • Using diagnostic and mediation tools. • Recording and analyzing the results by identifying mathematical

thinking processes. • Identifying gaps in the pupil’s knowledge. • Writing the summing report.

Experiencing diagnostic teaching:

• Setting targets and goals, as per the diagnostic findings. • Choosing intervention tools and grading them. • Performing a current intervention program, including diversifying

the teaching methods and means. • Planning accessories and appropriate assessment tools. • Combining mediation processes in teaching. • Reporting and discussing teaching process and writing lesson

layouts. • Structuring a summing-up test according to targets and

achievements, and parting from the pupil. • Analysis of work based on standards set previously.

During the year the students experience individual teaching twice a week, with a pupil having difficulties in math. The lessons take place at the Seminar, where pupils arrive from one of the elementary schools in Tel Aviv, being selected by their own school. Prior to the beginning of work, the students meet each pupil’s home class teacher, to be briefed. Following the meeting with the home class teacher the pupils arrive in the Seminar. The first meeting is an acquaintance session between student

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and pupil. This session is planned by the student, under my guidance. (The decision who will study with whom is arbitrary). On the second session a didactic diagnosis in math is performed. It may continue for the next for or five sessions. The students sum up the analysis, including relating to strong points and those to be improved. Also, the students are required to report of how the pupil makes use of his existing knowledge, of his attitude to subjects he regards as difficult - or easy; of the manner he copes with various tasks; the type of his errors; is there any formal – or intuitive - knowledge; does he know the procedures, arithmetical rules and computation procedures; is he familiar with required functions and does he have any mathematical thinking of the nature of functions. Following the findings and the information regarding the pupil, the students set up a prioritized intervention program. This is done personally, with each student, under my guidance. The results and the intervention program are then presented to the pupil, and learning process begins immediately. For every session the students prepare a layout (Appendix 3), which includes purposes, accessories, etc’. These layouts are constructed as per the purposes set by the intervention program, and include all the activities to be performed by the pupil, time planning, means and accessories – each as per professional considerations. During the session the students are required to record each pupil’s behavior and performance. At the end of the session they record it, jointly with the pupil, in their “communication notebook”. Following every session the students sum up their notes on a special form, consisting of 9 reflective questions, to record the work process with the pupil. This form is examined after each session, together with accessories used in the lesson, and receives a feedback from the instructor. Sometime a training session is set following subjects I read, or noted on, or questions arising in response to the follow up form. There are no lessons during the semester vacation. All through the year many training sessions, part of them on a routine basis, are held with each student separately, dealing with a variety of issues. These talks may include personal discussion with regard to an intervention program, assistance in determining the subjects to be taught, in phrasing or choosing a method or accessories. During these training sessions students raise various dilemmas and difficulties relating to their work with the pupils. Also, these talks serve as consultations and a means of reflection on issues, relevant to the teaching-learning procedure.

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Subjects are raised both by the students and by myself (following program and follow up forms, or personal observations). At the end of school year, the students take a summing-up test on all the subjects they taught. Sometimes they do not manage to complete the intervention, and on other times the intervention program may be changed to accommodate the pupil’s needs. During the last session with the child, every student interviews the pupil about the work they have done jointly during that year, and gives her feed back on his performance during the year. In addition, every students presents her procedure of work to all the group members, including her educational approach, the targets she had set, accessories used and her own learning from the procedure. The purpose of this is to share with other group members the processes of change and learn from each other. During all year I will follow the students, observing them during sessions, and eventually intervening – by their request or my own discretion. This close follow-up relates to every subject concerning their work. (As detailed in the “procedures” section). At the end of the first semester and at the end of the year the students assess their work, both by numerical grades and verbal description, according to standards set by me (Appendix 7). Following the assessment a personal session is held with me (instructor), and the final score is determined. (All courses in the college are assessed by numerical grades).

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1.4 Tools 1.4.1 Pedagogic Diary and Individual Reports: The rationale behind the choice of tools: Diaries always make efficient tools for gathering of information about the student’s process of work’ as well as developing the ability to reflect on the process of learning. Those who support the use of diaries during studies, agree with Vygotsky (1962), who spoke about the importance of inner talk for the development of thinking. There are various types of diaries used for recording. Keeping a pedagogic diary during the course is supposed to serve the student for self-assessment and communication, both with herself and her tutor (conducting the study). It is, in fact, a reflective tool. The student is required to answer daily, reflection-directed, questions, with the purpose that eventually these questions will be internalized and accompany her routine learning. Many studies (Birenbaum, 1997) showed that using a diary improves and promotes the thinking characteristics of students. It turned out that using the diary effected in various manners the cognitive processes of the students. It gave them a more sophisticated conception with regard to learning, a greater awareness of cognitive processes and better control thereof, using complex cognitive strategies – all of which indicate better organization of knowledge and developing comprehensive semantic skills at the base of knowledge (McCrindle & Christensen, 1995). Other studies showed that keeping a diary increases the student’s confidence and self-esteem (Doney, 1995; Flix & Lawson, 1994), improves inter-personal communication (Patrick, 1994; Collins, 1991) and increases the student’s level of creativity (Anderman, 1993). In order to develop the reflective skills of the student, constructed questionnaires should be used, at least at the initial stages (Birenbaum, 1997). A pedagogic diary resembles a work diary. Its advantage, unlike other verbal reports, is in the possibility to detect the process of writing continuously and within an authentic learning context, at the same time attaining a variety of information. As Birenbaum (1997) sees it, the diary serves important purposes in the process of teaching and reflective learning. The diary serves for records, awareness, reflection, follow up, inner dialogue, dialogue with the tutor, pinpointing difficulties and feedback for both student and tutor.

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In the present study, all students keep a pedagogic diary. They are responsible to collect all material and submit it to the teacher. This diary includes all documents, products and a variety of other materials creating an authentic evidence of the student’s learning process. The pedagogic diary includes the following:

• A questionnaire about their attitudes and feelings regarding the course and the future work. This questionnaire (called “Starting A New Way…”) consists of 15 questions, composed by the person conducting this study (and course instructor). The questionnaire is given to the students at the beginning of the course and will examine the changes in their perceptions and standpoints with regard to the course. The questionnaire is included in Appendix 1.

• Information sheet from the home class teacher, including personal details of the pupil, his social and educational state, and his expectations of the course. As the student working with the pupil in the course does not see him in his natural surrounding at school, his home class teacher is the dominant figure, and solid cooperation is required between all those who deal with the pupil.

• Records of the first meeting between pupil and student, including program, summary and accessories. This first meeting is vital in order to establish an acquaintance between the two, so vital – I believe - prior to starting the actual work.

• Didactic analysis in mathematics (as per Rivka Kidron,1989). For the purpose of planning the appropriate teaching program for the pupil, a didactic diagnosis, revealing the pupil’s maximum achievement and the reasons for not getting there, is performed. It includes, also, the methods, conditions and educational accessories by which he may achieve maximum goals within his personal abilities. This is not a formal procedure, and is intended to examine the ways in which each pupil act – the “what” and the “how” (Kidron, 1985). Following the results, the student will prepare her intervention program.

• Summary, consisting of: The pupil’s background, findings of the

math. Diagnosis and proposal of intervention program, as per a response rubric created by the author of this study in appendix 2.

• A feedback for the pupil’ of the diagnosis results. • A ‘communication notebook’ between pupil and student, in which

all the studied subjects are written, plus the pupil’s work, regulations and other reports.

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The lessons layout programs (composed by the author) are a significant part of our work, since they record all the work procedure. They may assist us in assessing changes and developments of our goals, contents and accessories, as well as our considerations. The complete learning procedure can be assessed as well. These programs consist of two parts:

• First section contains the plan for the lesson layout. Here the students are required to note the mathematical target for that specific session, and the emotional-therapeutic-functional target of that class. Also, they are required to detail the pupils’ intended activities for that class, their considerations in choosing them, allotment of time, means and accessories for that class, and the reasons for choosing them. The students are required to record the pupil’s activities during class.

• The second section includes the summing up of the class. It includes 9 questions, about the planning, course and performance of the lesson, as well as questions regarding future learning.

• The assessment of the lesson plan and its summing up is done by a Lesson layout rubric, prepared by the author. It is included in Appendix 3.

The rubric for writing the lesson layout appears in appendix 4.

• The product of both the student and pupil’s activities (work sheets,

games and accessories). • Follow-up sheet for teaching process, in which the order of lessons,

dates and subjects are entered. • Attitude questionnaire, including perceptions and reflections with

regard to the work procedure, to be done at mid-term (titled “We Are Already Half Way Through”), containing 15 questions composed by the author (see appendix 5).

• Summing diagnosis of the mathematical subjects learned, composed individually be every student, for her specific pupil.

• Written feedback for the pupil, dealing with the results of diagnosis and summary of the joint work (in addition to oral feedback).

• End of year interview with the pupil, following which the pupil will reply in writing. Questions to be composed by the student.

• Summarizing report of the pupil’s state in math (within the course framework), his progress and performance during the year, in light of the goals set previously, as well as recommendations for the future.

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• Reflective summary at the end of the year: The students will assess their own work and the process they have gone through, by a 12 questions questionnaire (composed by the author and named “Summing up the Year”). Also, the students may sum up the year in free writing, with reference to the questions asked (see Appendix 6).

• Self-assessment sheet, in which the students assess themselves both verbally and by grading, at the end of the first semester and the end of the year (Appendix 7).

All the above in addition to any other relevant material collected and recorded by the students. 1.4.2 Observation: The rationale for choosing this tool: Observation is an effective tool for gathering of information about the students and their learning behavior (Birenbaum, 1997). According to Sabar Ben Yehoshua (1990), observations are the main method of data gathering in a qualitative research. As she sees it, observation can be open, with the observer attempting to be impressed by most factors included in the examined environment, and then recording them. Alternately, it can be focused and record only, or mainly, pre-determined subjects. A qualitative researcher usually starts his/her research with open observations, changing them later to focused observations, after deciding upon the main issue of the study (Sabar Ben Yehoshua, 1990). Open observation starts with informal procedures of acquaintance, recording of demographic features of the population, mapping of the physical layout and description of the phenomenon or novelty. The extent of the researcher’s involvement, according to Sabar Ben Yehoshua (1990) is expressed in the type of observation. These observations can be sorted by the extent of the observer’s participation in the examined event, starting with external onlooker, non-participant, through all middle degrees, up to a participating onlooker. She distinguishes between two types of observation in a qualitative study: Participating observation – in which the researcher is part of the examined population, taking part in everyday activities and noting them as soon as possible to the time they took place, in the participants natural

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language. The records also include remarks, based on his/her concepts and effected by the role he/she has taken and the response of the surrounding people. Non-participating observation – in which the data is gathered by minimal contact, if any, with the participants. There are, so called, no inter-relations between the observer and the subjects, although in social situations the very presence of an observer creates some sort of relations, not necessarily verbal. The observing researcher should be able to do a sensitive, accurate observation. The present study combines participating and non-participating observations. At this stage the observation is open, and observation standards may be set at a later stage. By means of observation, the observing person can gather evidence about any individual, or group, of pupils. There are various methods and parameters to do these observations and record them. Birenbaum (1997) describes five methods of observation in class: Description of anecdotes: Factual description of behavior or any unusual event, such as insight demonstrated by a pupil. These records should separate factual description from interpretations and assessments, made by the observer. Behavioral labeling: The observer counts the number of times any specific behavior has occurred during a given period of time. Such labeling is useful for the recording of a defined, specific behavior known from the past, which is liable to reappear, such as, breaking into someone else’s words etc’. Ticking items in a list: Making use of lists containing behaviors, activities or other features, linked to a specific function (such as, operating of lab equipment). This tool of observation recording is useful, mainly, when comprehensive lists of behaviors/activities or other characteristics can be prepared well ahead. Such lists may include correct and incorrect procedures, so that performance errors can be recorder as well. Grading scales: Intended for qualitative assessment of specific characteristics of any given performance (such as, a lecture). Criteria, relevant for evaluation of performance, such as relevance of information, the manner it was presented, contact with the audience, eloquence, etc’ are graded on scales describing various levels of performance (low to high). Quality of the assessed performance, with regard to each criterion is graded on the correct point on the scale.

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Participation records: Intended to record the participation in group activity. Records are made by diagrams or graphs, showing how many time each individual has participated in the group’s activity, and what his contribution was. In the present study, observations are recorded in the teacher’s diary, by means of the two initial types. 1.4.3 Personal Interview: The rationale for this choice of tool: As per Sabar Ben Yehoshua (1990), there are three forms of interview: An open ethnographic interview; a standard structured interview – planned according to schedule; and an instructed, focused interview – which is not planned according to schedule. Open ethnographic interview is a sort of verbal event, resembling a friendly chat (Spradley, 1979). It includes two processes, complementing one another: One is a process of matching and creating a link between the interviewer and the interviewed person. The First encourages the latter to speak of his culture, wishing to create harmonious relations and trust, thus enabling a free flow of information. The second process is one that produces information, by encouraging the link. Sometimes such an interview takes place between two persons, but it may also be in a group. The ethnographer may attain the information he needs by a friendly chat, with ethnographic questions. The timing and rate of questions is of extreme importance, so that the interview does not become an interrogation, causing the interviewed person to stop cooperating. Therefore, during the interview, the interviewer may change it into a friendly chat to achieve more trust, and then revert again to his interview questions. As per Sabar Ben Yehoshua (1990), three ethnographic elements are of importance during the interview: An express purpose – both interviewer and interviewee have to be clear about the purpose of the interview. Ethnographic explanations – the interviewer has to explain and receive explanations from his interviewed persons. In this manner, the interviewed person knows how his culture is perceived by others, and he can clarify his thoughts by the help of the interviewer’s questions. Ethnographic questions – consisting of three main types of questions: Descriptive questions, enabling to sample the speakers’ language;

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Structural questions, revealing information about the manner the interviewed person organizes his/her knowledge; questions of contrast or comparison, allowing us to notice objects and events in the interviewed person’s world. This type of interview is friendly and informal. Questions are spontaneous. The interviewer has no definite plan and there is almost no direction of the interviewee, who is encouraged to disclose his experiences, major events and opinions. The advantage of such open interview is that it involves deeper understanding of standpoints and opinions, as well as better trust. On the other hand it is difficult to process. There are also problems of validity and credibility, mainly due to the influence of the personality of the interviewer, his skills and experience (Sabar Ben Yehoshua, 1990). A standard, structured interview, in which the structure, order, phrasing and explanations, allowed to the interviewed person are pre-determined. The interviewer does not add anything. Such pattern of interview matches mainly controlled experiment layouts. Bogdan & Bikeln (1982) rule out the structured interview in qualitative research. They argue that if a naturalist researcher wishes to ensure meanings and definitions, he should conduct a guided, focused interview. A Guided, focused interview – is mainly suitable for experiment-like layouts’ therefore it is less accepted in qualitative research. This interview is usually conducted by a written brief, which details the issues related to the purposes of the study. The questions, nevertheless, are not pre-phrased or pre-arranged. The interviewed person has considerable freedom of response, and the interviewer can react to new points raised by he interviewee, though he will not raise new ones of his own. The advantages of such an interview, as per Sabar Ben Yehoshua (1990), are that one receives personal responses, time is well utilized and important issues are addressed. Such interview is methodical, and responses of various interviewees can be compared. Though it focuses on the main points, personal opinions may be expressed. The disadvantages are in validity and credibility, due to differences in response. In this study the ethnographic interview will be open, whereas the guided one will be focused. The personal interview may be initiated by the author of the study, or by the student, it takes place 3 times a year (beginning, middle and end) and is recorded in the teacher’s diary.

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The Interview Questions The questions in the interview should be unequivocal and clear to the interviewed person (Sabar Ben-Yehoshua, 1990), preferably no “yes” or “no” questions. According to Sabar Ben-Yehoshua (1990) guiding questions – as if the interviewer is expecting certain answers -should be avoided, as well as expressions of positive and/or negative emotional connotation. In order to receive the participants’ cooperation, the questions should be presented in an order starting from the broad margins and advancing to the focus, with each question linked to the previous one and getting narrower (Nahmias & Nahmias, 1982). In such a manner the interviewed person can recall details. Another manner of doing it is the reverse sequence, where the questions start from specific ones and get broader gradually. Spardley (1979) identifies several types of questions in the ethnographic interview: Diverting question – usually one of the first in the interview, dealing with typical places, typical time descriptions, or they may be more specific, such as descriptions of specific places, or tasks performed by the interviewed person. Localized question – detailed questions about specific matters, resulting from the information derived from the diverting questions. Example question – the interviewer asks for examples to clarify descriptions in the diverting and localized questions. Experience questions – asking the interviewed person to describe his/her own experience. The present study includes questions of all types. 1.4.4 Training Sessions and Feedback Discussions: Training sessions are part of the course curriculum. Their purpose is to allow the student to raise questions, talk of her difficulties, dilemmas and any other issue related to the work procedure, both her own and the pupil’s. These sessions take place several times a year, by the student’s, or the instructor’s, initiation. They consist of feedback dialogues, requests for advice etc’, and are an important factor in the teacher’s training (Frenkel, 1997). During these sessions the teacher may attempt to assist the students understand their behavior, improve their ability to cope with new situations, and help them define, structure and include their knowledge for future teaching situations. Frenkel (1998) argues that the feedback

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session is a source and framework presenting activation and experiencing of procedures and contents defined as reflective thinking or reflective teaching. (see details in the literature survey). In this study, these training sessions are recorded in the teacher’s diary. 1.5 Procedures (Stages and Data Gathering): Gathering of data is done during the whole year by the study tools. During the month of September (prior to the beginning of academic year) 2001, the students were summoned individually for a personal interview with me. The interview lasted for ca. 30 minutes, in which the students were asked about their reason for choosing this course, their feeling about it and individual work with pupils, their perceptions about the subject of math and teaching thereof, past experience and expectations from the course. The interview was both structured and open, and both the interviewees and myself had a specific, clear purpose. I explained that I wanted to meet them in person, hear of their feelings and record them, to see the development and changes during the year. The interview was also guided and focused in a manner, whereas to me – as researcher – it was clear what I wanted to talk about, and I could respond to new points raised by the students. Sine I focused on issues that I wanted to clarify, I could compare the students to each other (Open ethnographic interview and structured focused interview, as per Sabar Ben Yehoshua, 1990). The interview was very leisurely and friendly, and created a feeling of mutual trust. On my first lesson with the students (October 2001, following the personal interview) I explained the nature of the course, and asked them to answer the “Starting on a New Way” questionnaire. (see appendix 1) The questions in the questionnaire were, in fact, identical to those asked during the interview (differently phrased, in a different order). The decision to use both tools was meant to create a personal connection (interview), as well an opportunity to express oneself in writing, adding things that were nor said before. All students reported, both orally and in writing, of a high level of motivation to work with pupils having difficulties in math. Following the interview and oral reports (by students) I decided to further examine several other parameters:

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• The strengthening of the sense of confidence. • Control of math teaching methods. • A change in the sense of capability. • A change in the degree of reflection.

On ourt first lesson (acquaintance) held by the students and their pupils, I have been observing them, for several minutes each, so I could see them all. Already during this first session I could notice many important things, such as: Body language, manner of speaking, looking straight in the eyes, making contact, the degree to which they made efforts (using ready materials or creating original ones), creativity, relaxation, embarrassment etc’. I noticed I have been observing many things related to the subject. I felt that though I had not decided on specific parameters to observe – my observation, from the first session, was a great deal more elaborate than in previous years, knowing I had to gather as much data as possible for my study. Observation was (always) done sitting close to the student and her pupil, so I could watch and see exactly what had been prepared, and how each of them acted and behaved. The lesson layout and summary were handed to me, so I could give them their feedback right on the spot. On the following lessons the students performed didactic diagnosis in math. I have been observing these lessons too, not focusing on specific issues, only in noting and recording everything I noticed. Already at that stage training sessions were held with the students (before or after the lesson), so I could give feedback on what I had observed and found relevant. The students raised many questions regarding content of diagnosis, the manner it was done and dilemmas that had arisen during diagnosis. (The students had learned the method of diagnosis on their previous year, but this was the first time they used it actually). At the end of the diagnosis the students submitted their results, as per the rubric. In spite of very specific instructions and training, they found it difficult to sum it up professionally. Also, many questions were raised with regard to the intervention program, which was also their first experience. The process of summing up the diagnosis required many training sessions. The students did several drafts until they could submit a professional diagnosis according to the rubric. They were also required to put in writing their own feelings and what they had learned from that experience.

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Following that, the students were required to give their own feedback to the pupils, which they also did for the first time, and did it under my observation and follow up. After having prepared a personal work program for each pupil, the actual lessons began – the main stage of this study. As already pointed out, each student worked with her pupil twice weekly, for 60 minutes each time. For every lesson the students prepared a layout in writing, as per the form I had prepared, and after each lesson they had to sum it up and hand it to me, together with the layout plan (Appendix 3). The rubric supplied them with a good professional tool for planning, so it was used in every training session to clarify what was required (Appendix 4). The material I read in the lesson layout and summary served me in my personal training sessions with the students. I observed the students during the lessons, and recorded these observations in my teacher’s diary. I made every effort to be present in all lessons, with all the students, though sometimes it did not work out, for some reason or other. But still, I can say that I have been observing all students at least once or twice a week. Sometimes they experienced difficulties, which made them ask me for help, like in cases where the pupil would not cooperate, or difficulties in teaching certain subjects, or any other issues which they could not cope with on their own. On other times the students approached me spontaneously to share with me some emotional experience, like a pupil having worked well, or discovered something new. Such approaches involved spending longer time with one student, on the expense of others. During the whole year, I made a point of taking notes and records both during lessons and after it (in my teacher’s diary). At the end of the first semester, on January 2002 (prior to semester leave) the students were asked to assess themselves, both in free writing and by grading of several subjects. At his stage the students had given between 7 – 10 lessons each, lessons which they have constructed in the intervention program. Following the self-assessment, a personal training session was held with each student, in which she received my feedback on her performance up to that day, the procedures she went through, what she had learned and for her future work. At the beginning of the second semester, on March 2002, after having given several lessons, another personal interview was held with each student (second, mid-year interview). On that occasion the second

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questionnaire was handed (“We Are Half Way Through” – 15 questions). In addition to the questions there was room to add notes in free writing (see Appendix 5). The timing for the second interview and the questionnaire was based on the fact that it was mid-year, with regard to the lessons given (part of the first semester was devoted to organization, getting acquainted and didactic analysis etc’). The purpose of the interview and questionnaire was to see whether any changes had occurred during that period of time, and if so – what they were and how did they express. Toward the end of the year, the students were asked to create a summarizing diagnosis, according to their goals and contents they have taught during the year. This was done during one or two lessons, and on their last lesson the students gave to their pupils the feedback for their performance during the year, heard what they, in turn, had to say, and prepared the last lesson. At that stage I let the students choose whether they would like to consult me regarding the summarizing diagnosis, or they wished to do it on their own. Some of them needed some assistance, other wanted my opinion, whereas other again did not approach me at all. The feedback for the pupil raised many dilemmas for all the students, and in spite of previous instruction, all of them required my assistance. It was their first time to do it, and they were not sure whether they should tell all the straightforward truth, how to relate to difficulties, should they write only the good things and ignore other things. In addition, the students were asked to summarize the status of the pupil, with regard to learning and performance, and make suggestions for future work. This report was sent to the pupil’s school. After the pupils had left, two more group sessions were dedicated to the students alone. Each student presented her pupil and the work done with him, as per my instructed guidelines:

• Background of the pupil, his strong points and points to be strengthened according to the findings of the diagnosis.

• The work program prepared for the pupil, with all the stages and considerations.

• The method or tools used in working on the subject, including reasons for choosing it.

• Presentation of accessories, realization means, work sheets etc’, again – with the reasons for choosing them.

• Presenting one dilemma involved in working with the pupil.

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• The present state of the pupil, and proposals for future work. • Personal and professional lesson from the process.

These sessions were extremely successful, both in the students’ opinion and mine. They could feel the mutual support and learning, their remarks were relevant as well as their questions. At the end of the year a personal interview, combined with feedback session was held, it was an open, unstructured interview. Each student told about her feelings, the changes she had gone through – all based on consulting her pedagogical diary. Each received a personal feedback from me, regarding her performance and development during the year, and we said our formal goodbye.

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Chapter 2 Theoretical Fundaments

2.1 Reflection in Teaching 2.1.1 Definition of Reflection The term “reflection” is used by all those dealing with teaching, and teachers’ training. Discussions about the term cause vagueness and confusion among researchers and teachers. The source of the term is Latin, and it means “turning back”. Literally it means projecting your point of view backward, on some action, event or concurrence. Silberstein (1998) claims, that reflection is an essential process in teachers’ efforts to improve their manner of teaching. As he sees it, teachers are constantly required to identify problems and difficulties, to decipher new teaching situations, to consider new methods of action, follow them up and learn the lesson for the future. Such teachers need to make use of reflective behavior – before, during and after the act of teaching. Van Mannen (1977) distinguishes between three types of reflection: Technical reflection – in which the efficiency of the means for a specific purpose is examined. Technical reflection can be seen, for example, in teaching class organization and managing skills. Students regard it as part of their training, and feel they are equipped with adequate teaching tools, upon entering the class for the first time. Teaching of small things may serve as a strategy in nurturing this type of reflection. Practical reflection – in which the purposes, too, are being tested. Practical reflection can be seen when the inexperienced teacher acquires experience, learning that teaching is a complex thing, consisting of contradicting ideologies and targets. Practical reflection is full with dilemmas, which both require and enable the making of choices. Critical reflection – involving moral and social aspects in procedures of judgment and assessment. Critical reflection appears when these aspects effect pedagogical-didactic considerations, and includes terms, such as, caring for other people and for the pupil’s welfare (Henderson, 1992; Noddings, 1984).

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All three types of reflection have a justified place in training programs for teachers. The link between the three can be regarded as a hierarchy of development levels, and as a function of acquired experience and knowledge, but not as a hierarchy of preference or importance. Some researchers argue that reflection is inherently connected to problem-solving situations (Calderhead, 1989). Dewy (1933) claims that this statement is based on the fact that reflection arises when a person is thrown into a state of wondering, confusion, cognitive imbalance, and doubts. As he sees it, reflection is an examination of the criteria guiding a process of decision making, both in teaching and otherwise. Reflection is not limited to thinking about acts, but can be of art, arguments or thinking itself. Thus, reflection is a meta-cognitive action. Reflection connects the inner world of the thinking subject with the outer world (Frankenstein, 1970). Thus, by reflecting we are judging and assessing all the things included in the individual’s experience, the insight of intuition, the evidences we collect with our instincts, and the conclusion we make with our minds (Louden, 1992). Louden also thinks that the main component of reflection is the tendency to look into, understand and appreciate oneself. Schon (1988) regards the openness for unexpected experiences and the ability to be surprised, as the first step of reflection. Reflection, as he sees it, is the creation of insight by the learner himself, with regard to the thinking process he activates during learning. Such insight is a meta-cognitive process, which will not occur by itself, without preparatory action of the individual. For this purpose, says Schon, introspective procedures of insight and thinking should be learned. These introspective thinking procedures are, no doubt, of extreme importance. Schon (1987) stresses their value in a wide range of occupations of artistic or professional nature, thus outlining operational ways of adaptation these procedures and actually operating them. The acquisition of such thinking habits can be achieved both by demonstrations by the teaching person, the teacher-tutor, and by diverse experience of the learner in “real-time” observations of other people’s and his own actions. Schon claims that these control processes can be divided into two main types: Operating of meta-cognitive procedures of observation and internal control, taking place simultaneously with thinking actions. He named it ‘reflection in-action’.

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Operating of delayed control procedures, based on the reconstruction of thinking procedures or actions. He named them ‘reflection on-action’. In in-action reflection the teacher identifies and deciphers situations of teaching, makes fast, in-action, decisions, re-phrases the situation if the results have not answered his expectations, and tries other solutions. Reflective, in-action thinking processes reveal the teacher’s hidden and unexplained knowledge. As Schon sees it, examining and correcting performance in-action, are clear signs of a professional, expert teacher. But, other researchers think that Schon’s definition is not specific, and may be interpreted in different manners. The question is - what is the time range for performance, following the making of a decision. For instance, should the reaction come during the same lesson, or the following one, i.e. Schon presented those dealing with professional training and promotion of teachers with the ideal of the reflective teacher. This teacher uses deliberation during and following work by reflectively thinking of it. Rand (1994) regards in-action reflection as the sole property of the thinking, acting teacher (unrelated to time range). He thinks that as soon as someone else is involved (such as another person interfering in class), the teacher automatically moves over to the on-action reflection, which enables others, such as counselors or colleagues, to participate. Eraut (1995) argues to some confusion between the two types of reflection in Schon’s model. He suggests a model, in which the time factor is the one effecting and determining the teacher’s conduct. He says there are three situations of teaching in the professional processes in which the teacher is involved: 1. Situations, which the teacher deciphers and interprets very fast and

reacts upon – automatically, conventionally, and without reflection. The teacher’s reaction, under the immediate pressure, is routine, and is usually based on rules, initially based on reflection.

2. Teaching situations, in which the teacher interprets quickly and reacts upon in a controlled manner, using reflective thinking. The teacher’s reaction is fast, though controlled. There is a process of reasoning, i.e. conscious consideration. This is in-action reflection.

3. Teaching situations, in which the teacher has enough time on his hands to deliberate and examine, and make the decision only after deliberation has ended.

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Situations 1 and 2 take place during the interactive phase of teaching, in which the teacher acts on his own. Teaching situations during the continuous phase 3 happen during the pre-active and post-active phases of teaching. Then, the teacher is able to share his thoughts and deliberations with others, if he wishes to do so. This is on-action reflection. Some researchers argue that, in addition to the mental action of reflection, it is a tendency, or standpoint, which people have or do not have, thus it can be nurtured (Buchman, 1993). Gore (1988) and Buchman (1993) define reflection as a disposition of self-examination and soul searching. Bengtsson (1995) argues that, although man is the only creature able to reach self-consciousness, in his natural state he usually is not self-conscious. Man turns his attention to the results of his actions, not to himself. This trait of man, which makes him turn to something else (events or things) – but not to himself – is a basic term in phenomenalist psychological theories. So, Bengtsson distinguishes between self reflection and reflection as part of a thorough process of deliberation and thought. He attributes to self-reflection a function of creating a distance between man and his actions. Usually man is not inclined to create a contemplative distance between himself and his actions, thus, by reflection he gets the chance to see and understand himself from a, so called, “outside” point of view. Self-knowledge, according to Bengtsson, consists of three main aspects: 1. The teaching of educational doing. 2. Taking a point of view, with regards to the educational action. 3. Having an opportunity to share the acquired knowledge with others. Rand (1994), with regard to Bengtsson’s words explains man’s natural tendency to turn outwards. As he sees it, man’s interaction with his external reality (both objective and personal-social) is often easier and more available to an individual, than reflectivity, which includes thinking processes aimed inwards, i.e. to the person himself. The numerous possibilities to act in the external world reduce the person’s level of anxiety of the unknown, and provide him with ways to escape unpleasant encounters, involving turning inward. In reflection, as a process of deep thought and study, the teacher combines self-understanding with ideology, a more profound understanding of processes and the processing thereof.

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Teachers, as a rule, are reluctant to cope with unexpected situations, situations of anxiety and uncertainty. Situations of surprise and embarrassment may shake their confidence (Schon, 1988; Connelly & Clandinin, 1992). Unexpected events disrupt the train of thoughts, so teachers usually prefer planned situations, where they can act according to the expectations. They do not welcome new experiences, and tend to take in only those experiences, which will re-confirm existing beliefs and viewpoints (Deforges, 1995). Many scientists, including Connelly & Clandinin (1992) argue that in an ambience of competitive, achievement-based culture, in which there is an answer for every question, the reflective teacher will have no room to develop. Funk & Wagnalls (1961) define the term ‘reflection’ by 4 different definitions:

1. Image, likeness. 2. Cogitation, consideration, contemplation, deliberation and

meditation. 3. Conviction, idea, impression, opinion and thought. 4. Evidence, indication, mark and sign.

These four definitions indicate different aspects of the term. In the first definition reflection is perceived as a momentary state or experience; in the second it is perceived as a process of active thinking; and in the last two reflection is a cognitive product: personal or deductive in the third and one that may serve as a means to convince others. Clearly, the dictionary definition, even though multi-faced, is by far not a sufficient guide for teachers’ training. Kalekin – Fishman (1995) says that in order to investigate the extent, to which reflection may contribute to the shaping of the teacher in the long range, the reflective activity should be anchored in a comprehensive theoretical perception. With that we could examine the extent to which reflection may contribute to the long term shaping of the teacher, on one hand, and assist us in deliberating our actions on the other. The next chapter deals with the theoretical construct relating to reflection. It is based on a synthesis combining psycho-social theories, as follows: Parsons’ action system (Parsons & Shils, 1951), Kelly’s personal construct theory (Kelly, 1955), Mead’s socialization theory (Mead, 1934), as developed by Berger and Luckmann (Berger and Luckmann, 1972, 1966), and Goffman’s dramaturge theory (Goffman, 1959). Each one of

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these theories describes and explains reflection, as an integral part of our nature as human beings. Each theory interprets the action in part, and their combination may furnish education and training personnel with tools to do so. The theoretical framework describes and explains the circumstances in which reflection occurs and the manner. It also describes its components and products. Theoretical framework is, in fact, a sort of “manual”. Theoretical framework enables us not only to guess who does reflect, what type of reflection and its purpose. It gives us directions of thought and describes the manner in which reflection links to the development of man and his integration in society and in work. 2.1.2 Reflection as Part of Man’s Development Reflection as Part of Each Man’s Activities The theory of the activity system (Parsons & Shils, 1951) binds together the human activity with the reflective process. Parsons & Shils argue that any activity takes place when an actor selects a target, adopts conventional means, which will help him realize his objective, and invests energy in order to ensure the performance of the required tasks. Reflection appears as consideration with regard to the mutual expectations (norms) prevailing between role partners in the relevant social environment (Kalekin-Fishman 1998). Fulfillment of these expectations requires complex considerations on the side of the actor in any situation, since his activity will necessarily express solutions of dilemmas. The actor has to decide on his behavior in every system of activity. He has to choose between norms focused on his personal benefit and others, focused on the general good, between expressions of emotions and those of neutrality, between behavior according to universal standards and particularistic behavior, and between relating to the characteristics of groups to which the duty partners belong, or alternately to relevant achievements in a shaping situation (Kalekin-Fishman, 1998). This theory of human activity expresses an approach suggesting that: People perceive a situation in a form of picture or reflection in the mirror. They divide every event into separate activity units.

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They consider the series of required actions in order to achieve the target, and adopt the activities relating to a general event and the social aspect. Activity is performed by norms and by the actor’s judgement, with regard to the manner the results may effect other people. The illustrated action, a result of reflection (analytically complex, even when instantly performed) is an evidence of the actor’s orientation. From the theory of the action-system one can conclude that nothing is ever done without reflection (Kalekin-Fishman, 1998). In order to understand the basis of the actor’s decisions, and the details of performance, more theories have to be considered. Reflection as part of the psychological construct of man Kelly (1955) argues that reflection is an integral part of the individual’s psychological construct. As he sees it, psychological processes are channeled to foresee the future. This has three aspects at least: Preparation toward the occurrences, ignoring other occurrences and avoiding events that are regarded as undesirable (Mair, 1995). Kelly describes man as a scientist, busy predicting situations, so he can act cleverly and have his predictions confirmed. Foreseeing the future and the reflection is not accidental; it is based on the “theory” guiding the individual in all his experiences. The “theory” is based on a general system of personal constructs, which guide the thoughts and emotions of the actor in repeated situations. This system is constantly being shaped and changed, on the basis of the entire life’s lessons. These lessons are linked to form and guide the foresight of the future, to interpret what may happen, and to plan the appropriate behavior in the expected event (Kalekin-Fishman, 1998). The organization of personal constructs determines the uniqueness of the personal view of each detail. The branched system of personal constructs consists of global super-ordinate constructs and subordinate constructs. Between them there are constructs, which occupy a central place in one’s consciousness, and others, which occupy a relatively marginal place. The most important constructs are gathered in the core of the system, and in Kelly’s theory the core construct is in fact an organized simile of the distinguished personal self. It turns out that in every event the actor takes part in, the personal construct system is tested, and above all the constructs of the core. When the behavior, matching the activating of the personal construct system, contributes to creating an acceptable reality – the constructs of the core, of the self, are validated. On the other hand,

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when the anticipations and the built-in ideas of the “scientist-man” are not valid (i.e., the resulting behavior does not match the requirements of the event, toward which a certain action was planned), the personal construct system has to be re-evaluated (Kalekin-Fishman, 1998). A new situation is created, in which the actor has to look for alternative constructs. These may bring about a change in the general construct of the system, a rather fundamental change. Kelly’s (1955) theory makes it clear that the psychological construct of man can be understood as basically reflective, in which a reflection of situations is a condition for life. Moreover, personal constructs are characterized by “inner conviction” and “evidence”, which have been validated. The theory expands about reflection as a situation and as a system of products, but it does not give a full explanation to the process, by which this system is formed. As for situation, the theory does not remove any “validation”. At best, it is hinted that such validation is a reflective process. On the one hand, there is an internal process in which the individual meets a reality interpreted by him, whether ratified or not. On the other hand, such ratification is transferred by others, who share the same situation. Modern theories dealing with learning and recognition remind us, among other things, of Kelly’s concepts. One could say that the philosophy and theory of constructive learning are largely based Kelly’s theory. To arrive at the description and explanation of this complex positioning mechanism’ we need proof from other theories. Socialization theory, presented by Mead (1934), further developed by Berger & Luckman (1966/1972) and illuminated by Goffman (1959) assists us in detailing what is at best merely implied by the theory of personal constructs (Kelly (1955). Interactions by reflection as a means of building the self According to Mead’s (1934) theory, the forming of the individual’s self is made possible only when a social self is formed at the same time. Man grows and develops within the dynamics of interactions, driven by reflection. Mead defined the self as a “reflection in a mirror”, a state which is the basis for any human encounter. Reflection is formed, because relations are formed between position holders, by exchanging “gestures, which are transmitted by words, symbols, body postures, shapes etc’. They evoke a response and an agreed upon interpretation, both on the transmitter’s side and the

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receiver’s side. Reflection is a process. This process includes intuitive imitation of the transmitted sign, and a repeat transmission of an appropriate response. The response and the interpretation were identified by Mead (1934) as the social aspect of the self, i.e. the “me” – that part of the self which reflects the perception of signs transmitted to the individual, by other individuals participating in situations, and mainly relevant participants. The responses are externalized by an interaction loaded with additional elements, which are a result of the genetic and physiologic construct of man. Mead named that aspect “I”. Naturally, the “I” can be directed consciously, which makes it the change-promising aspect of social relations’ construct. Finally, the “me” and the ”I” are one and the same: The self, which forms in the individual (Kalekin-Fishman, 1998). Thus, the forming of the self is directly dependent on reflection, both as reflecting other people’s attitudes, and as an ”inner” deliberation regarding the signs we are exposed to. As per Mead’s (1934) theory, each exchange of signs between role partners is possible, due to the interaction, taking place within each individual. While structuring the situations they take part in, people construct their unique self. The formed ‘self’ reflects the embedded interpretations, which were transmitted from the environment by signs, and the actual external responses. In that aspect, Berger and Luckmann (1966, 1972) detail various strata of interpretation and intentions. The signs, which reach the individual’s consciousness from significant role-partners at a given time, may be in the form of nominalization, behavior patterns, general principles or transcendental beliefs. The changing meanings link with the perception of the nature of participation required in every partnership, and the required product of the situation. Scientists point at the forming of a personal construct-system, activated in action-systems. The personal construct form changes constantly, for several reasons (Kalekin-Fishman, 1998). Role partnerships may enjoy more, or less, salience, and they may be more, or less, visible. During an individual’s development, the weight given to certain interactions changes as well. The meaning of therapists, colleagues, teachers, mates and friends may change in various stages of life. Based on these developments the actor can perform his role, within the ‘Personian’ action system, in different manners.

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All these processes include reflection (Kalekin-Fishman, 1998). As Goffman (1959) sees it, interactions actually take place according to the manner in which the participants momentarily perceive themselves as the characters they represent, and present. The characters are built gradually, because information is constantly flowing into the situation. The beginning of a situation is in premeditation (Kelly, 1955), and its continuance is in reflection, taking place as interpretations to mutual gestures (Mead, 1934; Berger and Luckmann 1966, 1972). These interpretations are constantly activated by interaction, in an essential attempt to understand the building in of other people, in order to adapt one’s self to those prevailing in the situation. Goffman (1959) emphasizes the information given both intentionally and unintentionally. In every situation there is a controlled supply of initial information about the self. This information can signal to others how the individual perceives the situation, and it directs others to reveal relevant information about their own self. During interaction there is also an attempt to make the best use of the situation. It turns out that (Kalekin-Fishman, 1998) reflection is initially in the basis of constant mutual accord, characterizing any situation. The theory of the creation of the self and the mutual matching of behaviors are a description of learning, motivated by reflection, deliberation, searching for signs and forming an opinion. The complex description of construction processes, signaling and interaction points at reflection as an integral part of any learning (Kalekin-Fishman, 1998). Although it is difficult to relate reflection, in its social-psychological meaning, to any neurological activity (Kalekin-Fishman, 1998)’ there are proofs for that in some neuro-physiological research. There is reason to assume that processes - similar to those of “planning”, mutual control and adaptation to expected situations – are also characteristic to learning of neurological systems, i.e. their plasticity (Churchland, 1986\1989). From the theoretical point of view, presented above, we can learn that man naturally acts by perception of targets and by choosing appropriate means to realize his objectives (Kalekin-Fishman, 1998). The starting point on every action is a reflection of situations. The type of the reflection and its nature depend on the perception style and the reservoir of personal interpretations of every observer. The system of personal constructs, following life experiences in which the self is being built by a series of validation, supplies us with tools for reflection.

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Thus, the reflection, with all its interpretations, expresses the unique side of each person. The description of the self, as well as its presentation in words, is the test for the integration of the spontaneous (I) and the social (me), which make the individual’s uniqueness. This is also the basis of adopting the image in each situation, and shaping it according to circumstances, as well as according to performances and messages given by “others”. The constructs are formed by a dynamic processes. Reflection is an integral part of man’s development, of his nature and interaction comprising his world. It occurs in every area of life, including education. From the theories we can learn that experiencing reflection (the first definition as per the dictionary) is the foundation of every event, which contains interactions. People’s (actors’) actions are enables due to reflecting in advance on targets and means, as well as on descriptions of future, expected situations. This process is motivated by a set of personal constructs, created from experiences. The most meaningful interactions in one’s life contribute to the creation of the constructs’ core, i.e. the individual and the social self, which cannot be separated. The making of a set of constructs and its use, combine to make the learning process in various situations, including the variety of images performed by men. In such situations man acts as a scientist, foresees the future, tests his expectations by reality and draws the conclusions with regard to the validity of prediction in each case – a process characteristic of learning the profession. Reflection is an integral part of a person’s development, his nature and interaction comprising his world. It takes place in all areas of life, reflects also in physiological actions, and such encounters are not unusual in the area of education too. So, the question that should bother us in our attitude toward the training of teachers is not how to bring teachers of students to a state of reflection, because the situations of reflection exist. The relevant questions are as follows: How can we make use of reflection, so as to serve the purposes of teachers’ trainers, and of institutions for training of teachers. How can we maintain and nurtures the teachers’ ability to cope with situation of embarrassment, unexpected situations, and confusing answers from students.

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How can we create school culture, which will support reflective teaching, leaving room for doubts and unanswerable questions, at the same time encouraging teachers to create a flexible learning environment. The next chapter deals with the various aspects of reflective teaching and the importance of reflection in teaching. 2.1.3 Reflective Teaching Reflective teaching as a formal category, or as a content-dependent category. In educational literature, reflective teaching appears in two versions: As a formal category, independent of any ideological content, and as a category, which is inherently attached to the constructivist perspective. Most researchers present reflective teaching on the basis of general definitions of mental processes, without any obliging viewpoint regarding the questions of the education objectives, educational ideology or school point of view. In these definitions, reflective teaching is presented as a formal category, generic in nature, which can be applied in the context of various educational ideologies. Beyond the question of defining the nature of teaching as an occupation, there is another question of what good teaching is, to which there are several answers? Several researchers who analyzed various teachers training programs in the USA (Doyle, 1990; Zeichner, 1994; Feiman-Nemser, 1990) suggested a typology by which training programs could be sorted, based on conceptual frameworks or paradigms representing various educational ideologies. Feiman-Nemser suggests a model of five orientations, which can be found in the conceptual frameworks of the training program: The academic orientation – which places in the center of teaching the translation of disciplinary contents, by means of pedagogic didactics, into accessible, interesting and meaningful contents, to all pupils. Standards and achievements are a result of academic disciplines, mainly.

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The technologic orientation – which emphasizes the scientific knowledge of teaching research. Good teachers, with efficient teaching skills, who teach by principles formed as a result of research. The critical orientation – emphasizing the social commitment of the teacher, regarding the caring and nurturing of democracy and equality values, as well as correcting the wrongs of our society. The practical orientation – emphasizing reliance on experience and practicality. Skilled and experienced teachers are a model of good teaching. The personal orientation – which argues that learning to teach is, first of all, a transformative process, in which the student changes and rebuilds his concepts of learning and teaching, and develops his personal style, beyond the acquisition of knowledge and general teaching skills. According to this orientation, the teachers understand the pupils’ development processes and their behavior, and match their teaching with this understanding. In Feiman-Nemser’s model (1990) there is no separate orientation for reflective teaching or for training of reflective teacher. Feiman-Nemser (1990) argues that the purposes of reflective teaching are linked with various conceptual frameworks. Since, as she sees it, reflective teaching is a formal category - it can be linked with any educational theory, independent of ideological content. Schon (1988) thinks that reflective teaching has a distinct ideological direction, which do not conform to part of the educational traditions. Only teaching that accepts the principles of constructivist perspective in understanding the process of learning, can be reflective, he says. Also, a reflective teacher is capable of being surprised by his pupils, of phrasing obscure teaching situations, of supplying mediation in order to promote a pupil’s thinking, and is in a constant process of learning. Reflective teaching, according to Schon, is in fact a responding teaching which forces the teacher to enter the cognitive world of the pupil, his motives and desires. Such teaching, argues Schon, doe not conform with educational tradition, which regards it as an applicable science, even if it is of academic, technical, critical or practical orientation. In responsive teaching, the center of its being consists of the nature of relations between teacher and pupil. Rand (1994) claims that in this type of teaching the teacher supplies the pupil with tools, with which he can enrich himself by himself, rather than varied, extensive information. The teacher creates in the pupil readiness for self-involvement in the process of education.

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Turning one’s attention to developments in the understanding of learning process during the last two decades, as well as to forecasts of the future self directed graduate, requires acceptance of the viewpoint, which regards reflective teaching as depending on a well-defined ideological content. There is room also for regarding reflective teaching as a formal category, linked to other orientations. Schon (1988) argues that reflective teaching does not exempt the teacher from his professional responsibility to be able to process disciplinary, academic contents. He should activate reflective thinking processes, so that the learned subjects will be interesting and understandable for the pupil. The teacher’s professional responsibility obliges him to pay attention to other orientations, as well as making use of reflective thinking processes. From the above-said, it can be concluded that, in forming the conceptual frameworks of training programs for teachers, there is room for both versions of perceiving reflecting teaching, at the same time searching for a way to combine the two. Most scientists agree that teachers need two types of knowledge to contribute to their professional work: practical and theoretical knowledge. In reflective teaching, the theoretical knowledge, the principles and generalizations supply the framework to relate to and the patterns of interpretations to the experience and educational making. Shulman (1988) too, thinks that any teachers’ training program should combine the learning of principles and practical experiencing. Indeed, teaching – as many researchers claimed – is a practical-reflective occupation, in which the teacher learns from his experience how to use the accumulating knowledge. Knowledge of theories and principles is stored in the long-term memory, later supplying a framework to relate to for interpretation and judgment of other contextual situations. Goodlad (1988) thinks that experience without theory to link its various pieces of experience, may lead to conservatism and perpetuation of the present situation. On the other hand, theory without practical experience will soon become far-fetched and illegible. Fenstermacher (1988) suggests a model to bridge these two different worlds – research and theory versus practice. He thinks that conceptual behavior on the teacher’s side is a chain of deliberations made by the teacher in order to reach a decision to act in order to achieve the desirable

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teaching situation. These considerations are based of two types of assumptions, claiming as follows:

• Assumptions or situational arguments, unique and contextual, resulting from personal opinions and circumstances in which the teacher acts.

• Assumptions or empirical and logical arguments, i.e. proven or provable in research test or logical thinking.

The model assumes that the teacher’s conceptual behavior combines idiosyncratic and contextual knowledge with public knowledge, of all its types. Butler (1992) claims that the teacher’s conceptual behavior can be explained by means of reflecting on contents from the public knowledge, in a social context, and on contents from his personal knowledge. The teacher has both personal knowledge and a point of view, opinions, beliefs and standpoints toward the human, physical world around him. On the other hand, there is public knowledge, which is a result of meditation and research, and that of a general teaching character. These contents are the object of a teacher’s reflection in various teaching situations, and with that reflection he is supposed to make the link between them. The question arising here is, how to link these basic elements of the social context with the personal context elements to make a new knowledge to be used by both student and teacher. Leinhardt et al. (1995) argue that in the teachers’ training program there should be an integration of two knowledge sources, relevant to teachers’ training: The academy which represents the research and meditation and school, which represents the field experience. As they see it, these sources supply quite different knowledge. Research and meditation supply us with universal, formal, explicit, conceptual and abstract knowledge. Field experience supplies us with knowledge, which is situational, contextual, interactive, inexplicit, specific and performing. A true integration between the two requires processing of knowledge from one source (academy or field) by ways of meditation, typical to the other source. Leinhardt et al (1995) suggested that theoretical courses integrate case analyses based on experienced learning (personal, colleagues, case reports and various images), in order to combine contextual situational knowledge with theories and principles.

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On the other hand, frameworks of experienced learning, such as use of case reports, will lead the reflective thinking and discussions to the basics of theoretical, formal knowledge. Undoubtedly, this point of view opposes the splitting viewpoints and the need to choose one attitude of the other. As I see it, theoretical and practical knowledge combine in the teacher’s field work, and make his professional knowledge. In light of all this, the question arises how to include reflection as a component in teachers’ training programs, and what changes in that program will assist in the training of reflective teachers. The next chapter will discuss the place and importance of reflection in the process of teachers’ training, with a special emphasis on tool and methods of development. 2.2 Developing Reflection in the Process of Teachers’ Training 2.2.1 Reflection as part of teachers’ training The term “reflection”, as defined by researchers and other people dealing in education and the training of teachers, is usually perceived as a communicative process, taking place among teachers. Taylor (Taylor, 1978) claims that reflection is part of a process of examination of one’s beliefs and opinions. What do teachers mean when they are speaking of the need to include reflection in their training? What are the ways by which reflection can be turned into an integral part of the curriculum? Are the students receiving appropriate training as reflective professionals? Calderhead (Calderhead,1989) distinguished between different approaches to reflection in teachers’ training. Sometimes it focuses on the students themselves, their beliefs, the way they perceive teaching and pupils, their hopes and fears. Reflection may also be directed to the examination of the purpose of education and teaching, and to the understanding of the unique circumstances of educational environments. Calderhead (Calderhead,1989) argues that constraints of time, requirements and practical work, and the belief that the experience of teaching are the basis for the increasing professional knowledge of

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teachers – all make the creation of frameworks for systematic, critical and supporting reflectivity very difficult. Korthagen and Wubbels (Korthagen and Wubbels,1995) studied programs of reflective teaching in teachers’ training. Their study dealt with three main questions, concerning the training of reflective educators. These questions may assist us in understanding the process of reflective training.

• What is good teaching? • What is the role of reflection in good teaching? • How do reflective teachers differ from their colleagues?

Korthagen and Wubbels (Korthagen and Wubbels, 1995) claim that nurturing an inquisitive approach to teaching is a basic purpose in teachers’ training. They define reflection as the ability to re-built a problem, experience or existing knowledge. Their definition is directed to a reflective process, which necessitates making the term of reflection operational. This process arouses questions regarding the nature of the renewed building-in of the reflection’s object, be it the perception of learning situation, or re-defining of an educational problem. Based on their study, Korthagen and Wubbels (Korthagen and Wubbels ,1995) distinguish between teaching students who direct themselves and those who are directed by external factors. As they see it, the reflective teacher is characterized by inner self-direction. He does not need guidance and external tutoring. Reflective students are aware of the subjects they want to study, and have no difficulty in naming them. Also, these students are able to analyze and describe their own functions, in inter-personal relations with others. The complexity and differences of educational situations create a state, in which reflection has to relate to a variety of factors, in order for it to be efficient and useful for the process of educational improvement. Korthagen and Wubbels (Korthagen and Wubbels,1995) found out that the more opportunities given to students to reflect, and the more their training program encouraged reflection – their reflective ability grew. Ben Peretz and Rumney (Ben Peretz and Rumney,1991) studied the process of practical work of teaching students. The students had received a feedback on their lessons, their methods of teaching, discipline, and disciplinary problems. The study found that the training teachers did not encourage the students to use reflection for their work and be aware of this complex process.

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Schon (Schon,1987) argues, in this context, that reflective practical work should be the center of professional training for teachers, as a bridge over the academy and practice. Only in this manner will the teachers develop new knowledge. Following Korthagen and Wubbels’s study (Korthagen and Wubbels,1995), many questions arose and were directed at the teachers’ teachers:

• Is reflective ability connected to the personal traits of the student? • How can the future teacher’s reflective ability be influenced by

training programs, if at all? • What factors in the training program are suitable for encouraging

reflectivity? Professional literature dealing with this issue, proposes several things and changes in the training program, which may assist in realizing reflective educational activity of future teachers. This change should be made in three dimensions: The structure of the training program, which will be based more on tasks requiring systematic reflection, and less on formal studies. The nature of the training program will focus on developing a new, common, professional language, of terms, symbols and the ability to describe and analyze various situations. Another factor is the developing of a critical approach, following observation, reading and doing. Brown and McIntyre (Brown and Mclntyre,1993) found that teachers find it hard to analyze and explain the “secret” of their success. Appropriate steps, such as keeping a pedagogic diary, colleagues’ stories, usage of metaphors, etc’. Bruner (Bruner, 1986) says that besides pragmatic knowledge, storied linked to educational doing may also serve the reflective process. One of the ways to change the training process, which includes the above-mentioned dimensions, is to experience qualitative research. The next chapter deals with the position of qualitative research in the process of training program, as a tool for developing reflective teachers. 2.2.2 Experiencing Study as a Tool for Developing Reflective Teachers One of the ways to nurture reflectivity in teaching and in teachers’ training is experiencing research. Today there are several types of

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research, of which the leading ones are the quantitative and qualitative research (Kaniel, 1977). The terms ‘quantitative’ and ‘qualitative’ research can be interpreted in different manners, “cutting” into each other. Qualitative research has gathered around it concepts such as experiment, review, laboratory research, field research, and empirical and experimental research (Kaniel, 1997). The qualitative research is linked with terms such as theoretical research, phenomenological research, ethnographic research (describing traditions and customs of people, tribes or communities), content research, descriptive research, case reports, narratives (personal story or experience) and action research. All these terms point at a great deal of confusion (Kaniel, 1997). Kaniel argues that all researches have one common structure, the essence of which is the argument that planning and performing of any research is a private case of decision making. This argument is based on the well-known perception of classic research (Dewey, 1933; Schwab, 1971). In other words one can say that in the base of each and every research lies ta question, an intention to answer it, carrying out the intention and giving the answer. These phases exist in any optimal decision making model (Kaniel, 1997). The term ‘decision making’ expresses the whole sequence of actions, including performance and moral lesson. In includes: Problem solving, critical thinking, systematic thinking and reflective thinking. Thus, every research generates reflective thinking (Kitchner & Fische, 1990). Qualitative research is a general name for a variety of studies: Ethnographic, case studies and others (Shulman, 1988). Qualitative study focuses on processes, analyzes and explains phenomena, thus giving them a meaning. According to the positivist approach, scientific knowledge is valuable, only if it is based on pre-meditated systems of categories for sorting behavior and standpoints. It can also be systematically quantified by statistical tools (Alpert, 1992). Qualitative researchers deal in the examination of phenomena and processes, as they happen in the natural world, with no previous attempts to structure them. They are trying to interpret them according to meanings given by both the researchers and the researched, in a developing process of observation and assumption. Dewey (Dewey,1933) was the first to suggest the term ‘reflectivity’ in teaching and in teachers’ training. Reflectivity, as per Dewey

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(Dewey,1933), derives from a situation experienced directly, causing us embarrassment, doubt and mental difficulty. Reflective thinking turns situations of vagueness and conflict into a clear, coherent and harmonious situation. Grimmett and Erickson (Grimmet and Erickson,1988) claim, in this context, that the phenomena of the practical world are unique and contextual, so there are no ‘book solutions’ to match them. Reflective thinking is intended, first and foremost, to assist in coping with dilemmas and practical problems. The qualitative study aims at creating knowledge per se, without necessarily aiming at applications and actions. The purpose of reflectivity, just like the purpose of qualitative examination, is interpretation and looking for a meaning in a world of complex phenomena requiring identification, explanation and meaning (Alpert, 1998). Developing research qualities is the basis for our coping ability with the practical world. Thus, experiencing qualitative study may contribute to the development of reflective thinking in teachers’ training. Dewey (Dewey,1933) and Schon (Schon,1987) stated that feelings of difficult and problematic character are a resource of reflective thinking. The same thinking, in which students learn to name phenomena, is translated to writing. Writing, according to Vygotsky (Vygotsky,1962) is am elaborate way of speaking. Writing assists learning due to several traits, in which it differs from verbal expression: Constancy, visibility, fluency and explicitness. In spite of the difficulties, writing contributes to the deepening of observation and clarifying of thoughts (Gregg and Steinberg, 1980). During their experience in writing, the students prepare drafts to be checked by their tutor. He, on his part, makes his remarks with regard to description, analysis, interpretation and general aspects and rules of academic writing. Alpert (Alpert, 1998) guided a group of students in the teachers’ seminary (in one of the courses) in preparing a qualitative study. Reading and analyzing their papers produced several categories describing the contribution of the experience. She divided her findings into five characteristics: Developing an awareness to the complexity of educational situation, and discerning details of phenomena and happenings; Identifying problems, naming and framing phenomena as characteristics of reflective thinking; Connecting the individual to the general, and theoretical terms of educational science to he field; “Conceptual growth” and production of personal, original categories;

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Expanding of personal and practical knowledge, learning of approaches and methods, in way of acceptance and criticism. The above-mentioned characteristics are detailed as follows: 1. Developing an awareness to the complexity of educational situation, and discerning details of phenomena and happenings Observing and watching of learning environments are part of field experience in the process of teachers’ training. A scientist conducting a qualitative study, with the use of ethnographic tools, makes the “classic” observation, usually documented in “pedagogic diaries” (Alpert, 1998), into a process of strict recording of phenomena, as they actually happen. These phenomena crystallize later as a complex and intricate existence. Geertz (Geertz,1973, 1990) named it “a packed description”. He thinks the researcher locates and records various layers of phenomena and happenings: First, on the external, apparent layer, and later in the latent ones. Only deep observation, together with understanding of the link between those layers, enables the retrieval and identification thereof. The students’ papers were based on quotations from teachers and students, discussions at class, descriptions of expectations, interviews and gathering of documents. Out of all that material, the students could identify repeat patterns, and cross check the data. According to Fetterman (Fetterman,1989) this is the way to understand patterns and phenomena. 2. Identifying problems, naming and framing phenomena as characteristics of reflective thinking Reflectivity relates to the manner in which a person deals with practical situations, which he observes, or is involved in. Schon (Schon,1983) speaks of “in-doing” reflectivity, i.e. when a certain act is made and examined by immediate experiments. He also speaks of “post-doing” reflectivity, when the act is planned and based on retrospective thinking and observation of past experiences and situations. In both cases, the problems of the practical world do not appear as well designed structures, but rather as vague, indecisive and complex situation, that cannot be matched, as is, to familiar theories and rational techniques recommended by scientific research. The first task is to construct the problem with the materials of the situation, in a manner that will make it clear, and enable dealing and solving. Constructing and presenting a problem are a process in which phenomena are named, and the context in which they appear is framed.

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Schon (Schon,1983, 1987) argued that naming and framing are important characteristics of thinking and reflective action. In the process of reflective thinking, naming a problem and characterizing its context are a central process, which derives from a real situation in a complex, indecisive, multi-variable, practical world. The problematic situation is a unique case, not easily compared to other cases. What Dewey (Dewey, 1933) and Schon (Schon, 1983, 1987) are calling “a problem” in the usual sense, is not necessarily a problem in qualitative research. These problems are a basis for learning. In any case, they say, whether there are difficulties and conflicts in a situation, or whether the situations are positive – naming and framing of the situation are important. 3. Connecting the individual to the general, and theoretical terms of educational science to the field Usually, professional training program consists of several layers. The first layer includes basic subjects, introduction to philosophy, sociology and educational psychology. The second deals with general pedagogy, the third includes methodology of teaching professions and the fourth is actually practical experience – the “practicum”. The usual course starts from theory and moves on to practice. The assumption is (Silberstein, 1994, 1995) that theoretical and verbal knowledge, produced by educational and behavioral and social studies, serves as a basis to practical teaching and training. According to the perception of teaching as a practical-reflective occupation, teaching is a unique combination of particular phenomena dependent on the context in which they take place. The process of thinking and acting, as per Silberstein is inductive in nature: from the individual to the general, and from theory to practice. In the process of conducting a qualitative study, the particular observation is assisted by many factors: Personal experience, general pedagogic knowledge, disciplinary pedagogic knowledge, intuition, etc’. The students’ papers in Alpert’s study (Alpert, 1998), included two types of generalizations derived from particular observation: Generalizations relating to verbal knowledge, acquired in didactic and theoretical lessons, confirming or opposing that knowledge, or suggesting changes to be made. New generalizations, which contribute to the expansion of verbal theoretical knowledge. Terms and theoretical arguments nurture the

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interpretation of unique phenomena, and these in turn give theoretical knowledge (often perceived as distant) a real, dynamic meaning (Arnon and Persko, 1988). 4. “Conceptual Growth” and production of personal, original categories. Developing concepts and producing categories of characterization, understanding and interpretation of gathered material are the crown-point of any qualitative study. It requires a considerable intellectual effort within a variety of research activities. The researcher is required to process he material and give it comprehensive meaning. I.e., take an specific case and use it to expand our insight on phenomena. A characterizing, interpreting concept becomes a tool to enrich our world of ideas and experiences we encounter. The use of terms and categories to interpret phenomena in students’ papers (Alpert, 1998) consisted of two types: The most prevalent one was a combination of an accepted term from he area of education, and its re-designing by analysis of cases, events and patterns observed in the study. It is a sort of “conceptual growth” on the researcher’s side, when the concept dealt with during theoretical classes comes alive and expands to include the real phenomena observed by the student. The second type of use of concepts and categories to interpret phenomena is less common. Its is about an attempt to release oneself of prevailing concepts in the theoretical literature and in educational rhetoric, as well as an effort to produce new, original categories. These categories are, partly of the cases, names focused on unique phenomena, and partly concepts characterizing a phenomenon beyond name of title. 5. Expanding of personal and practical knowledge, learning of approaches and methods, in way of acceptance and criticism Since the 20th of last century a substantial change has taken place in research, together with the turn to researching teachers’ thinking. Reviews done by Clark & Peterson (1986) indicate a multitude of approaches and the intention of researchers to learn about teaching by field testing, though cognitive approach based research is still considered important. With time the term ‘knowledge’, which symbolizes a more holistic approach in the teacher’s work, has replaced the term ‘thinking’ (Clandinin, 1985; Elbaz, 1983).

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Clark and Peterson (1986) suggest a cognitive model of teachers, by which two interactive components are involved: The teacher’s thinking and the teacher’s actions. They classified research into three categories: Planned thinking of teachers, including pre-active ideas, prior to the active teaching, and post-active thinking as feedback, following the act of teaching. Teachers’ thinking about ways of teaching, includes interactive decisions taking place during teaching. Declared theories and beliefs of teachers, which are a part of their thinking process, and effect their behavior. Schon (1983, 1987), who examined the professional knowledge of professionals, including teachers, defines the components of professional knowledge in a similar manner. He distinguishes between knowledge declared by the teacher, and knowledge expressed during the teaching itself. According to Schon, professional knowledge consists of: Theories in action – guiding the actions of the professional. Such theories are anchored in real acting situations, they can be observed or exposed in actual professional behavior. Espoused theories – serving the professional to communicate with others. These are theories about learning and teaching, expressed by teachers when asked about their conduct in certain situations. They may include beliefs, principles, tactics, perceptions etc’. Acting theories may differ from espoused theories, without the teacher being aware of it. Schon suggests that the teacher’s knowledge may be sometimes latent. Some expressed theories may be hidden and can be exposed only by asking a person how he acted or will act in certain situations. The knowledge in within the individual’s actions, sometimes without him having the ability to express specifically the basis of his skills. During research the researcher may assist the teacher to exchange a set of hidden, private theories for an open description of his behavior and understanding his knowledge construct. Practical personal knowledge of he teacher (Elbaz, 1983),as well as his practical wisdom (Shulman, 1987) have long been accepted by education researchers as significant, central components of teaching. Such knowledge is more accepted than formal and verbal knowledge, resulting from the work of researchers and other initiators of learning and teaching programs. The acknowledgement of these types of knowledge gave birth

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to a vast variety of studies about the thinking of teacher considered to be experts and professionals (Berliner, 1986; Silberstein, 1994). Shulman (1987) first defined, in 1987, the conponents of the teacher’s professional knowledge. It included the following categories:

• Knowledge of the content of the subjects taught. It included facts, concepts and processes within a given content, relating to the organizing of which in the teacher’s cognition. The teacher is required to understand the content of the subject matter, propose an explanation to arguments, point at the link between knowledge of mind and other disciplines, and bind theory with action.

• General pedagogic knowledge. This category includes knowledge of manners of presenting the taught subjects, knowledge of principles and strategies to manage a class, and organize a learning ambience. The teacher is required to control didactic aspects of teaching, on a level of planning and performing.

• Curricular knowledge. This includes knowledge of material and curriculi serving the teacher as “professional tools”. The teacher is required to know the subject matter, teaching materials of any given subject, and the way to use them. In addition, he should know curricular material of other subjects and those learned in the past, or to be learned in the future, of the same subject matter.

• Pedagogic, content-dependent knowledge. This category includes knowledge which is a unique product of teaching material and pedagogic principles, combined together. He should be able to examine alternative manners of pedagogic organization of the discipline, and to translate this knowledge to learning events at class.

• Knowledge of the learning persons and their nature. This category includes knowledge of learning theories and the development of children. The teacher is required to adapt the content and complexity of material to the children’s cognitive ability at any age.

• Administrative knowledge. Including educational context, society, culture and community. The teacher should take into consideration such factors in his teaching situations.

• Knowledge in educational philosophy. This category includes knowledge of targets and educational values, as well as knowledge of the historic and philosophic basis from which the targets were derived. The teacher should understand the rationale behind the curriculum and identify the needs reflected in it.

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Several months later, Wilson Shulman, & Richert, (Wilson Shulman, & Richert, 1987) re-phrase these components of professional knowledge as follows: General pedagogical knowledge – which includes theories and principles of teaching and learning, knowledge of the learner and of principles and behavior in class and its management. This component includes the following categories: general pedagogic knowledge, curricular knowledge, knowledge of the learners and their characteristics, knowledge of administrative and educational philosophy. Subject matter knowledge – including substantial (ideas, facts and concepts) and syntactic (ways by which new knowledge is formed and evaluated) structure of the subject. This component includes knowledge of the content of subjects taught in class. Content dependent pedagogical knowledge – which includes understanding of the nature of any specific subject, and the principles and manner of teaching thereof. This area is effected both by the general pedagogical knowledge and the knowledge of the subject matter. It also includes the category of content dependent pedagogical knowledge. The concept that enrichment of personal experience is so important for the making of professional, philosophical and practical identity, claims a central place in the process of teaching and learning. Any practical experience expands the world of teaching trainees. They draw conclusions, learn new methods of teaching and develop educational perceptions. The experience of conducting a qualitative study helps them deepen these processes. It enables them bring to the surface various finesses, put insights into words, and define specific arguments and concepts. Thorough reading and analysis of the results of experiencing qualitative studies (Alpert, 1998) have proven that students learned to identify difficulties and clarify problematic situations or conflicts, as well as situations of educational doing. They learned to identify the framework of a situation and name various phenomena in a manner that promotes thinking of possible solutions for problems, when these arise. The students learned to use various types of knowledge for the purpose of interpretation and thinking – both field knowledge and theoretical general knowledge. By experiencing qualitative research the students re-developed and re-designed concepts to which they had been exposed in the training program. Some of the students managed to get more from the study, and reached a more profound reflective thinking than their mates.

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In this context, we can relate to the researchers’ argument that there are students of many degrees of reflectivity (Day, 1993). Generally, students find reflective thinking difficult, because of their tendency to focus on the technical performance of teaching and their lack of both theoretical and practical knowledge, and lacking the skill to analyze their practice (Calderhead, 1989). Some of the students can be characterized as more reflective than other, having a caring, open personality in addition to some philosophical tendencies – unlike their less reflective peers. What they have is the need (LaBoskey, 1993) to look for something better that will justify their actions. Reflective students are characterized by the need to pose questions, by ability to evaluate themselves and their ability to express themselves easily both verbally and in writing (Korthagen & Wubbels, 1995). The present paper (Alpert, 1998) includes traits of reflective thinking, as expressed by the written word. This may be the indication to Alpert’s words that such model of thinking may pass also to practical teaching of the trainee. Kaniel (1997) supports Alpert. He argues that writing has two aspects. In the first it serves as a means of communication and transferring of messages from the writer to the reader, by an agreed language of symbols. The other one is an inner process, which enables the writer to phrase his standing points, analyze his ideas and process them. The product of writing is characterized, says Alpert, (1998) by an organized text, of which the various parts are united and lead the reader to a central message. This is the process of decision making and problem solution. We could say that by research method the researcher is supposed to perform efficient procedures of decision making, using meta-cognitive systems. Spiral combination of all systems enables a person to integrate into every problem solving his own self and the requirements of the task. Such meta-cognitive, effective process is significant in the training of teachers. The performance and writing of research make the researcher to undergo reflective procedures. There is no doubt, says Kaniel, (1997) that teachers should be researchers and prepare their students to be independent learners able to decision making based on intelligent choice and research. Qualitative study can examine, verbally and in writing, many points: To what extent is the student aware of the complexity of situations? How does he characterize problems and name them? To what extent is the student able to generalize, based on specific cases, and link between

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theoretical concepts and field practice? What is the personal knowledge he manages to produce from his experience in teaching. All these things can be performed by feedback and dialogue between student and his colleagues and teachers. Feedback talks can be treated as a framework and a source for activating, evaluating and experiencing processes and contents defined as reflective thinking (Frenkel, 1988). The following section is focused on the meaning of feedback sessions in the process of teachers’ training. 2.2.3 The Role of Feedback Sessions in the Making of a Reflective Teacher The feedback session is an important component in the process of teachers training. It can be considered as an activity representing and summarizing the processes taking place in the training of teachers. As per Frenkel (Frenkel,1998) during feedback talks, the tutor attempts to assist the student in understanding his own conduct, as well as his pupils. Feedback talks are meant to improve the student’s ability to define, build-in and include his knowledge, and turn them into meaningful knowledge units. Also, this talk is intended to assist in future teaching situations, and link spontaneous knowledge with formal one – a function, which renders new and extensive meaning to the event. Feedback sessions include a variety of dialogues: The student comes from a single personal experience into the expanded, comprehensive dialogue, which organizes and identifies linking principles. The process, which takes place, reinforces experience as representing the teaching process, with all its complexity. The talk makes a framework by which the student can get a clear answer regarding his own image as a teacher. An efficient feedback session (Frenkel, 1998) depends on the readiness and skills of both participants: Student and tutor. It depends on the personal style and the professional “credo” of the participants. According to the developmental approach of Vygotsky (Vygotsky,1978) and Berliner (Berliner,1986) the feedback session is a mediating process. It is a dialogue which contributes to significant learning and growing of the student, and indirectly also to the student’s pupils. As they see it, the dynamics between the student and his pupils is the main test of the feedback talk. The counselor is a human mediator between perceptions, beliefs and skills understood due to his professional knowledge,

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understanding and experience – and intuitive knowledge based in principle on the learner’s personal knowledge. The interaction between these two kinds of knowledge is a dominant factor in the student’s professional development. The first question arising in a feedback session concerns the “how”. How should this talk be conducted? What are the roles of the tutor and student? What ambience will enable the development of the student? What patterns of response and guidance are efficient to promote professional conduct on the student’s side? Schon’s ideas (Schon,1987, 1988) may help us understand the importance of feedback talk. The Feedback Talk as a Reflective Means of Improving Reflective Skills, as per Schon’s Approach: Schon (Schon, 1988) relates to several characteristics, linked to the term ‘reflection’ in the context of teaching. It defines reflection as listening to the learner and responding to problems the learner has. The main feature of reflection is meant to express itself in leading the learner or the student to himself, and in a joint outing to investigate the unknown, which have no other solution. The tutor enables the student to reflect upon his thoughts and actions in some sort of “mirror hall”, which helps him understand and give a meaning to what he is saying and doing. Schon (Schon, 1988) points out seven features of reflective tutoring during the feedback session: 1. Reflective tutoring, as per Schon, is a joint process in which the

student is invited to solve – together with the tutor – a riddle of surprising and intriguing elements. It is supposed to lead the student to learn from his experience and that if his colleagues.

2. Reflective tutoring includes characteristics of counseling, criticism and description. With the assistance of such tutoring a person assists another person in experiencing reflective teaching, in the context of specific contents he deals with.

3. Good reflection does not judge and has no room for a correct answer. It exposes the student to uncertainty, and the direction and place to look for answers in are within the student and not outside.

4. The tutor helps the student to clarify for himself “what had happened and what is the meaning of things” in order to achieve reflective teaching.

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5. At the feedback talk the tutor encourages and directs the student to reflect on his own experience, prior, during and following his experience with pupils.

6. The tutor will try to reflect for the student, what he had seen and what had happened during his actions, thus helping him reach meaningful discernment about them.

7. Reflective tutoring includes characteristics of presenting and asking of questions and completion of circles.

In addition to the above-mentioned 7 features of reflective tutoring during the feedback session, Schon (Schon, 1987, 1988) points out five criteria of evaluation for the action itself and the qualities of the feedback talk:

• The ability to listen and respect the learner’s considerations. • The ability to respond and examine, with a specific intention of

helping another person to overcome specific difficulties in understanding. Also to reflect, pose questions, criticize and steer the student to self-understanding.

• The ability to analyze interpretations of actions, and of the manner in which the student explains his actions.

• The ability to help a student to understand what had happened, and the meaning of things.

• The ability to conduct a dialogue with the student and arouse his curiosity.

Schon’s ideas (Schon, 1987,1988) could make a basis of reflection for the training work. A profile of the feedback can be planned and evaluated by the degree of its closeness to Schon’s ideas (Frenkel, 1998). The second question in the feedback session is the question of “what”. What are the relevant pedagogic contents to be discussed in the talk following experience? What qualities of teaching and evaluation could be the axis during the feedback session? What is the theoretical knowledge fit to explain authentic situation of experience? How should the student be tutored to learn from his experience, as well as from others’? How to create frameworks, which will enable significant perceptions of the knowledge acquired during the teaching process? Answers to the “what” questions can be found in Shulman’s approach (Shulman, 1988)

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Feedback Sessions as expressing the definition of teaching characteristics, and as a source of “teachers’ knowledge of pedagogic content” – according to Shulman: Shulman (Shulman, 1987) doubts Schon’s assumption (Schon, 1987, 1988) that students should be directed mainly to build in the knowledge buy themselves, in a process of experiencing and “reflection in action”. He thinks that one cannot ignore the fact that there is a world outside the teacher, which is conducted by principles, even if a person, or a group of persons, choose not to agree or behave according to these principles. The feedback session makes a framework in which the student is given an evaluation. This framework expresses the link between the features of teaching and the means of evaluation. According to Shulman there is room to define, during the feedback talk, characteristics of teaching which are salient in the experience. Dealing with these features in the talk may be a framework of evaluation of the feedback itself. Shulman (Shulman, 1988) and Collins (Collins,1991) defined four basic assumptions with regard to the features of teaching and the meaning they have in an attempt to evaluate teaching: The complexity of teaching – the ability to treat “complexity” and multi-dimensions of every experience. Shulman and his colleagues hold that teaching is a complex task. Any evaluation of a teaching process requires a tool that can relate to a variety of components and the interactive relations between them. The feedback, as a personal framework, enables to relate specifically to every event in class, and personal attitude to the student’s needs. Reflective tutoring, as a process, is a means to relate to sections of teaching and all their components. The tutor helps the student “dismantle the complex situation” and focus on those components, which are relevant with regard to subject and the student’s characteristics. The tutor will also develop awareness and ability to function in complex situations. Contexts of teaching process – the ability t cope with a phenomenon in a variety of contexts. In the process of teaching experience, one should relate to various factors, which may effect the process: The area of specific knowledge, a specific group of pupils, the specific teacher, defined time, place and the social-educational environment. Any change in one of the components will change the meaning and weight of the experience. An educational experience is a one-time, unique phenomenon.

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The feedback session, as per Shulman et al. Has to deal with each one of these factors and their influence in class. The tutor is supposed to guide the student and teach him to identify and analyze the factors and the contexts, which influenced experience. Also, the tutor should direct the student to reach certain conclusions and deductions from the total, as expressed in his teaching experience. The link between theory and practice in teaching – coordination of theoretical knowledge and practical skills. Shulman et al. argue that the feedback session has a potential of creating a two-way meaningful link between the practical aspect of the teacher’s work and the theoretical one. This two-way link between practice and theory gives the process of training its unique place among academic professions. Various events, taking place during this activity can illustrate and explain repeated complex theories. The tutor, as the connecting person between theory and practice, has an important role during feedback talk, by expanding the student’s generalization level. His vast experience in teaching should assist him to direct the student to his reflective insight, at the same time analyzing and drawing the conclusions from his teaching experience as an experienced teacher. The tutor’s varied academic knowledge on theories and principles of teaching, his learning and personal experience – all make him the most significant mediating means for the student in his training. He can assist him in focusing and identifying processes and phenomena, which illustrate certain theoretical principles. This turns the process of learning theoretical and abstract concepts into something concrete and meaningful for the student. The tutor can suggest reading of many things, not studies in class, though relevant to the subject, i.e. Shulman et al think that the purpose of evaluation is to teach the student to think of his work, and justify his considerations on a professional basis. The student’s role in the reaching evaluation process. Shulman et al. Argue that teachers know their work better than any external evaluator. Therefore, evaluation should be conducted by teachers. It is important to recognize the teachers position (the student in this case) in the process of evaluation, as someone familiar with himself. He should take part, allowed to take a standpoint and explain his actions. The evaluation, made during the feedback, is made by the tutor, himself an experienced teacher, with theoretical knowledge of education. Due to

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these reasons he can relate, following his observation, to the student’s experience with all its complexity, to evaluate it and weight its qualities. This approach is presented also by Shafriri and Bozo (1998), who argue that inner evaluation process is made by a person all is life. According to the constructive learning outlook, where it is man who creates his personal knowledge structure in his mind, the process of evaluation is part of this process of learning (Shafriri & Bozo, 1998). In order for the evaluation to integrate in the process of learning – which is internal – it should derive from the learner’s perception of his situation. The ability to evaluate and criticize one’s progress toward the targets is of internal self evaluation nature. The learner evaluates his performance in light of collected evidence (Silberstein & Geva, 1992; Skager, 1984). To develop the learner’s ability of self evaluation, an external evaluation (by teachers and colleagues) is required, to assist in construction of standards and criteria, by which the learner is to examine his inner evaluation and will also receive encouragement and support. External evaluation may expand his perception and enable him to reach understanding not likely to be reached on his own (Talbot, 1997; Wolf, 1993; Corno, 1994; Shafriri & Bozo, 1998). The constructivist approach is based on the assumption that man creates knowledge from interaction between existing knowledge and art, and new ideas and situations he encounters (Airasian & Walsh, 1997). These new understandings are expressed by application. A substantial part of learning is thinking about doing, which requires reflection and feedback both on the process and the products. As per this concept, evaluation is part of learning intended to integrate within. The features Shulman suggests for the evaluation of teachers’ teaching quality may be a framework, or starting point for relevant discussions during the feedback session. They could be both theoretical and practical generalizations, with which the tutor interprets the events in the feedback session, or starting points for the guidance of students to their own reflection, conclusions, and evaluation of their field work. From other studies by Shulman (Shulman, 1988), dealing with various types of “knowledge of pedagogic content” acquired by the teacher during teaching, and from Silberstein’s model (Silberstein,1994) and analysis using Shulman’s terms to explain the relations between teaching and curriculum, one can define and map the relevant areas for the evaluation of student’s professional knowledge. Shulman distinguished between three contexts, which can express the “insight behavior” of a teacher, i.e. his reflection upon his work, explanations and arguments:

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• The context of pre-active behavior • The context of inter-active behavior • The context of post-active behavior

The third question to be asked during the feedback session is the “what for” question. What did the tutor choose to stress certain viewpoints for? What is the desired image of the teacher with respect to futuristic educational principles? How does he furnish the student with tools to find out and set up his professional “credo”? The answers to these questions are given by Solomon and Almog (Solomon and Almog,1994). The feedback session as a framework for creating the ”desired teacher figure”, as per Solomon and Almog: The main problem observed by Solomon and Almog (Solomon and Almog,1994) is how should the education system adapt to the requirements and characteristics of the cultural changes around us. The suggested solutions focus on the features of the graduate of this system In order to create the “desired figure of teacher in the educational system” one should, according to Solomon and Almog, create this figure. This approach should dictate the process of training in the broad meaning of planning the curriculum and choosing the teachers and tutors to train the suture teachers. It also effects significantly the nature of every feedback session following practical experience. Solomon and Almog (Solomon and Almog, 1994 )argue that even if the talk does not include any phase in which the tutor specifically declares of his intentions toward the figure of the desired teacher, still – his viewpoints of the subject do effect and dictate the nature of the feedback. They also indicate several features of the future teacher: The intellectual skills have to be varied, general and adaptable to complex situations and varied contexts.

• Extensive, active knowledge. • Tendency to be involved and innovative. • Ability to judge and take a standpoint, even in situations without

clear and agreed standards, or relevant social precedents. These features, as per Solomon and Almog, can be confirmed and strengthened during feedback sessions. The feedback talk can be regarded as an efficient leverage and a means to change learning and behavior

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patterns of teaching training students. This process provides a new opportunity to prove intellectual abilities in outstanding situations, at the same time coping with new knowledge and experiencing complex problems. The feedback session can contribute to higher motivation, improved learning methods and a better “learning self image” (Blum, 1978) of the students. One of the important components of the feedback is the dialogue between the trainee and his tutor. The dialogue plays a central role in voicing the “personal voice” of the participants. In the present literature, this “personal voice” is regarded as a means to develop insight and sensitivity of those participating in the process of teaching and learning (Richardson, 1994). The following chapter focuses on the meaning of dialogue and its role in reflective tutoring. 2.2.4 The Reflective Dialogue as A Means to Intensify and Change the Basis of Knowledge During the recent years, there has been a growing recognition of the fact that the teacher is the source of knowledge in educational research. Thus, building of knowledge in education is regarded as a process of joint work of the teaching trainee and his tutor. Fenstermacher (Fenstermacher1978, 1986) emphasizes the fact that the purpose of training teachers is not to tell them how to act, but to educate them to voice their considerations in teaching and do their actions expertly. Such learning is within the context of their work, during a constructive process of inter-actions between the teacher-trainee and his tutor. As per Fenstermacher (Fenstermacher,1986), Shulman (Shulman,1987) and Schon (Schon,1988), the role of the tutor is to evoke constructive processes of the tutored (pupils, teachers or any other position holders in the education system). The tutor should assist them in activating reflective thinking, and encourage them to construct their teaching programs on the basis of knowledge and reflective thinking. Shafriri and Bozo (Shafriri and Bozo,1998) argue that in reflective learning there are two types of distinguishable dialogues: A dialogue between two participants or more, interested in the their own point of view. A dialogue as some sort of investigation, striving toward a product or output that will satisfy the participants (Burbules, 1993).

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In a constructivistic learning environment the dialogue serves as a central tool in the interaction between teachers and pupils. By that dialogue the learner can, with the assistance of the tutor, identify his “real” level of knowledge, and advance to the “potential” level of knowledge in each phase of learning. The dialogue (between two or more participants) makes a framework, which enables every learner to expand and elaborate the re-organized or re-built knowledge. Such knowledge is being built within the “near development area”, following the social, physical and intellectual experience of the learner (Vygotsky, 1978). These terms are taken from the theoretical model of “near development area”, by which Vygotsky (1978) explains the connection between development and learning. According to this model, learning takes place in the range between the real, completed level of development, and the higher potential level, which the learner reaches with the mediation of an adult or jointly with his colleagues. The range between these two levels is dynamic and may change with each developmental situation. The passage from one, existing level of development to another, higher one depends on learning assisted by social mediation (Penuel & Wertsch, 1995). The social mediation, which exists in dialogues, enables the learner to make a progress in building his knowledge, with the assistance of others (teacher or colleagues), and being trained for reflective skills. The dialogue, both as a talk, and as an investigation, is an essential condition for a reflective dialogue, but it is not enough. The dialogue as a talk enables us to accept differences, mutual respect and open mindedness. Dialogue as an investigation enables the analysis of possibilities, choosing of alternatives and focusing on solutions or products. Reflective dialogue is characterized by activating the meta-cognitive thinking. A reflective dialogue between several learners, guided by a teacher, applies the advantages of joint studies, and creates a framework for joining, i.e. training in processes of joint study (Shafriri and Bozo, 1998). Such learning creates an exposure to various viewpoints, and joint investigation, which enriches the individual’s experience. It also makes an excellent stage to discover personal knowledge, externalization of one’s personal thoughts, receiving and giving feedback, as well as supporting learning-partners to help them overcome their difficulties. Learning of participation through dialogue is characterized, among others, by an atmosphere of respect and non- competitive experience,

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thanks to the learners’ need to share their initiative and product with others. A reflective dialogue is, first and foremost, an authentic expression of “thinking culture”. It includes cognitive and meta-cognitive occupation, the purpose of which is to enhance the learner’s awareness to self-criticism on the process and product of his learning (Shafriri and Bozo, 1998). During the reflective dialogue, the learner can clarify for himself his personal standings, as well as compare them with those of his friends. Experience and personal thinking are then exposed to verification or conflict, and to criticism of others, thus creating new contexts, refining concepts and creating more solid and stable structures. It seems that the social-cognitive psychological approach, from Vygotsky’s(1978) school, completes, expands and intensifies the perception of constructive learning. Therefore, reflective dialogue should serve as a basic pattern of teaching in a constructivistic learning environment (Shafriri and Bozo, 1998). A study, conducted by Ezer (Ezer, 1998), included a prolonged dialogue between the researcher and a coordinator of erudition in an elementary school. The dialogue took place at the same time with her work as a coordinator and teacher, when she made use of a new perception of teaching, in her class and in all the school. The dialogue, which had lasted for two years, brought upon personal growth as coordinator, with regards to her perceive the subject of erudition, her position as coordinator and teaching n general (Ezer, 1998). This dialogue between the two can be a model or “prototype”, as per Shulman (1987), for any tutor’s work with his tutored student. Definition of the Dialogue between the Tutor and his Pupil, and Its Nature Fernandez-Balboa and Marshall (Fernandez-Balboa and Marshall,1994) define dialogue as an active process of a continuous serious discussion, which enables the personal voice of people to develop and be heard. Burbules (Burbules,1993) defines dialogue as a communicative-pedagogic component, characterized by conversational interaction, aimed at teaching and learning. This component, he says, includes voluntary partnership and mutual collaboration, trust and caring. The activity of the dialogue is aimed at a new revelation and understanding. The purpose of this new understanding is to improve knowledge, insight and sensitivity of the participants.

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The perception of the dialogue opposes the old fashioned perception of “pedagogic monologue”, by which the tutor-teacher knows what is best for his pupils and gives them knowledge. The dialogue perception matches the change that has lately taken place in educational practice and research, a change which reflects terms like force, personal voice, character and research methods (Richardson, 1994). There is a strong tendency to allow the trainee to express his “own voice”, and assist him in improving and changing his experiences and beliefs (Hargreaves, 1996; Cochran-Smith & Lytle, 1990). Burbules (Burbules,1993) describes four types of dialogue: A dialogue as a talk: Used usually when we are interested in the other party’s point of view. For example, a conversation between friends about what their families gave them, and how they grew up. This is a multi-lateral dialogue. A dialogue as an investigation: Intended to answer a specific question, or solve a problem. This is a unilateral dialogue, aimed at one purpose, with the wish to get a result that will please everybody. A dialogue as an argument: A critical, multi-lateral dialogue. Atmosphere may be skeptic and there is specific purpose. Dialogue as teaching: This is a critical, multi-lateral dialogue, used in critical questions aimed at a clear conclusion. This is the leading form of dialogue, and it takes place in the “hypothetical development range”, as per Vygotsky (Vygotsky,1962), and the trainee may do the conceptual contexts matching his own readiness. The strategy of dialogue, according to Vygotsky (Vygotsky,1962), is largely based on the model of “hypothetical development range”. This is the gap between the level of real development of the learner or tutor, expressed in one’s own ability to solve problems, and the level of potential development, expressed by one’s own ability to solve problems of higher degree. According to Vygotsky (Vygotsky,1962), progress from the real level to the potential one takes place under the tutoring of an adult or a more experienced person, sometimes jointly with a more talented colleague. Ezer (Ezer, 1998), in her study, identified the “real level” of the trainee. Eventually she located the “potential level” of the trainee. During the dialogue the tutor/researcher made her best not to harm the “personal Voice” of the trainee. Her own “personal voice” as a teacher, coordinator

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and person, was identified by the researcher during the dialogue, by a questionnaire she completed, and by phrasing her “credo”. The dialogue, which took place between the researcher (Ezer, 1998) and her trainee (coordinator of erudition at school), was partly a talk-dialogue, and partly a teaching-dialogue. In this dialogue, the external knowledge of the tutor blended with the coordinator’s own perspective. Her voice became significant (Contreras, 1993) and her thinking became increasingly critical (Cochran-Smith, 1992). The Characteristics of the talk-dialogue The talk-dialogue, which took place between the researcher and the trainee, proved to consist of some fixed characteristics (Ezer, 1998). The tutor/researcher’s utterances focused on the following aspects:

• Practical and theoretical professional knowledge. • Reflection of occurrences. • Assistance in interpretation.

The utterances of the trainee focused on the following aspects:

• Re-conceptualization (Fernandez-Balboa & Marshall, 1994). • Specification of awareness and new understanding.

The reflective tutoring presented in the study, placed before the trainee a “hall of mirrors”, says Schon (Schon, 1988). By these mirrors she constructed her basic knowledge in three subjects: Knowledge, position and profession. The “Hall of Mirrors” served as a double role: -A hall in which the mirrors reflect strategies and world-outlook of the trainee. A hall in which the mirrors reflect strategies for reflective teaching.- The dialogue that took place in this study emphasizes both the practicality of dialogue and the theoretical approach of reflective tutoring. It is expressed in fact in a fruitful dialogue, that should change the insights and understanding of the trainee. It should also add a theoretical layer to anchor its activity in the knowledge area, and encourage us to re-think its practice. This case could be a prototype to be enacted in similar situations (Shulman, 1986).

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The dialogue described here is in fact a situation of “private investigation” – a way to work with teachers so that they will be able, by reflection, to better understand their own experience and change things (Richardson, 1994). Such a dialogue agrees with the idea presented by Cazden (Cazden, 1988). She claims that the new knowledge of the learner is built on the basis of previous knowledge by reflecting previous processes. This is possible only when based on relationships, or unique communicative system, made by the teacher/tutor. As she sees it, the role of the teacher/tutor is not to furnish his pupils with knowledge and tell them what is good or bad. The tutoring teacher should lead the learner to a new way of thinking, generalizing, a different categorization of things and a revised understanding of the discussed phenomenon. Shulman (Shulman, 1987) argues that the tutor id the source of built-in knowledge, no less than the professional literature, the books and the practice of the trainee. This idea, according to many others, including Hunsaker & Johnston, (Hunsaker and Johnston,1992), should be reflecting on the education system, as well as on teachers’ training. One of the main conclusions of studies that examined teachers’ training programs (Silberstein, 1998) was, that there is no link between theoretical studies and practical teaching. Goodlad (Goodlad, 1990) suggests doing it in two manners: Combining case reports in theoretical courses. Making observation and experience the object of discussions. Goodlad recommends to start training programs by analysis of practice, and only later to add theory and principles. He does not recommend teaching theory and hoping that students will eventually discover the link between theory and practical teaching. Teaching, he says, as a reflective individual occupation is characterized by contextuality, by multi-significant and multi-solutions changing situations, and by uncertainty. The teacher, during teaching, is overflowed with a stream of information. He should perceive it, filter the main issues, make decisions and plans (Silberstein, 1998). Constructivistic opinions regarding the definition of the nature of learning process, regard it as a result of thinking, of active construction of concepts and involvement of he learner in the process of creating ideas and changes. If the trainee or the teacher are in a state of learners, in any

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aspect – then the traditional training program, built on passing of verbal propositional information does not match these views (Silberstein, 1998). The updated approaches in cognitive psychology, in the area of transmission studies, emphasize the element of connectedness, which points out closeness and images between the world of learned contents, to which the transformation is needed as an essential condition. Gardner (Gardner,1991) argues that there should not be a gap between situations in which knowledge is acquired, and those in which the learner is required to use it. The more the situations of knowledge acquisition are close to situations where this knowledge is used – the better the chances of creating active, usable knowledge. In order to analyze situations, choose lines of action and solve dilemmas – they should be taught in authentic situations (Gardner, 1991). Shulman (Shulman,1987) and Schon (Schon,1988) claimed that the role of the tutor/teacher was to evoke constructive processes in the trainees. They also argued that n the teaching-learning process the place of the trainee should be recognized as close to himself. The next chapter deals with the link between reflection, between processes of evaluation and construction of knowledge in a constructivist environment, and the place of all of them in the progress of teachers’ training.

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2.3 The Connection between Reflection, Evaluation and Building of Knowledge in a Constructive Environment 2.3.1 The school of constructivist learning and self guidance In the times we live in, called the era of knowledge, all knowledge and information have magnified, developed and changed at an extremely fast rate. There is no possibility and no use in teaching all that is known in every subject (Birenbaum, 1997). A graduate of any education system is required to be able to learn all his life – so regarded by the system. Thus, the role of education is to develop in students skills which will help them acquire information of any type and process it on their own (Tishman, Perkins & Jay, 1996; Levin, 1995; Solomon et al, 1993). Rogers (1973) describes the learned man as one who has learned how to learn, who knows how to adapt and change. A man who has learned to learn, says Rogers, has an inner motivation to study. He has to recognize his need for personal growth, and then plan and perform appropriate learning activities, by himself or with the assistance of others, and evaluate his progress as per the targets. Such a learner - who uses various strategies intelligently, and is aware of cognitive processes he activates – is a self guided learner (Skager, 1984; Schunk, 1994). According to this approach a learning environment is required that will support learning as structuring knowledge (constructivism). Constructivism is a general name for various psychological, philosophical, methodological approaches in education, all of which are characterized by structuring. According to them, knowledge is a product of human structuring. The first buds of constructivist concept can be seen in Piaget’s (1974) theory. He was the pioneer of this school in the 20th century. Hew argued that real learning is the constructing of ideas rather than repeating information. Significant knowledge, as per Piaget, must be processed by the learner, thus it cannot be an exact copy of what was taught. Piaget made use, in an analogous way, of terms from biology describing a creature’s adaptation to its environment. Acquisition of knowledge was demonstrated by terms of assimilation and adaptation of new information into a set of concepts previously created by the learners about the world. The constructivist concept has slowly penetrated the area of education, since it required extreme changes in basic concepts and terms, such as: Reality, truth, knowledge etc’, as well as the way to acquire them (Von Glaserfield, 1995). Von Glaserfield argues that for many years people have misinterpreted Piaget’s doctrine about constructivism. Ironically, this very misinterpretation is the proof of his theory that man creates the

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cognitive reality, which is not necessarily an objective representation of something concrete (Yehieli, 1997). The common basis for the various constructivist approaches developed since, is that people construct their knowledge by themselves, using existing knowledge in a process of active thinking. During this constructing process they develop solid models of beliefs and practical coherent knowledge, based on their experience. Since this process is effected by a variety of social experiences – hence the knowledge of each individual is not entirely personal. On the other hand, two individuals exposed to the same events may interpret them differently, due to a world of previous experiences, knowledge and beliefs. From the constructivist point of view man cannot go further than the limits of his personal experience. Knowledge cannot be found or discovered – it has to be constructed. Von Glaserfield (Von Glaserfield, 1995) defined the radical constructivism. He points out two principles that distinguish between his approach and other concepts of constructivism. The first principle is, that knowledge is constructed cognitively by man. The second is, that cognitive activity serves the organization of the experimental world, rather than the discovery of an ontological reality. I.e., people create reality by processes of thinking, which is not necessarily a real representation of the world. The radical tendency does not pretend to expose the objective structure of reality, but serves as a coherent way of thinking, helping us to understand various phenomena in the world, and explain them. Also, it emphasizes the transferal of responsibility to thinking and learning to the individual thinker. Von Glaserfield (Von Glaserfield, 1995) believes that experiencing is necessarily subjective, therefore his experiencing differs from that of other people, resulting in the fact that his knowledge is different from other people’s knowledge. Von Glaserfield (Von Glaserfield, 1995) deals also with the motivational aspect of learning. Motivation to cope with new problems, results usually from the satisfaction of solving problems, of achieving the challenge posed. Understanding the reason for a correct result and the logic of things gives the students a feeling of capability and skill, which are by far stronger than external reward. When students cannot solve problems of their own, they do not acquire the confidence in their ability, thus they cannot be expected to have motivation to deal with future problems. Von Glaserfield (Von Glaserfield, 1995) focuses his message on the subject of the constructivist concept in that the teachers’ role is not to convey knowledge, but strengthen the art of learning.

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The basic principle from which most constructivist proposals stem, is that concepts and the organization of concepts are mental structures which cannot be transferred from one mind to another. Every learner has to structure his concepts individually, and the teacher’s part is to guide the students in the process of structuring. According to this approach, teaching is regarded as a dialogue between teacher and student, during which the teacher assists the student in internalizing the knowledge, sometimes by a conceptual change (Posner et al., 1982). The vital components for conceptual change are: Exposing the student’s previous knowledge of the subject, presenting a situation which creates a significant cognitive conflict in the student, or using relevant analogies (Yehieli, 1997). Studies show that, in fact, a conceptual change occur only rarely (Hewson et al., 1998). Therefore the process should be combined with conditions supporting conceptual change, such as: Interest in the studies subject, motivation to study it, awareness to concepts, and appropriate climate in class. The social constructivist concept emphasizes the importance of creating these conditions for the process of learning. Davis and Sumara (1977) too stress the importance of social interactions in cognitive activity. As they see it, constructivism is a theory based on knowledge and experience intended to bridge the gaps between the learner and the world, and between the learner and himself. From a constructivist point of view, although the acquisition of knowledge is a personal process, it includes some significant social aspects. Knowledge can be distributed and shared with members of any community, thus acquiring knowledge is a combination of an individual and social processes (Hewson et al., 1998). As noted above, the constructivist approach is based on the assumption that man creates knowledge from the interactions between knowledge and beliefs (existing knowledge) and new ideas and situations he encounters (Airasian & Walsh, 1997). The new understandings are created and expressed by application. This approach claims that learning requires an action of building models or representations by the student. Every person has a set of ideas in various areas. In order for a learning to take place when the student meets new ideas or information, he should think and see how they match the existing structure. He has to re-organize his mental scheme in order to contain the new knowledge (Birenbaum, 1997). The pedagogic concept in the base of the constructivist approach emphasizes the control and responsibility of the learner in leading the process of structuring and shaping of knowledge, concepts and skills. This situation is opposed to

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the one in which the teacher just “pours” his knowledge into the student’s mind. According to the constructivist school, the student achieves full control of the material when he develops his conceptual map of the subject matter. The meaning makes learning easier, because the learner knows where to place the new things within the mental framework he had made for himself. Also, it makes knowledge practical, since application is part of understanding. As per this approach, the purpose of teaching is to help the student in broadening his conceptual understanding, not to supply him with rules. Effective teaching should assist the student in using what he already knows, to figure our new stuff (Birenbaum, 1997). Therefore, teaching should be adapted so as to arouse and bring forward relevant previous knowledge, related to the context and experience of the student. A substantial part of learning is thinking about doing’ which requires reflection and feedback on processes and products. A maningful understanding is a continuous process of active building, which can take place by phasing of meanings, opposing them, bilateral examining and drawing joint conclusions. This process occurs both in the inter-personal and social context (Solomon et al., 1993; Perkins, 1992). The teacher’s part in such learning, as per Vygotsky (1978), is to assist the student in progressing from his level of “real” knowledge toward his “potential” level of knowledge, in each and every stage of learning, following the learner’s experience. For that purpose a dialogue is created between teacher and students, a dialogue in which their roles are re-defined: Teacher – students and students – teacher. Students and teachers teach one another with the mediation of the world. The teacher, according to this approach, is not supposed to ask questions and answer them, but act as a coach, or assistant, accompanying the learning process of his students. The teacher should create opportunities for learning and propose activities, appropriate to the student’s readiness to learn, in a manner that will enable him to make connections and understand in his own. Such effective teaching focuses also on supplying the learner with purposeful targets, derived from the student’s background, that will teach specific learning strategy. This teaching uses the students’ intuition as a basis for discussing their mental models. Supporters of the constructivist approach emphasize that every learning involves thinking (Perkins, 1992; Perking & Blythe, 1994; Resnick & Klopfer, 1989). Cognitive research of learning basic skills showed that reading, writing and arithmetic all involve factors of concluding, judging and activity of mental structuring. This concept is opposed to the

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behaviorist school of the early 20th century, according to which learning takes place by reinforcing low skills, which are the basis of building more complex understanding. The behaviorists argue that basic material can be learned by memorizing, and only later will come the turn of thinking and consideration. It turns out, among others, that thinking and consideration regarding basic concepts are delayed to later stages, and for some students they are delayed indefinitely, since they will never be exposed to such levels during their studies (Birenbaum, 1997). The supporters of the constructivist approach, on the other hand, think that practicing arithmetic, algorithms, memorizing rules of lists of new words, as well as practicing coding skills without developing a conceptual model or seeing the overall meaning of activities will create difficulties in retaining knowledge, retrieving it, applying and generalization (Resnick & Resnick, 1992). In addition, the supporters of the constructivist approach argue that linear, systematic and consistent learning of one unit at a time does not develop critical thinking or any significant learning. They deny the traditional approach by which every subject can be taught after breaking it into separate parts, and teaching them one at a time, with no connection to their context. This traditional approach is called “the brick laying system” – laying of the information bricks one on top of the other, in order and in small steps. This approach does not relate to the question how much conceptual understanding should take place, or what mental organizational structure is required to understand the material (Birenbaum, 1997). In teaching this way those students who experience difficulties are punished twice: once by being denied of the possibility to learn in a context that will make the skill more significant and relevant to their life experience, and then again because the studied material in a manner of memorizing, detached from its context is much more difficult. A change in the teaching – learning approach, as per the constructivists, requires a change in the manner of evaluation. As mentioned before, the issue of evaluation of achievements has been through many changes during the years. As many of the researchers of behavioral sciences today have their reservations of the positivist approach, so many of those dealing in evaluation of achievements turn from the traditional quantitative approach to an approach based on qualitative evaluation, called alternative evaluation. This subject will be dealt with later. 2.3.2 The role of reflection in the building of teachers’ curricular knowledge and teaching skills

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Of the total research activity, focusing on the teacher’s reflective ability in class, an important question arises, regarding the role of reflection in the teacher’s process of development, both in class and out of class (Levin & Nevo, 1998). It is important to examine to what extent and in what supporting conditions the reflective processes assist in changing educational viewpoints of the teacher, following the exposure to new curricular and teaching approaches. Levin & Nevo (Levin & Nevo,1998) conducted a study with the purpose of learning the role of reflection in the process of building curricular and teaching knowledge of teachers. The dynamics of our life, according to these two researchers, express themselves also in changing of the accepted perceptions of various areas of knowledge, as well as in methods of research and understanding the nature of learning processes and transferring knowledge (Levin & Nevo, 1998). It also emphasizes the perception of the teacher as a learner, since teachers are regarded as central change agents and as having a central role in shaping educational goals, and nurturing learning and teaching processes suitable for our time. The essential condition for such involvement of teachers in the shaping of up-to-date educational processes, is in fact a change in their educational perceptions. Other studies (Cohen et al., 1990) point at the fact that existing educational perceptions are a major obstacle in the way of making essential changes. Strauss (Strauss, 1993) too found that teachers stick to outdated theories, which significantly project on their expectations of themselves and of their teaching methods in class. According to Villar (Villar, 1994), reflection allows a person to move from a state of uncertainty, doubt, confusion and embarrassment to a sense of control of complex situations, and a feeling of satisfaction resulting from coping with dilemmas. Thus, it can be concluded that reflections has a significant role in shaping the teacher’s learning, when exposed to new educational approaches. Soter (Soter, 1995) regards the sensitivity of the teacher to reflective processes as a central factor in a model of change in the teachers’ thinking, in the context of exposure to a new teaching approach in the subject of language. She studies the processes of building new knowledge, and distinguished between radical and superficial building-in. She states three criteria for her discernment:

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• Reflection – high on radical build-in and low on superficial build-in.

• Toleration of dissonance (contradiction) – low on radical build-in and high on superficial build-in.

• Tolerance of imbalance (vagueness) – high on radical build-in and low on superficial build-in.

Levin & Nevo (Levin & Nevo,1998) examined the link between the teacher’s reflective ability and his sensitivity to reflective processes, and his ability to change routine, safe, thinking patterns. They examined the role of reflection in the process of building-in the teachers’ knowledge. What happens when a teacher is exposed to a super-subject constructive curricular and teaching approach after many years of thinking and working within a framework of disciplinary curricular approach, based on a model of knowledge transferal. Their study was conducted in three elementary schools taking part in a process of change and building of a new curricular perception. Seventy teachers in these schools participated in the study, out of which the researchers focused on four female teachers. The teachers’ training for the new curricular approach is based on constructivistic learning principles (Darling-Hammond & McLaughlin, 1995; Lieberman, 1995), and includes workshops, personal and team counseling, learning and teaching, as well as in-class observations. 2.3.3 The constructivist approach to the super-ranged curriculum Two important characteristics distinguish the curricular approach we are dealing with from the common approach to curriculum:

• It is based on constructivistic principles of children and teachers’ learning.

• It is mainly integrative and not arranged by subjects. The constructivistic approach to learning is considered as some “open system”, emphasizing the learner’s action. This means that the curriculum is not evaluated as a product, but rather as a complex integrative process (Levin, 1995). The integrative nature of curriculum moves the center of gravity from the disciplines, well defined in their structure and content, to the learner and the reality he is living in.

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The super-ranged approach to curriculum is one of several other options to plan an integrative curriculum (Drake, 1993; Jacobs, 1989). This approach focuses on the real world, its meaning and relevancy to the learners. In the super-ranged framework, the various knowledge subjects are investigated in their cultural contexts, with the contents defined according to general ideas and the learners’ interest. According to this approach, contents do not adhere to a pre-defined uniform plan (Drake, 1993). It is characterized rather by contextuality, relevancy and awareness, directed to the knowledge flowing around, and the learning processes of the learner. Whereas other integrative approaches (inter-ranged and multi-ranged) are committed, in one way or another, to the subjects of knowledge (Jacobs, 1989), the starting point of the super-ranged approach is the relevancy and authenticity of the knowledge and information to the learner in his scholarly environment. It is expressed by the fact that the super-ranged curriculum deals with cultural and intellectual subjects, focusing on man and his life (Levin & Nevo, 1998). The constructivistic principles involved in the super-ranged framework, render the curriculum dynamism, flexibility, significant thinking and authenticity. All these are involved in the creative cooperation of teachers and pupils. In this process all parties express viewpoints, emotions, values, questions and knowledge – all of which integrate in learning and teaching. This is not a closed, pre-defined, system, and it does not regard itself as imparting knowledge from teacher to pupil in the easy way of going from the easy part to the more complex one (Levin, 1995; Brown et al., 1989; Spiro et al., 1991; Drake, 1993). It is an opening of a pioneer journey, on an unknown terrain, to the best possible process of learning and development, both for the teacher and pupil. Planning a super-ranged curriculum on the basis of a constructivistic approach requires open mindedness and daring on the teachers’ side, with a great deal of flexibility and the ability to have a dialogue with the pupils. Levin and Nevo (Levin and Nevo,1998) point out seven characteristics describing the main features making a super-ranged, constructivistic, personal and unique for teachers, curriculum. Emphasis on contexts rather than subjects of knowledge.- -Emphasis on concepts rather than specific contents, so the disciplinary knowledge will be a means and not a goal. -Emphasis on dynamic, interactive, vague planning, rather than precise, definite and pre-defined.

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-Emphasis on the process of structuring the meaning, both for teacher and pupils, rather than presenting a defined, guided product by the teacher. -Respect for the different and unique and the nurturing thereof (among pupils, teachers and classes). Rather than expecting uniformity and standardization. -Encouraging teachers to express different types of thinking (spontaneous, creative, intuitive, associative, etc’), in addition to systematic, rational thinking. -Emphasis on processes of reflection and structuring of personal knowledge by teachers and pupils (with regard to beliefs, standpoints, values), rather than focusing mainly on technical and rational planning. 2.3.4 The connection between structuring a new curricular knowledge and the degree of teachers’ reflection The study conducted by Levin and Nevo (Levin and Nevo,1998) examined the link between the degree of reflection of teachers, their toleration to situations of imbalance and the type of interaction they have with others – and the structuring of a new curricular knowledge. The findings of this study indicate some complex, un-equivocal connections, between the reflective skills of the teacher and the degree of her sensitivity to reflective processes – and the extent of the process of structuring new knowledge. All three teachers demonstrated characteristics the characteristics, which Dewey (Dewey,1933) pointed out to be highly significant for the teacher’s reflective skills: openness, responsibility and high personal commitment. Levin and Nevo also traced the teachers’ high level of rational analysis, as well as the ability (though different) to develop a sensation of objectivity with regard to their experiences. This ability enabled them to evaluate their thinking and new experience, and is considered significant, if not essential, in reflective processes (Binkley & Brandes, 1995). There is no doubt that reflection is important for learning and personal development (Dewey, 1933; Schon, 1987). If Reflection is not spontaneous, then it can and should be encouraged, and then a radical structuring of new knowledge can happen. Levin and Nevo (1998) also claim that a relatively high level of reflection is not necessarily a sufficient condition for the structuring of new knowledge.

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The researchers indicate additional factors, take a substantial, critical part in the process of knowledge structuring. These factors are toleration for situation of imbalance, and the interaction of the adult learners (teachers) with their surrounding. These findings support Soter’s (Soter,1995) findings that high toleration for situations of imbalance is a significant factor effecting the quality structuring of a new curricular knowledge. Levin and Nevo (Levin and Nevo,1998) suggest two standards by which significant interactions of structuring processes should be evaluated: Who were the interactions made with, and on what basis. The findings of their study showed full, unequivocal correlation between toleration for states of imbalance and radical structuring of new knowledge. High toleration for situations of imbalance may be connected to different levels of openness demonstrated by the teachers. Dewey (Dewey,1933) argued, to that effect, that a high level of openness is expressed not only in one’s readiness to cope intellectually with a new approach, but also in the ability to take risks and cope with vague, unbalanced situations, just as Levin and Nevo (Levin and Nevo,1988) claim. The findings of the study showed, that significant interactions of the learning process were made both by experts and children. The new knowledge presented by the expert on one hand, and the child’s authentic process of learning, with his ideas and originality on the other – enrich the teacher. Those teachers, who reported that interactions from these two sources were the most significant for them, were those who demonstrated radical structuring. Teachers working by the constructivistic approach are more attentive to inner processes of learning. The study of Levin and Nevo (Levin and Nevo, 1998) suggests two important factors effecting the teachers’ learning, in the context of dealing with the new curricular approach at school: -The level of teachers’ awareness to their own learning process, including the level of sensitivity to reflection, and the ability to operate in situations of imbalance. -The ability to create interactions with experts and children, on a cognitive, social and emotional basis. The conclusions of the study reinforce the learning theories, which claim that the best learning is done by active involvement, accompanied by thinking and phrasing of thinking (Dewey, 1933; Schon, 1987; Lieberman, 1995). They also correlate with the theories of learning which describe optimal knowledge structuring as taking place in the assumed development area, out of the interactions between student or novice teacher and the expert (Vygotsky, 1978).

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One of the most prominent findings in Levin and Nevo’s study is the exposure of the different, unique way each of the studies teachers had made. These findings support Soter’s conclusions (Soter,1995), that even when teachers’ post-graduate studies are intended for teachers in a team, each one of them goes through a personal, unique process. It is a process of structuring the new knowledge, and assimilating and adapting to the existing one it at the same time. Children go through the same process in their learning, and one should take this difference into consideration in the process of learning and teaching. New knowledge in built by a personal, inner process’ and includes many aspects: Personal, social, cultural, etc’. The findings of the study emphasize the argument that basically, teaching should aim to a process of learning rather than transferring knowledge, and pupils should be directed to that. The process of learning is linked to the process of evaluation and evaluation. The question arising here is, how these learning processes, discussed here, should be evaluated. The findings of the study stress the perception of alternative evaluation process as part of the learning process. 2.3.5 Traditional evaluation compared with alternative evaluation in constructivistic learning. The perception learning as a reflective action regards reflection and reflective dialogue as vital mechanisms for the building of knowledge, in a constructivistic learning environment. The quality of learning depends on the quality of the accompanying reflection (Shafriri and Bozo, 1998). The reflective mechanism is one of the ways to self-evaluation of learning in surroundings, which encourage “self directed learning”. As per Shulman (Shulman, 1987) a dialogue can be an alternative manner of evaluation. Evaluation can be interpreted in many ways. Any action of giving value has many aspects. When such action accompanies learning, we attribute a value to behaviors or objects during the process of learning. Shafriri and Bozo (Shafriri and Bozo,1998) point out two types of evaluation in learning: An inner process of evaluation, done by every person, all his life. It is automatic and natural, and derives of man’s ability to live in two worlds at the same time – one world in which he performs certain actions and the other in which he can think of his actions (the meta-cognitive ability).

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The moment someone has a personal interest and he manages to define an achievable goal, there begins a process of evaluation of actions and strategies to achieve his goal. An efficient process of evaluation improves performance, and if it lacks change or causes poor performance – it is meaningless. The quality of such evaluation process, as per Shafriri and Bozo (Shafriri and Bozo,1998) depends on the degree of man’s awareness to himself, and his surroundings. An external process of evaluation – taking place by inter-personal interactions. It is a formal and standard process. External evaluation is a basic human need, and one man’s attitude to another includes a factor of evaluation. External evaluation is usually done by the system. The findings of the study point at the fact that external evaluation cannot evaluate individual achievements in a valid credible way. Studies made by Shavelson, Baxter & Pine (Shavelson, Baxter & Pine,1992) show that even when the same complex performance task is given to the same pupils on different times – their performance will not be consistent. Some of them tend to use different strategies for the same problem in different times. They claim that performance of one task cannot be included in another, thus external evaluation cannot reflect a process and development. Man, as a social creature, needs something to relate to, a ”mirror” that will reflect his functions in the social weave. This “mirror” strengthens or weakens behaviors, values and perceptions, by reflecting reality. External evaluation greatly effects the shaping of personal traits, such as: focusing control, self-image, self-motivation of ambition. These personal features have an influence on the process of learning and its results. There is a constant tension at the meeting point of inner and external evaluation. In the past, school was perceived as a supplier of formal knowledge (Aviram, 1994). This perception gave rise to a model of learning that emphasized comprehension and memorizing of the objective knowledge. This knowledge was evaluated by lectures, papers and exams, and the purpose of that evaluation was to check how much the pupil manages to repeat this objective knowledge. The scientific and technological resolution of the 20th century changed the world, together with the point of view. The relativistic world we live in contains an enormous amount of knowledge of various degrees of truth (Shafriri and Bozo, 1998). Every truth is determined by changing research perceptions and by contexts relevant to the studied phenomenon

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and the studying person. In this world a different perception of the learning process has developed – the perception of constructivistic learning. The model of constructivistic learning emphasizes the learning subject. The pupil is the one creating in his mind the structure of personal knowledge, which is an open, dynamic structure, differing from one person to another. The process of learning is not passive; but an active process of creating mental structures. In such models the teacher organizes and offers an environment in which learning can take place, though the main responsibility of learning is with the learner himself (Shafriri and Bozo, 1998). The evaluation, accompanying this process of learning should match an open world of knowledge, of dynamic learning centered within the learner. The question arising now is how does any evaluation (inner or external) effects the pupil functioning. External evaluation, accompanying learning processes, has a significant weight in creating a learning environment. The nature of evaluation, the atmosphere in which it takes place, its apparent and concealed purposes – all have a profound essential effect on the pupil, on his motivation and on the process of learning. Learning something new means moving from not knowing to knowing. It is characterized by vagueness, sometimes by insecurity and fear of the unknown. It is a state of motion, dynamic and changing. Shafriri and Bozo (Shafriri and Bozo,1998) claim that using a summarizing evaluation turns the situation into a static one, since it defines unequivocally the situation of the learner, thus fixing him in place and obstructing motion. The usual evaluation at school is external, thus summarizing. Its purpose is to have a general view of the pupil’s achievements at the end of any subject unit, semester or school--year. The teacher evaluates the pupil by grades in the card, or by reporting to other addressees (Birenbaum, 1997). The most prominent characteristic of such an evaluation is the grading, i.e. setting a number which places the pupil on an objective scale of success in studies (Gardner, 1983). An external, teacher-controlled evaluation, makes the teacher responsible for learning – the person responsible for the process is also the one to evaluate it. Such an evaluation creates a hierarchy of learning, which determines the type of relations and roles: The teacher holds the knowledge and the correct answers and the pupil is his subordinate.

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In this situation, the teacher’s skill, too, will be measured by the summarizing evaluation of the pupils’ work. Learning, thus, becomes a tool to serve the final goal – the best grade. Shafriri and Bozo (Shafriri and Bozo,1998) argue that the process of getting a good mark is not necessarily a process of learning, whereas it includes various manipulations, some of which are contrary to the very essence of learning, and others are clearly not educational. This process makes use of short-term memory, to memorize the subjects, without the involvement of varied mental schemes. It creates short-term learning, detached from any context to significant mental schemes in the pupil’s life. The conclusion is that the standard grading-evaluation is cognitively inefficient. It does not relate to the part or future in the learning process, but rather “photographs” the pupil in a given moment. Giving a present, accidental “picture”. This picture does not reflect the processes leading to this specific moment, therefore the information it gives is extremely superficial. It is not connected to any future processes the pupil is about to go through, unlike a forming evaluation, and the information it gives has no significance for the improvement of future learning processes. External evaluation, expressed by grading, is made by a numerical scale, and is in fact the result of mathematical manipulation deriving from the will to grade the pupil on the axis of “normal graph”. One of the problematic aspects of this evaluation (common in schools) is its psychological effect on the pupil (Shafriri and Bozo, 1998). The pupil’s attitude to traditional evaluation is mainly based on the fear of damage to his self-image and of losing the approval and support of significant people in his life (Nissan, 1980). The single, normative grade assumes indirectly that there is one factor which effects learning, and can be compared. The study shows that there are in fact many factors, some of which independent, that effect the learning ability and intelligence. Gardner (Gardner,1983) thinks that this is the reason why the variation of pupils cannot be measured by one general standard. In the same learning situation, different pupils will learn in different manners and perceive different contents in a different rate. Not understanding will also differ from one pupil to another, i.e. in the same class, same situation the pupils will be in different processes of learning. Evaluation, attempting to compare pupils artificially, by a normative grads, creates one status of “succeeding students” and another of “failing

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students”. It enhances competition and tension between them and fixes both types in their status. Comparison on a normative basis has adverse effects, both in the short and long term. In the short term it creates inefficient learning, because the competition for the normative grade creates tension and anxiety. On the surface competition creates motivation to study, but it is external, creates an apparent learning and not a significant one. When pupils are threatened and under stress, they are not open to perceive information, and will not learn by trial and error. The gravity is shifted from a learning process, which allows trail and error to a competition, which has to be won. This form of learning does not approve of differences and encourages conformity. On the other hand, shaping evaluation (Birenbaum, 1997) is more appropriate for an individual-adjusted teaching. Here, every pupil proceeds in his/her own pace, and his individual learning needs should be detected. The pupil takes part in his evaluation, and his progress is evaluated in relation to himself. Such an evaluation is extremely important in a culture of evaluation framework, in which the pupil is required to be sensitive to his own learning needs (Wise, Plake, Johnson & Ross, 1992; Rocklin & O’Donnell, 1987). Thus, following such personal process – anxiety decreases. Any evaluation aimed at nurturing the process of teaching and learning of the relevant participant is included in the caption of shaping evaluation. The differences between the traditional and alternative teaching methods are based on new learning theories, which in turn are based of new models in the study of intelligence. These models, best represented by Sternberg (Sterenberg,1985) and Gardner (Gardner,1983) speak of the link between intelligence and the individual’s inner world, his personal experience, developing skills and ability to solve problems. Various theoreticians, when speaking of the present models to explain intelligence (Birenbaum, 1997) base their words on the following assumptions: Intelligence is not a single entity, congenital and fixed, thus one can learn how to learn. Thinking includes meta-cognition, or the ability to guide learning and thinking processes. Development of meta-cognitive ability contributes more to improving the intelligence than development of thinking skills of lesser degree. Developing intelligence relates, therefore, to the

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development of the meta-cognitive ability, which can develop naturally or by directed teaching. Mental procedures depend on social and cultural contexts, and their shaping takes place by the child’s interaction with his surrounding. Intelligence is multi-dimensional. A person can excel in specific dimensions and be rather poor in others. Classifying pupils by one dimension only can discriminate against those who are lower on this dimension, but may be higher in others. This is the reason why not everybody can be taught by the same method (Birenbaum, 1997). The assumptions about the nature of intelligence were used as a basis for the school of constructivistic learning. At the same time, some changes take place also in the perception of evaluation of achievements. From a culture of quantitative measuring, of measurable things, there is a movement, at least on the rhetoric level, toward a culture of evaluation, i.e. qualitative examination. Hence, the purpose of teaching is to develop a thinking, self-directed learner, and not just to transfer knowledge. The emphasis in learning is not on memorizing, but rather on investigating, using knowledge and constructing the meaning. The emphasis of evaluation of achievements shifts from the quantitative, psychometric approach to the contextual, qualitative approach. These changes are of like nature with the statement that roles, rules and rituals of modern society in the 21st century require some kind of teaching, learning and evaluating culture (Kleinsasser, Horsch & Tastad,1993), and the constructivistic learning school and self-guidance represent these changes. 2.3.6 The principles of the alternative evaluation in constructivistic learning The prevalent term of the recent years, in the field of achievement evaluation in the western world, is alternative evaluation. This term consists of terms as evaluation of performance, direct evaluation, balanced evaluation, teaching-based evaluation, authentic tasks, digests etc’ (Birenbaum, 1997). The need for an alternative evaluation resulted from the discontent of the closed tests, which has been going on since the late seventies (Baker & Herman, 1983; Birenbaum & Shaw, 1985; Linn, 1983). Some people define alternative evaluation as any form of evaluation, other than the standard of the choosing type. Madaus and Kellaghan (Madaus and

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Kellaghan,1993) divide this type of evaluation into three elements: Performance, digest and product. Gardner (Gardner,1992) defines evaluation as retting information about the individual’s skills and potential, with a double purpose: Giving practical feedback to the evaluated individual, and production of practical data for the community. As he sees it, what makes an examination different from evaluation if that for the purpose of evaluation we prefer information-producing techniques, during the daily routine performances, whereas the examination arouses uncomfortable feelings due to the use of formal tools, in a neutral, context-detached situation. The emphasis in the culture of evaluation is placed on combining evaluation with teaching. On the other hand, the examination is detached from the specific process of teaching in class, unless the examination gives any evidence with regard to the pupil’s thinking, what he knows and is able to do regarding the studies material (Birenbaum, 1997). What changes in the process of evaluation is the perception of the pupil’s status and responsibility. From a pupil, submissive to evaluation processes to which he is no partner, he becomes an active partner, taking part in setting evaluation standards and self-evaluation of his rate of progress. The pupil requires self-reflection, and self-awareness to his learning process; he holds a constant dialogue with his teacher about evaluation, and participates in evaluating is mates’ achievements. Alternative evaluation comes in many forms and shapes, characterized by the use of tools and auxiliaries for a real performance. The tasks to be performed are authentic, in real situations or imaging of such. The tasks are supposed to test high thinking levels, at the same time being challenging and interesting. The evaluation of performance includes both process and product. Results are reported not by numbers but by descriptions intended to serve as significant feedback in the managing of learning. Within the framework of alternative evaluation a variety of tools and methods has been used, among others performance tasks, digests, diaries, papers, observations, interviews, discussions, and evaluation of colleagues. Evaluation in constructivistic learning emphasizes the fact that evaluation should be made opposite human, inaccurate imperfect truth. Meaning that the most important index in this interaction is the degree of its humanity, human qualities and values in includes and expresses (Shafriri and Bozo, 1998). Just like other processes in the constructivistic learning environment, evaluation should also be shared by all participants, open for discussion,

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with a rationale that can be criticized, and expressing all its three reflective elements: Description of the case, causative explanation and drawing of conclusions (Shafriri and Bozo, 1998). According to Shafriri and Bozo (Shafriri and Bozo,1998) alternative evaluation is characterized by the following elements:

• Control and responsibility for the process of evaluation are in the hands of the pupil.

• Evaluation is internal, assisted by external evaluation. • Evaluation is shaping and process directed. • Evaluation is qualitative and not quantitative. • Evaluation is verbal, multi-parameter, not normative and not

public. • The central mechanism in evaluation is the reflective dialogue. • The main criterion for evaluation is “rationalism” – everything

argued by the pupil is valid. 2.3.7 The role of the teacher and the pupil in alternative evaluation, and in creating a self-directing pupil In the alternative evaluation of constructivistic learning, both the teacher and the pupil have central roles. The teacher is a central figure in the learning situation: He is he one to shape the learning environment, thus determining the nature of learning process. The manner in which the teacher uses various evaluation tools, transmits – whether openly or secretly – his set of values and beliefs (about learning, nature of man and the specific pupil) to the learner. This way the teacher establishes the nature of evaluation and its effect on learning (Shafriri and Bozo, 1998). The teacher’s role as evaluator in an environment of constructivistic learning, is to render services of molding evaluation to his pupils. The teacher’s attitude is critical for the process to succeed. Such attitude should be a result of understanding that positions, perceptions and understandings on the side of the learner, cannot be changed without entering his thinking and emotional world, or without his consent (Shafriri and Bozo, 1998). As they see it, the learner is the one to create the schemes of knowledge in his mind. He can update, or change them by his logic and his set of beliefs. The teacher, as render of the service of shaping evaluation, should

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assist the pupils according to their needs, as they define them. His role is to help the pupil activate self-reflection of his work, and diagnose his present state in light of the goals he had set for himself. The teacher, as designer of the constructivistic learning environment, legitimizes errors and mistakes, which are a natural part of the process of learning. It is an open process of guidance, which does not define its goal of contents. In this process the teacher has to be objective and without any hierarchic authority. His only authority should be professional, in the subject he specializes in. In order that the evaluation fit in such a process of learning, it should result from the learner’s inner perception of his status. Thus, the emphasis in the model of evaluation is on inner evaluation, which is dominant in the balance with external evaluation. In order that the learner should associate inner and external evaluation, he should recognize external evaluation as a significant contribution to his set of understandings. The more the learner “unites” with his own process of learning and recognize it as his, in an inherent manner not linked with external manipulations – the higher his need to perform self-evaluation. Evaluation of the skills of a self-evaluating learner (Birenbaum, 1998), among which we include efficiency of learning strategies, meta-cognitive thinking, ability to work in a team, inner motivation etc’, requires evaluation according to the contextual approach. Contextual evaluation sets the context and interaction between the pupil and his surrounding, relates to multi-interpretations and variety in follow-up and control, and does not separate between cognitive, effective and social aspects. According to this approach, evaluation is part of learning. It is a prolonged process, documenting the development of skills during a long period of time. It is done mainly in learning contexts, using academic tasks for the evaluation (Birenbaum, 1997; Wolf, 1993). For the purpose of integrating evaluation in the process of learning, which is an internal process, it should result from the learner’s perception of his situation and his evaluation of himself. The ability to criticize and evaluate one’s progress is the ability of internal self- evaluation. The learner evaluates his own performance, in light of the evidences he has gathered (Silberstein and Geva, 1992; Skager, 1984). To become a qualitative evaluator, the learner should be trained and he should experience processes of self-evaluation. A learner, who is educated to lead the process of learning, gradually develops the ability of self-reflection. He also defines the parameters and criteria by which he would evaluate his work. The quality of evaluation, including self-

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evaluation, depends on the level of awareness of the learner to himself, to his purposes and the surrounding in which he is active (Shafriri and Bozo, 1998). In constructivistic learning the pupil has to cope independently with difficulties. He has to develop the ability to cope with frustration, failure, uncertainty and dissatisfaction. His learning environment should supply the bedding in which these abilities can develop positively. The competition will strengthen the learner and prevent a situation of over-dependence on the teacher. Nevertheless, the pupil needs some external relating in various phases of his work – external evaluation with which he can check his inner evaluation and receive some support and encouragement. Evaluation from a teacher can increase the “short term development span” of the pupil, broaden his perception and enable him to reach understandings he would not reach by himself. External evaluation accompanying the process of learning, as per Shafriri and Bozo (Shafriri and Bozo,1998) is extremely important. It enables a long view on processes the pupil goes through, directions of progress, and products of his work. This type of feedback requires a perspective of time and experience of an adult – all of which the teacher has. External process of evaluation will accompany the internal process, and the integration between the two will be done by the learner, who will decide between the two in situations of conflict. In other words, in order to develop the ability of self-evaluation the pupil needs external evaluation to help him check his inner evaluation, support and encourage him (Talbot, 1997; Wolf, 1993; Corno, 1994; Shafriri and Bozo, 1998). Mutual trust between teacher and pupil will enable a situation in which the pupil is ready to accept external evaluation, even if it creates a conflict with his internal one. In order that the external evaluation process by effective on the one hand, and does not cause any harm on the other, both teacher and pupil need to have a common cause and interest in the process of evaluation. The balance between the relation and assistance offered by the teacher to the pupil, and the pupil’s independence in leading his learning and evaluation, should be sensitive and adjusted for each pupil, with one objective above all – the pupil’s success. One of the central humanistic principles in the process of alternative evaluation, is an attitude of respect for the learner. He is the only authority with regard to his life and learning. He holds full responsibility for his actions and their results. Consistent behavior, according to this approach, will result in mutual respect between teacher and pupil.

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The teacher’s profit is his professional satisfaction of one who contributes to the process of learning, whereas the pupil’s profit is his ability to direct his progress in agreement with real needs established by him. In the process of evaluation, the pupil enjoys a wide range of freedom. It is not anarchy, since it exists only with a clearly defined framework. In this context, the teacher represents the expert for creating this framework, with terms that will enable meaningful learning. The importance of self-evaluation lies in its contribution to self-guidance. Out of processes of self-evaluation the pupil receives information about his performance, abilities and limitations. It enables him improve his learning , with respect to the purposes. One of the most beneficial tools to develop the skills of self-evaluation is the use of an indicator (Birenbaum, 1998). The indicator is a series of guidelines for grading and evaluating pupils’ work. It includes criteria, which are the conditions each performer has to stand up to, in order to succeed. The indicator is based on standards, made to state what level of criteria one has to stand up to. The indicator can be expressed in numbers of words (Wiggings, 1998). Usually, the task of developing the indicator, is performed by teachers. They pass it on to their pupils, thus supplying them with tools to evaluate and direct themselves. In the long term, Birenbaum (1998) suggests the participation of pupils in developing the indicator. The question arising here is what would be the best tools to gather evidence with on achievements in the process of learning, according to the approach of evaluation. The study will discuss these tools.

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Chapter 3 Results and Analysis

Fifteen (15) female students participated in this study. For the detailed description each was given a serial number, to retain anonymity. At the beginning of the school year, personal interviews were held and questionnaires were handed out. The interviews consisted of the same questions as in the questionnaire, in a different order, due to the fact that some students found it easier to answer in detail in writing. The students were asked to give their reasons for choosing to specialize in corrective teaching of math. In principle, I usually ask the students in every course, which is not obligatory, for their reasons. In this manner I can get a general picture of their motives, expectations and feelings. In previous years I asked this question during a group session, and the students replied in their turn. On that occasion most of them claimed that they wanted to acquire tools to teach math, broaden their knowledge, importance of the subject etc’. Very few actually spoke of personal difficulties and the wish to overcome them via the course. Only during the school year some of them exposed their true feelings by telling me things they had not mentioned at the group interview. This led me to think that personal interviews are better, enabling me to study in detail the student and his/her motives. In my pilot research (which lasted two years) I interviewed each student in person. They told me many things that had not been expressed in the group session, but still I could feel they did not open up, and had more to say. Thus I decided to add the personal questionnaire, twice a year – beginning and middle – to acquire more detailed information, and maybe even notice the differences in between. The detailed questionnaires are included in my paper. Table no 1 (Question 3 in the “New Way” questionnaire) shows the students’ answers as written in the questionnaire. Table no. 1: Reasons for choosing the course, as given by the students Student No.

Why have you chosen to specialize in corrective teaching of math? Please detail.

1 To acquire the tools which will help me in teaching math. I may want to teach math in the future, so this is the place for me to broaden my knowledge of the subject. To get closer to the subject of math and discover its less “threatening” aspects.

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2 During all my years of teaching I tried to avoid the subject, which had been my “weak point”. I went for reading and comprehension – areas I am good at. So now, for the first time in my life I want to face the challenge, and hope to succeed too.

3 The main reason is my natural inclination to the subject, as well as the recommendation of my pedagogic tutor, whom I think highly of.

4 I chose the course because I am very apprehensive of the subject and thought that it may help me cope with the problem. In addition, it is a subject I have never dealt with, and I want to try something new.

5 The course is obligatory. 6 I wanted to acquire tools to cope with a subject I am scared

of. The poor manner of teaching in high school gives the pupil a sense of failure. I hope it can be repaired in the Seminar. As a humanistic person, coping with exact answers and numbers has always upset me.

7 I have difficulties in math. I want to help those who have difficulties, in locating the problem. I want to learn methods for teaching math. Since, as a child, there was no one who could support me, I decided to choose this course in order to help the pupil I am working with, as well as acquire the tools to help other kids.

8 My natural inclination is to avoid math, though some part of me likes the subject, especially when it works. I had difficulties in choosing the subject for specializing, and my choice was mainly determined by system’s considerations.

9 I could not decide between math and reading, but finally I decided on math, because I find in it elements of reading, and it relates to almost any aspect of life. It is important, difficult to learn and understand, and I love the subject and feel vigorous and confident working with math.

10 It is more interesting. It may help me. It will give me more working opportunities in the future.

11 Because I keep avoiding math, and I decided to do some corrective teaching for myself. I have more tools to teach reading than for math, so I decided to enrich my knowledge.

13 I chose the course because of my “fear” of math. I know that

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eventually I’ll have to study the subject and I want to overcome my fears, so that the children will have no fear. I also want to be more professional in this subject.

14 I have no other choice. I have no difficulties with reading, but for math – I had private tutors all my life. I have to acquire the tools, help and counseling - to help me overcome my problems.

15 As a teacher in a special education class, one of the most important things to know is how to teach math. I do not wish to be in a situation where a pupil will ask for my help and I will not be able to give it to him. Math is my weak point, and I would like to strengthen it.

In this data we can see that 11/15 student reported of choosing the course in order to overcome fear, concern and personal difficulties. There is no doubt that these things indeed are a cause for lack of confidence, and even lack of efficacy. One student (no. 3) reported of being naturally inclined to math; another (no. 12) reported having interest in math. No 9 reported math as being her favorite, and that she feels confident, whereas another (no. 5) claimed that the course was obligatory (and probably would not have chosen it if she could). Seven (7) students admitted to their need for professional tools to teach math. Fear and concern claimed a major part of the students’ arguments, and some gave the reasons for them. It is important to note that even those who did not mention fear as the reason for choosing the course, did so in further questions (details in the chapter dealing with strengthening the sense of confidence). From these data we can see five substantial motives to choose the course. Table no 2 presents these data, according to motives, number of students reporting, and main expressions reflecting each type.

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Table no. 2: Types of motives for choosing the course Motives for Choice No. of

Students Typical Expressions

1. Acquiring the tools, teaching methods and better knowledge.

7 Acquisition of tools, broaden knowledge, personal knowledge

2. Coping with personal difficulties, self assistance

11 My weak point; it scares me; I find it difficult; it sets me back; corrective teaching for me.

3. Personal interest 4 I have natural inclination; I am personally interested in the subject

4. Assistance to pupils having difficulties in math

4 Helping the pupil I am working with; helping my pupils; helping others locate the problem; help them overcome their fears.

5. Making use of this knowledge in the future

3 I may want to teach math in the future; having better tools to help my own children; better professional options in the future.

There are several motives for choosing the course, which can be divided as follows: - - Motives related to the student as such (no. 2, 3), expressed in overcoming personal difficulties, self-assistance and personal interest. - Motives related to the student as a teacher (no. 1, 4, 5) expressed in acquiring tools and teaching methods, helping pupils and using this knowledge in the future.

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3.1 Strengthening the Sense of Confidence: In this chapter I will attempt to describe, expose, record and characterize the process of change the students underwent, with regard to their sense of confidence. The tools selected to describe the change in the sense of confidence were as follows: Reports made in the “New Way” questionnaires (appendix 1), the “Half Way Through” questionnaire (appendix 5). The reflective summary handed in at the end of the year – all these in addition to the personal interviews and observations. Beginning of School Year During the personal interviews, held at the beginning of the year, some of the students reported of being concerned and anxious, of not knowing what to teach and not being sure of being able to promote the pupil. Such arguments repeated themselves in the majority of questionnaires. The fact that they came up only in the questionnaires is probably due to the fact that in an interview one is embarrassed and in need to impress – a known phenomenon in teaching and training. The students’ answers to question no. 4 in the “New Way” questionnaire (Are you anxious? If so, why?) are shown in Table no. 3. I regard this question as very open and straightforward, assuming that there are, indeed, some anxieties. Based on pilot studies, I decided to use this kind of question. Table no. 3: Concerns about the Course According to the Students’ feeling at the Beginning of the year Student No.

Answers to the question: Do you have any anxieties of the course, and if so – what kind and why?

1 Yes. I am so nervous about some mathematical subjects, that I will not be able to teach them to my pupil.

2 I have fears of the course because I have to work with a child, and I feel I am lacking the tools to do so.

3 My main fear is that I will not have the time to prepare the lessons for the pupil, because my work (apart from my studies at the seminar) is time and energy consuming.

4 Yes. There are many fears, because my own experience with math was a series of failures.

5 Many fears. I have difficulties in the subject.

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6 No 7 A little. I worry about the difficulty in coping with the pupil’s

problems. 8 Yes. I am somewhat anxious of not being able to carry the load

of the course. 9 Yes. Teaching math seems difficult, since it is an abstract

subject, and I am afraid I will not be able to do it. 10 Yes. Due to my past experience I am afraid I will not be able to

learn something that may help me in my future work. 11 No. 12 Yes. I‘m afraid I will not have adequate tools to help me teach;

things I learned at the seminar have not helped me in field-work.

13 My only worry is that I am not very confident on this subject. I have no earlier knowledge and I do not know many teaching methods.

14 Yes. I am quite apprehensive because I have difficulties in math, and I think I will not be able to teach a pupil with problems, due to my poor control of the subject.

15 I’m afraid I will not be able to teach and promote the pupil. From the above table we can see that 2 students (no. 6 and 11) unequivocally claimed of having no concern whatsoever. Their answers are different from their stated reasons for choosing this course (Table 1). Student no. 6 claimed that the subject (math) scares her until this day, whereas student no. 11 stated that she is still trying to avoid math, and decided to take the course as corrective teaching for herself. As I see it, both students are afraid of the course, but do not express it explicitly so as not to show weakness. 13/15 students stated their concern of the course. It seems that they could not always focus their fears and the reasons for them. Student no 4, for instance, stated that her fears result from her own history of failing math, i.e. she states the source of her fear but not the fear itself. On the other hand, student no. 15 states her fear of not being able to help her pupil, i.e. stating the fear, but not the reason. Some of the students expressed the fear itself and the reasons for it, such as student no. 1, who claimed that her fear of mathematical subjects will affect her teaching, linking her inability to teach with her lack of control of the subject matter. A similar answer was given by student no. 14, who claimed that following her own problems, she would not be able to teach a pupil with problems.

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It seems that at this stage the sense of efficacy is still rather low, and expressed in fear of coping with the pupil’s problems, and inability to help him. Five main reasons for worry about the course appear in these data. The next table (no. 4) shows the reasons for their fears and the number of students having each type of fear. Since it was rather difficult to separate “what” question from the “why” – I treated them as one. Table no. 4: Origins and Reasons for Concern about the Course at the Beginning of Year Reasons for fearing the course

No. of Students

Typical Expressions

1. Fear deriving from lack of tools and teaching methods

3 I have no tools; no teaching methods for the subject

2. Fear deriving from personal problems with math, and previous failures

5 My experience is full with failures; I cannot handle the subject

3. fear of failure in teaching and promoting the pupil, difficulty coping with the pupil’s problems

5 I’m afraid of some mathematical subjects, thus I cannot teach them. I’m afraid I cannot transfer the meaning to the pupil. I cannot teach someone else as long as I have not complete control of the subject

4. Fear deriving from poor control of math

2 I’m afraid of some mathematical subjects. I have no full control of the material.

5. Fear that the course will be a burden, too heavy to handle

2 I’m afraid I won’t have enough time to prepare the lessons for my pupil. I may not be able to handle the course’s load.

The types f fear (as per table 2) can be sorted as follows: Fears related to the student as a learner (no. 2, 4, 5) expressed in personal difficulties and lack of control of math. Fears related to the student as a teacher (no. 1, 3) expressed in lack of tools and teaching methods, failure to promote the pupil and coping with his problems. Concerns related to the burden of the course, as expressed by 2 students are connected to the students, both as learners and teachers.

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Generally, from the students’ answers one can realize that they all expressed concern related to problems and previous failures, lack of tools, knowledge, and fear of coping with the pupil’s problems, as well as the course’s load of work. There is no doubt that all those fears expressed by the students, result in lack of confidence and a sense of poor efficacy. Some of the students knew, already at the beginning, how to focus their feelings, whereas others reached that point later, i.e. acquiring personal insights by interaction with the pupil and training sessions. Studying answers to questions, such as: “What feelings does the course evoke”? (no. 13) we can see that 11 students expressed a great deal of concern, giving the following answers: - “Curiosity, interest and concern”. (no. 1) - “Some fear, much curiosity and challenge” (no. 2) - Positive feelings, though mixed with concern of the work load” (no. 3) - “Some concern at first, more optimistic in the future” (no. 4) - “Mainly fear” (no. 5) - “Some concern, but positive excitement” (no. 7) - “Expectation to broaden my knowledge, mixed with some concern” (no. 8) - “Mixed feeling. On the one hand I was glad to respond to the challenge, on the other hand fear that I might not be able to cope with my difficulty in math” (no. 10) - “Concern” (no. 14) - “Concern, curiosity”. (no. 15) From the above mentioned statements we can see that 7 students used the word “concern”, whereas 3 others used the word “fear” to express their feelings. These answers support their answers to previous questions. On the question “What do you expect of the course?” (no. 14) most of them replied that they expected to acquire tools, support and assistance. Student no. 5 said that she expected to overcome her own fears of the subject, and no 13 claimed that she expected the course to give her confidence and professional knowledge. All this supports the data presented in Table 2, dealing with the motives to choose the course. In that table, 7 students claimed that their motive was to acquire tools, whereas 11 others said it was their will to overcome their own personal problems. These things also support the data presented in table 3, in their answers to the question dealing with their concerns

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about the course. 13/15 pointed out that they indeed were somewhat concerned. In the “New Way” questionnaire, handed out at the beginning of the year, another question was asked, relating to the sense of confidence (no. 5 in the questionnaire). This time it meant confidence in teaching math. Table 5 shows the students’ replies (literally) to the question: “Do you feel confident enough to work with a pupil and teach him/her math?” Table no. 5: The Sense of Confidence in Working with a pupil on math, at the beginning of the year. Student No.

Answer to the question: Do you feel confident enough to work with a pupil teaching math?

1 I believe I will manage teaching math, in spite of my concerns.2 No. I feel confident to work with a pupil in any other subject,

but not so sure about math. 3 Yes. It seems to me more convenient to work with an

individual pupil than with a whole class. 4 I fell quite confident to work with a pupil, and I am sure that

with a lot of good will and motivation I have, I can manage math as well.

5 No! 6 No. 7 In spite of my concerns, I feel confident, since I am going to

study the problem together with him, we will work it out together and try to overcome it.

8 Yes. I feel I have much to contribute, and I am confident in the training and support I will receive. Usually I am not afraid to admit when I don’t know, and I trust myself to ask for help, in case I need it.

9 No quite. It is important for me to know that I have a solid basis and my teaching method is correct and appropriate.

10 Yes. 11 With the training I feel confident. 12 I feel confident to work with the pupil and teach math, though

I am sure I still have a lot more to learn. 13 I am not so confident in teaching the subject, because I lack

the knowledge. 14 It depends how much help I receive and how difficult the

subjects will be. 15 Today I do not feel very confident, but I believe that when I

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am more familiar and experienced with teaching methods, my fear will vanish.

From the data in table 5 we can notice 3 types, or levels, of confidence at the beginning of the year. This question was more focused and served as a cross-check and support for other questions. Table 6 presents the main types apparent in the questionnaire: Table no. 6: Types in the feeling of confidence regarding math. work at the Beginning of the year. Type of Confidence No. of

Students Typical Expressions

Feeling confident 4 Yes. Not feeling confident 6 No. I am not quite confident, due to

lack of knowledge Concerned, but believe they will succeed

5 I believe I will succeed in teaching math, in spite of my concerns. I feel confident because we will solve the problems together. With the training I feel confident.

2 students (no. 5 and 6) made it clear that they did not feel confident enough to work on math with their pupils. Another one (no. 10) claimed to be definitely confident. Some of the students expressed some concern and lack of confidence, though things were not stated directly. For example: “I do believe I can manage teaching math, in spite of my apprehension"(no. 1), words that express hope, belief and concern – all at the same time. Student no. 14 conditioned her sense of confidence in training and support to be given to her, and the level of material she had to teach. She said: “It depends how much help I get, and how difficult the subjects are”. She tends to transfer the responsibility to external factors, and is afraid to take charge. Asked (table 3) whether she had any concerns regarding the course, she admitted to having many, because she herself had problems with math, and she thought it difficult to teach it to a pupil, not being in full control of the subject. I.e., she is indeed concerned about working on math, but cannot express it in so many words, probably because of her fear to expose her weakness so as not to be unappreciated.

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Table no. 5, dealing with the sense of confidence in working with a pupil having difficulties in math, expresses the following explanation, the motives of which are presented in the next table. Table no. 7: Reasons for the feeling of confidence, or lack of it, at the Beginning of the year. Reasons for lack of confidence Reasons for feeling confident Lack of knowledge. Not knowing teaching methods. Lack of previous experience in teaching math.

Working individually with the pupil, not a whole class. Motivation. Training and guidance to be given.

It seems that at the beginning of the year it is easier to define the reasons for feeling insecure than the opposite. Students find it difficult to identify real reasons for their lack of confidence, because they have not had yet any experience, and probably all the reasons they gave were based on assumptions. Similar things were said during personal interviews, even if not in so many words. Mid-Year: At the beginning of the second semester, upon returning from vacation and following several lessons, another personal interview was conducted with the students. (As mentioned, they have all given about 8-10 lessons each). At the interview they were asked the same questions given in the “Halfway” questionnaire (appendix 5). At this stage the students were all more relaxed, more frank about themselves and their feelings, and answered the question at greater length. In question 5 of the questionnaire they were asked whether they were still concerned about the course, and what about? Their answers are presented, word-by-word, in the following table. Table no. 8: Feeling of confidence or lack thereof at mid-year Student No.

Are you still concerned about the course? If so, what about?

1 No. 2 Today I am not as concerned as before, but still, I am not so

confident in what I’m doing. 3 Yes, I am concerned about the load it may put on me.

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4 Today I am less concerned, because things are well constructed and I know what I am supposed to do.

5 Not concerned any more. 6 No. 7 My only concern is the pupil’s frustration, should I not

succeed in teaching her. I know there are unexpected things, but I shall try and do my best to say: I did it, even if not with great success.

8 Still concerned, due to the great burden. 9 No. I am not concerned. 10 No. 11 No. Not concerned. I am trying to do my best. 12 At this stage I am a little concerned about future work and the

pupil’s response. 13 I am still concerned, because I have no tools to cope with the

mathematical subject. 14 Not concerned. 15 I am somewhat concerned. Sometimes I do not know if my

method of teaching suits the pupil. Maybe it confuses her, or is just inappropriate.

It seems that at this stage 5 students are still concerned about the course, 7 others are not concerned at all, and 3 have some concern, for various reasons. Table 9 represents the students’ answers with regard to their concerns at mid-year. Table 9: Types of concern regarding the course, at mid-year Types of concern, mid-year

No. of Students

Typical Expressions

Still concerned 5 Concerned about the workload involving the course; about not succeeding in my teaching. Concerns result from lack of tools. I do not know if my teaching method suits the pupil.

Not concerned 7 No. I am not concerned. Somewhat concerned (less than before)

3 I am less concerned, but still not sure of what I’, doing. Things are well constructed for me, and I know what I

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have to do, but am still concerned about continuing my work with the pupil, and his response.

At this stage, at mid-year, there is a change for the better in the number of students still concerned. Their number has decreased from 13 at the beginning of the year to 8, of which 3 reported less concern. From 2 students who reported they had not been concerned at the beginning of the year, the number increased to 7. Another change observed in mid-year, based on the students’ reports, was in the reasons for their concerns, as presented in the following table. Table no. 10: Reasons for concern – Mid Year Reason for Concern

Number of Students

Typical Expressions

Concern due to lack of tools

1 I am concerned, because I do not have the tools

Lack of confidence in teaching methods

4 I am still not sure in what I’m doing; sometimes I don’t know whether my teaching methods suits the pupil

Academic load of the course

2 I am still concerned about the academic load of the course

From the above mentioned data we can see that concerns still exist. There has been no change in the students’ concern regarding the academic load of the course. In both cases the same 2 reported of concern, though the reason for it has changed. At the beginning of the year the reason was their fear of the unexpected, whereas at mid-year it resulted from their experience in the course and its requirements. Also, the same student reported both at the beginning and in mid-year of her being concerned about lacking tools. Another concern expressed at mid-year was lack of confidence in their teaching method. It was expressed by 4 of the students and it is a result of the work process with the pupil. I.e., at mid-year they students regard themselves as teachers, concerned about their work as such. They do not express concerns related to their being students, as was the case at the beginning of the year. Their concern about the academic load results too from their new perception of themselves as teachers, who understand the work-load.

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In that questionnaire the students were asked (question no. 3) whether they felt more confident to work with their pupils and teach them math, and if so, what caused that increase in confidence. Their actual answers are presented in the following table. Table No. 11: Sense of confidence in working and teaching the pupil at mid-year Student No.

Are you feeling more confident to work with the pupil and teach him math? If so, what caused the change?

1 Yes. Personal experience and dealing with the questions of how and what to teach, have increased my confidence.

2 I am more confident today, due to experience, feedback sessions, and lesson planning.

3 Yes, of course there is still a lot to be learned, but the experience in the course contributes very much.

4 I could say I am more confident today, but still, I am concerned about subjects taught in grade seven and up. Working on math with my pupil has helped me to cope with my fear of the subject.

5 At this stage I feel more confident. Mainly because of the support and training at the course.

6 Yes. Because of the knowledge and teaching methods I acquired.

7 Yes, somewhat. The pupil’s will to learn and my will to teach made me realize and understand that one can learn and teach in an informal way, in my own way.

8 I feel more confident now, as a result of experience and training, but still I am not that confident.

9 From the beginning of the year I have felt quite confident, after establishing good contact with my pupil and receiving positive feedback, in spite of the problems.

10 Yes. After a while, getting to know the pupil, his problems and his general performance, is helping me construct the curriculum and plan the lessons as per his needs.

11 No. I still have not found the appropriate method to work with my pupil. Working by personal knowledge and intuition is not enough for me at this stage.

12 At this stage I feel more confident in my work with the pupil, following the analysis, feed backs and training sessions.

13 At this stage I feel more confident than at the beginning of the year, but I am still somewhat concerned. My confidence has

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increased with experience and knowing the pupil better. 14 At this stage I feel more focused on planning the lessons –

which increases my confidence. 15 I do indeed feel more confident in working with my pupil,

because I have very defined targets, and I know what I am supposed to teach. But, There still are some concerns. I feel I have not adequate tools to cope with the subjects I want to teach her.

Based on what was said by the students, we can see that at this stage the student are identifying the reasons for their increased confidence. The next table (no. 12) shows their answers with regards to their sense of confidence in work with their pupil at mid-year. Tale No. 12: Types of the Sense of Confidence in working with the pupil, at Mid-Year Sense of Confidence in working with pupil on math

No. of Students

Typical Expressions

More confident 11 Personal experience and dealing with “how” and “what” increased confidence, as well as feedback sessions and lesson planning, support and acquiring knowledge. The pupil’s will to learn, as well as my will to teach, brought upon an understanding that teaching can be done in my special informal way. I made good contact with the pupil, and this acquaintance with the pupil’ his problems and performance, helps me construct the curriculum and lessons according to his needs. Following written feedback and training sessions I am more focused on planning the lessons, which in turn increase my confidence.

Not confident 1 I still have not found the method, which will suit the pupil’s needs.

Confident, but somewhat concerned

3 I can say I am more confident. Work with the pupil helps me cope with fear, but I am still concerned about

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higher level material. I am not fully confident, though my targets are clearly defined and I know what I am going to teach. I am still concerned about not having enough tools to deal with the material.

According to the data, the improvement in confidence is very clear. At mid-year only one student claimed not to have confidence in working with the pupil, as opposed to 6 at the beginning of the year (table no. 6). If, probably, at the beginning this concern resulted from uncertainty, now it is a result of certainty and experience. These things were supported also in the personal interviews, as can be seen below: - “The diagnosis, analysis and summary have helped me understand mathematical issues and ideas I had not known before. They gave me some confidence and a feeling that now I understand more”. - “ The very action of preparing lesson layouts made me focus on my work, which in turn increased my confidence. I come to the lesson knowing what I am going to teach, even if it does not always materialize”. - “At the beginning of the year I had difficulties communicating with my pupil. I was very frustrated and tense already before the lesson. It decreased my confidence, thinking I was in the wrong. As I learned to know him I understood the problem and started to use games. Today I come to the lesson with more confidence, feeling I can cope with his problems”. - “ I always felt a failure in math, and wanted to work on myself. My purpose was to work with pupils who had problems in math and help them. At the beginning I was afraid to ask about things I did not understand, but after your encouragement, and your letting me know that not knowing is OK – I felt better. Improving the pupil’s sense of confidence is important to me. I know today how important it is for learning”. From the above said, we can see that the reasons for feeling confident or not are identified. These reasons will be presented in the following table (no. 13). Table No. 13: The reasons for feeling confident or not in working with the pupil, at Mid-Year Reasons for Not Feeling Confident Reasons for Feeling Confident

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Lack of tools. Coping with high-level material.

Coping personally with the pupil’s difficulties. Experience. Feedback and training sessions. Planning of lesson layout. Support and assurance from the tutor. Acquisition of knowledge. Knowledge of teaching methods. Making contact with the pupil. Knowing the pupil. Written feedback. Clear purposes in working with the pupil. Transferring the analysis and summary to the pupil.

At mid-year the students identify two reasons (lack of tools and dealing with high level material) for their lack of confidence, reasons related to their perception as teachers. On the other hand, they find many reasons for being confident – all of which are evidence to the contribution of the course and the process they have gone through. They include factors in their work with the pupil, developing reflective ability, and a constructivistic approach - standing for personal experience and active construction of knowledge and strategy as a result of feedback. Some reasons for their sense of confidence may also be related to their ability to cope as teachers, whereas others are related to training, support and feedback from their tutor. End of the Year At the end of the year, after completing the course, the students were asked to hand in writing a reflective summary. They had about six weeks for the task, so that they could examine things in a different perspective, outside the doing of things. They received guiding questions (appendix 6), and were asked, among others, to reply whether their concerns from the beginning of the year have disappeared, and if so – due to what reasons? Do they feel more confident today in their work with a pupil with math problems, and if so – what do they attribute it to? At the same time, they were given the option to write it in freehand, adding their own thoughts, according to the guiding questions.

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The next table represents expressions related to the sense of confidence and level of concern, as related by the students in their end-of-year reflective summary. Table No. 14: Sense of Confidence at the End of the Year Student No.

Expressions Related to Concerns and The Sense of Confidence

1 My concerns disappeared during the course. The work process, interaction with the pupil and planning of lessons helped me and made me confident that I was going to teach something very clear.

2 Today I feel more confident to make a graded program and work with the pupil with the required means, All this with less concerns than before.

3 Today I am more confident in working with a pupil on math. The pupil has, no doubt, taught me a lot/ He is an excellent example of a pupil with low mathematical thinking and his problems clarified many things for me.

4 My choice of the math teaching workshop was mainly a result of my fear of facing the subject. My fear of math made me think that I would not know how to help a pupil having math problems herself, and by what methods.

5 I learned not to be afraid of math, though I still consider myself a very small mathematician. I feel I have acquired great confidence as a teacher by your counseling sessions, which broadened my professional background and strengthened my confidence in my ability to teach.

6 My concern about teaching math disappeared. Today I know I can handle teaching math in class. It does not frighten me as it used to, and I think it is a result of my coping with the material and the way I learned to find and invent various teaching methods. I feel more confident working with a child with math problems, and I relate it to the experience I have gathered and the knowledge I acquired in the workshop.

7 Following the work in the workshop I acquired confidence and proved to myself that I can handle a subject to which I have not been exposed previously. I managed both to learn it and even succeed.

8 At the beginning of the year I was afraid of the academic overload, and not being able to bear it. As time went by, I realized I could manage all tasks. I expected to be more confident after the workshop, with more theoretic knowledge.

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I would be much more confident upon arriving in school, if I knew their teaching methods, or could propose an alternative.

9 At the beginning I had no confidence, having never taught math. My confidence grew from one lesson to another, my concerns decreased, but have not disappeared entirely. I still feel I lack knowledge, but am more confident now. I think that knowing that I could always stop and consult Liora helped, that would always receive a professional answer. I feel more confident in my work with a pupil having math problems, and I relate it to the good experience I had with that pupil.

10 I was not concerned, and I don’t feel more confident today. 11 At the beginning of the year I was not concerned about

working with the pupil. I am never concerned about the future, and so it was in the workshop. I was not especially concerned before it. But as I started to work with the pupil, facing purposes and difficulties – I started to be concerned about coping. The workshop helped me by experiencing teaching methods and means. Now I feel more confident in my abilities than before.

12 At the beginning of the year I was very nervous about the course, but my nervousness disappeared when I started to teach my pupil, discovering new teaching methods and coping with problems. Today I feel more confident in teaching math; I was exposed to various teaching methods and a variety of materials.

13 I came to the workshop from a position of fear of the subject. Math scared me already as a pupil, and as a teacher I could not escape and avoid it any more, so I chose to face it and cope. I expected to be an expert on teaching math after the workshop, thus suppressing my fears. During the year I realized it would not happen, but my fears decreased, mainly as a result of experiencing field-work with the pupil. Today I feel confident and am prepared to try and teach math, a thing I could not do in the past.

14 I am more confident today, because I learned how to teach. 15 The apprehension I felt at the beginning f the year

disappeared. My main fear was managing the lesson. Writing a plan, setting goals and planning layouts helped me organize the material, So I managed to conduct a lesson and achieve my goals. Today I feel more confident in my work with pupils with math problems. I think it is a result of the coping I did, both with the

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pupil and the material I experienced in the workshop. From the above data we can see that 13/15 students reported that their concerns were gone, and they feel more confident in their work with pupils having math problems. Two students (no. 8 and 10) reported at the end of the year of poor confidence. No. 8 claimed that she expected to have at the end of the year greater theoretical knowledge and more confidence, and no. 10 said she does not feel more confident today. These two reported at mid-year (table 11) of feeling more confident due to experience, knowing the pupil etc’, I.e., They felt a significant improvement from the beginning until mid-year, but did not feel as confident at the end of the year as they had expected to be. From the students’ reports at the end of the year, one can conclude that the change took place for several reasons:

• Planning the lesson focused their work. • Learning from the pupils. • Coping with the subject they taught. • Exposure to various teaching methods. • Experience acquired during the year. • Consulting, support and training given during the course. • Experiencing teaching aids and methods. • Coping with the pupil’s difficulties. • Knowledge how to teach. • Writing work plans, setting up purposes, making lesson layouts and

time management. Similar and additional things were said at the end-of-year personal interviews, in addition to reflective written reports handed in by the students. According to the reports, training sessions and observations – the sense of confidence at the end of the year expressed itself in several areas:

• Use of appropriate teaching methods. • Making a graded work plan. • Creating realization means. • Working with pupils having math problems. • No fear of math. • Confidence in coping with the pupil’s problems. • Knowing how to teach.

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• Theoretical knowledge in math.

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3.2 The Change in the Sense of Efficacy In this chapter I will attempt to describe, expose, record and characterize the process of change, undergone by the students in their sense of efficacy. The tools chosen to describe the change are as follows: Answers to questions relating to the subject and self reports by the “New Way” questionnaires (appendix no. 1), the “Mid-Way” questionnaire (appendix no. 5) and the reflective summary handed in at the end of the year. In addition, I used the personal interviews, training sessions and observations. Beginning of the School Year At the beginning of the year the students were asked to appreciate their efficacy as teachers, and as math teachers (question 10 in the “New Way” questionnaire). Their answers are presented in table 15. Table No. 15: Appreciation of efficacy as teacher and as math teacher Student No.

How do you appreciate your capabilities as a teacher, and as a math teacher ?

1 I think of my capabilities as good, but still am trying to improve them. I hope and believe they will assist me in teaching math.

2 It’s hard to answer this question. I appreciate myself in other areas as having good teaching capabilities, but do not know about my capabilities as a math teacher.

3 I appreciate my capabilities as fairly good, and I’m sure the workshop will help me.

4 I cannot appreciate my efficacy as a math teacher, not having experienced it ever. My general capabilities as teacher are good.

5 As a teacher my capabilities are good, but I do not know about teaching math.

6 As a teacher my efficacy is good, but not so good as a math teacher.

7 I find it difficult to appreciate my efficacy as a teacher, but I am aware of the fact that I have a rather high giving efficacy, will to help others, educate and influence – which I hope to apply.

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8 I cannot actually say, I have not yet experienced it (teaching math). I believe in my efficacy to make good contact with my pupils, create an open atmosphere in class, and teach various subjects.

9 My teaching efficacy is good. I don’t know how I will be as a math teacher. This remains to be seen. ‘Chemistry’ is imperative when meeting the child.

10 As a teacher, I generally appreciate myself as highly able. In math, I think I can handle only up to a certain level.

11 I think my teaching capabilities are good. I have problems in planning.

12 I have teaching capabilities. I will gladly acquire and develop more tools.

13 I am highly motivated to teach and help problematic pupils. My efficacy is expressed mainly in the unusual, creative area. Regarding math – I have not experienced it yet, so I have no criteria for appreciation.

14 As a teacher, I think I can contribute, at the same time also gain something. I don’t know about my efficacy to teach math.

15 I thing I have good capabilities to be a teacher, and I would like to develop them as a math teacher.

From the data in table 15 we can see that all students appreciated their efficacy as teachers as fairly high or normal, but could not appreciate it as math teachers. Two of them (no. 2 and 8) claimed not to be able to appreciate their teaching efficacy, but believed in it. Some students appreciated certain teaching related capabilities in their personality but did not indicate specific capabilities for teaching (i.e., transferring material to the pupil). The next table (no. 16) sorts the students’ answers by to their appreciation, as per criteria derived from table 15. Table no. 16: Classification of Students’ Capabilities as Teachers and Math Teachers. Appreciation of capabilities as Teacher and Math teacher

No. of Students

Typical Expressions

Appreciating efficacy as good

15 I think my teaching capabilities are good.

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I think I have good capabilities to be a teacher.

Difficulty in appreciation 2 I find it hard to appreciate my efficacy as teacher

Appreciation of capabilities as math teacher as good

0

Difficulty in appreciating efficacy as math teacher

10 I don’t know my capabilities as math teacher. I cannot appreciate my efficacy as math teacher, not having experienced it yet. I don’t know how I will teach math.

From the above said, it seems that at the beginning of the year all students appreciated their teaching capabilities as normal, based on their past experience (scarce as it was). Some attributed their efficacy to their awareness of their personal traits, such as: making contact, creativity, efficacy to give, willing to help, etc’, i.e. normal sense of efficacy in inter-personal relations. “I am aware of my efficacy to give. I want to help others, educate and influence”. “I believe in my efficacy to make good personal contact with pupils, create an open ambience in class – base my teaching on that”. They believe in their success as result of their qualities. With regard to teaching of math, it seems the students could not very well appreciate their capabilities (not one had appreciated it as good, as per table 16), probably due to the fact that very specific skills and knowledge are the matter here. At this stage, the students have not yet experienced teaching math, and maybe their answers result from their concern about mathematical knowledge and teaching. As admitted by some of them (see table 3) their sense of ability and efficacy at the beginning of the year are extremely low, as a result of their lack of knowledge and experience in math and the teaching thereof. Another question asked relates to loving to teach math. It was not asked directly with regard to ability and efficacy, but we may well assume that a person who likes a given subject will feel capable to deal with it. The following table (no. 17) presents the students’ answers to question no. 12 in the “New Way” questionnaire: “Do you like teaching math?”

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Table No. 17: Liking to Teach Math Student No.

Do you like the subject of teaching math?

1 So far I don’t. I hope it will change. 2 I don’t know enough about the subject, so I don’t know whther

I like it or not. 3 Yes. 4 I’m not familiar with the subject. 5 Not al all. 6 I have no experience, so I don’t know. 7 I don’t know. 8 Too early to say. 9 Yes. 10 I have problems to connect with the subject, but I have

motivation. 11 I have no experience in that. 12 I am interested in math, therefore I chose this course. 13 I am not familiar with the subject, so I cannot answer that. 14 No. 15 I still have not really experienced the subject. We can see that 2 students decisively reported they liked the subject, 3 others claimed not to like it, and the remaining 10 gave no unequivocal answer. To sum up, it is clear that at the beginning of the year the sense of efficacy to teach math is still somewhat poor, though it exists in general. At this stage it relies on personal factors and short experience. These data support the findings presented in the previous chapter, which pointed at the students’ low sense of confidence in teaching math to problematic pupils. The students expressed their lack of confidence both as students and teachers, the latter due to lack of knowledge, of teaching methods and of previous experience in teaching math (see table 7). Similar things were said at the beginning of the year with regard to concern about the course (table 4) which were mainly personal difficulties and inability to promote the pupil.

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We could well state that a feeling of confidence results in a feeling of efficacy, which in turn brings confidence – thus these two are linked and dependent on each other. Mid Year At mid-year the sense of efficacy was examined again, in addition to the “Half Way” questionnaire. In question no. 10 the students were asked to report of their efficacy to cope with emotional and learning difficulties of their pupil, and how they do it. The next table (no. 14) shows their exact answers. Table No. 18: The Sense of Efficacy in Dealing with the Pupil’s Emotional and Learning Difficulties. Student No.

Do you feel capable of dealing with the pupil’s emotional and learning difficulties, as they arise during the lesson? If so, how do you do it?

1 I deal with these difficulties as the lesson progresses. I try to understand her difficulties, keeping my composure and addjust the lesson to the given moment.

2 I feel I can deal with most emotional and learning difficulties. I do it by preparing the appropriate lesson. I have learned to arouse her motivation, and act progressively, so as not to frustrate her. Preparing ahead is of great help to me. There are always other alternatives and realistic expectations from the pupil.

3 Yes, definitely. I deal with every difficulty in turn. I have no formula, but what helps me a great deal is my experience at the workshop, knowing the pupil and your support. I am frustrated when I put many hours into preparing the lesson and the pupil does not appreciate it, or makes cynical remarks.

4 It depends what the difficulties are. With the subject matter it is easier, because there are methods and one can consult the tutor. As to emotional difficulties, I also consult my tutor and try to figure out how to do it. I think I am coping rather well.

5 Right now I am coping quite well with learning problems. Emotionally, I found the pupil to have difficulties. I am trying to talk to him, thinking that once I establish trust on his side, I can deal with his emotional problems.

6 Some difficulties I can handle by preparing the material.

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Emotional difficulties are more of a problem to me. 7 Definitely yes. When I discover emotional or learning problems

during the lesson, I change my plans. I talk with the pupil, if I feel I should. I encourage her, support and assist her, if necessary.

8 I can deal better with learning problems than with the emotional ones. I do it by preparing lessons, adapted foe the pupil. With emotional problems I am coping mainly by consulting and receiving training how to help him unload his burden, and together with my tutor I can determine my actions.

9 I feel that coping with the problems depends on the lesson. Sometimes it is easier for me to cope and support, whereas in other times things are more difficult. I try to listen to my pupil in every lesson, even if things are not directly related to math.

10 Sometimes it is difficult for me, mainly due to the child’s character - unpleasant, unfriendly cheeky boy. But I am consistent and insist on achieving the goals, in spite of his objection – with encouragement and leading questions.

11 Yes. I think I can handle various situations of emotional problems. I cannot put my finger exactly and say how I do it, probably by intuition and experience, short as it is.

12 I have no time to deal with the pupil’s emotional problems, though I cannot avoid dealing with them since I encounter them, at least twice weekly.

13 I feel that during the lesson I manage to cope with the pupil’s emotional problems by use of humor and jokes. Regarding learning difficulties, I make use of the tutor’s training. I feel I can handle the u[il thanks to my experience.

14 I feel I have the ability to deal with emotional problems, by using – for example – the “star” method. Her motivation rose unbelievably, and the stars enhanced her ambition to succeed.

15 Today I feel I can cope with both emotional and learning problems of the pupil. I did not always know how to handle her learning difficulties, and by what method. But with time and experience I learned to put boundaries and be strict. I also understood what methods to use to transfer the subject in its best manner, and cope with her difficulties.

The above table shows the improvement in the students’ ability to cope, at mid-year. 12 students claim to coping with emotional problems in a different manner than with learning difficulties. 3 of them found emotional

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problems more difficult to deal with. 2 students related only to emotional problems and claimed to being able to cope with them. One student (no. 12) claimed she did not have the time to deal with emotional problems, still she takes notice and finds it extremely difficult to deal with them. (Maybe she regards her role of a teacher as being only to teach him knowledge, and less to help him with his emotional problems). The next table will demonstrate various types of coping at mid-year, as derived from table 18. Table No. 19: Manners of Coping with the Pupil’s Emotional and Learning Problems Type of Problem

Emotional Problems Learning Problems

Manner of Coping

Understanding the difficulties. Support and counseling by the tutor. Change of lesson layout. Talking to the pupil. Humor and jokes. Setting boundaries.

Adapting the lesson to the needs. Preparing graded activity, alternative methods. Consulting the tutor. Changing the planned lesson. Leading questions. Choosing the appropriate teaching method.

Assisting factors Intuition Experience acquired in the workshop

Realistic expectations Experience acquired in the workshop

As already mentioned, a real change and increase in the feeling of competence and efficacy can be seen at mid-year. These findings support the conclusions of the previous paragraph – increase of the sense of confidence, as related to the increased sense of efficacy. The reasons for the improved sense of confidence were sorted and presented in Table 13, and they both enhance the sense of efficacy and derive from it. At this stage an increase in the awareness of cognitive and meta-cognitive processes exists. The students discover their abilities and manage to

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identify their ways to cope, though there is still no relating to all aspects of efficacy and the expression thereof. The sense of efficacy at mid-year (as per Table 18) is expressed by as follows:

• Dealing with emotional and learning difficulties. • Ability to increase the pupil’s motivation. • Ability to teach mathematical subjects. • Ability to prepare a lesson, appropriate for the pupil’s needs. • Ability to introduce changes during the lesson. • Ability to set boundaries.

They claim to be able to deal with emotional and learning problems thanks to experience and training sessions. A large part of what the students said was a result of many training sessions they had with me. Some of them pointed that out in table 18. (As I see it the process did take place due to the training sessions and support, plus – of course – personal experience, even if they did not say it). The insight, that the changes occur as a result of the trainer’s reflection of the process, was not clear to all of them, though some did notice it at this phase. As one of them (no. 8) wrote: “I am coping mainly due to the training and counseling help me in interpreting my pupil’s problems, and working them out together with my tutor”. I.e., experience and training make them discover their existing abilities, of which they are not aware. Their talks with me gave legitimacy to their difficulties and frustrations, at the same time there existed a process of learning and interpreting of events and the student’s place in it all. Here is one detailed example: Student no 15 continuously claimed to having difficulties with her pupil. She blamed her of not obeying instructions, of wanting to do anything but math etc’. All these caused the student to feel incapable of coping with the girl, as well as anger and sense of failure. During my session with her I led her to identify the pupil’s conduct, which was typically manipulative as a result of her own problems and her inability to cope with them. She came to the conclusion that she did not know how to set boundaries, and admitted to being “too soft”, which in turn caused the pupil to behave as she did.

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What I did was to reflect for the student her own behavior and lead her to perceive her role in the process and her responsibility in the teaching-learning process. In our following sessions we worked on ways to cope and the student, via feedback and counseling found her own solutions to set boundaries and cope with her pupil’s difficulties. In table no. 18 she described her process of developing a sense of efficacy after acquiring understanding and insight following experience and counseling. In my observations and training sessions I can assume that the sense of efficacy increases as a result of repeated success, experience and self confidence in personal performance efficacy. At this stage, there is a connection between the students’ sense of efficacy and the achievements of their pupils. Those who made progress were taught by students with a high sense of efficacy, which means that their progress does not necessarily depend on their problems or ability, but rather on the students’ sense of efficacy. In some of them it was from the beginning and increased with time, whereas others developed it only later and discovered it by feedback and sounseling. The change took place at each student’s own pace These mid-year findings support other mid-year findings regarding the sense of confidence, reported in the previous chapter. Here too we can notice the tendency in the sense of efficacy. The sense of confidence expressed itself in inter-personal relations and the ability to promote the pupil by teaching math. The sense of efficacy in mid-year, unlike the same at the beginning of the year expressed itself in: Confidence regarding the ability to promote the pupil, in spite of his/her problems; Teaching mathematical contents and; Coping with emotional and learning difficulties, though the ability to cope with learning problems was better than that in emotional problems. End of the Year At the end of the year, in the reflective summary, the students were asked to write about things related to the sense of efficacy: How they assess today their ability as math teachers, and corrective teaching? How they developed personally and professionally? Did they achieve the goals they wanted to? The next table (no. 20) presents the students expressions in that reflective summary.

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Table No. 20: Sense of Efficacy at the End of the Year Student No.

Expressions Related to the Sense of Efficacy

1 Today I am capable of identifying the pupil’s needs and construct a work plan that would fit them. The analysis at the beginning of the year, continuous training, and experience have helped me in the process.

2 Following the course I can today prepare a personal program for the pupil. I know how to construct the subject, prepare lessons in various levels to fit the pupil so as give him an experience of success.

3 During the year I have developed professionally thanks to experience. Today I can better improvise and find solutions for unplanned situations. What I mean is that in spite of planning and layouts, the pupil’s state not always enabled him to perform the planned tasks, and I had to change them. I know how to explain things in different ways, I can understand the children’s problems in math and am able to match the material and aids to the learning persons.

4 Thanks to the experience and counseling I discovered I am able to cope with the pupil’s problems and fins appropriate working methods. I learned how to identify learning and emotional difficulties, and in spite of my own problems, I think I can function as a corrective teacher of math.

5 I learned that I have the ability to understand the pupil’s thinking and give her efficient learning strategies. I coped with her emotional and learning difficulties.

6 The course gave me an experience of success with regard to coping with mathematical subjects and my ability to plan and organize a lesson according to the pupil’s needs. I learned how to cope with situations in which the pupil has difficulties dealing with unfamiliar subjects, how to teach lessons that will be a challenge and give him an experience of success. I learned not to give in to his manipulations by setting boundaries. Today I am more attentive to his needs, and I believe I can find a way of corrective math teaching, for any pupil I have to teach.

7 I learned to know myself better and understand the pupil’s way of thinking. I have proved to myself I can handle a subject I have not been exposed to before, and of which I was even afraid. The course was just the place for me to prove my

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skills as a teacher in general, and in this subject especially. It was expressed by constructing lesson layouts, preparing aids and adapting them to my pupil.

8 Experience has helped me crystallize my identity as a professional teacher. I coped with the tasks though I was afraid of the overload, I managed to promote my pupil and learned how to organize the lesson’s timetable, tasks and work-plan.

9 I developed professionally. I am more attentive to small details, which did not look important. I learned to be more flexible and take into consideration the pupil’s needs. I learned to conduct a lesson with definite boundaries, cope with emotional problems and understand their effect on learning. The course was an experience of success for me. I have more knowledge in math and have the skill for corrective math teaching.

10 I did not develop professionally and the course did not contribute anything to me. Grading the work-plan helped me focus on the goals I have set for myself.

11 Experiencing and coping with a difficult pupil have contributes to my personal development. Today I believe in my ability to work with such pupils on math, though I still have a lot more to learn about contents and methodic. The course undoubtedly was a significant contribution to me and I feel more confident of my teaching abilities than before.

12 I learned to be more assertive with my pupil, and I am more confident now in teaching math. I know how to change things when needed, and I am more flexible. I discovered teaching methods and ability to cope with new problems as they appeared during class.

13 Today I feel I am ready to try and teach math. When I was working with my pupil’ I sometimes felt he did not take me seriously enough, but I learned to separate emotions from my purpose – to teach him.

14 I learned that in spite of my frustrations I can cope with both emotional and learning problems and promote my pupil. I can tell when she is trying to manipulate me in order to attract attention and I am assertive. I learned how to handle her lack of motivation by varying and changing the manner of teaching to fit the work-plan. I learned not to give up – not to her and not to myself – when facing a problem. Following the course I regard my ability as a math teacher as much better. I am more confident because I learned how to teach.

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15 I feel more confident to set goals, be assertive and express authority. I know how to identify manipulations and deal with them. I can prepare a lesson layout to fit the pupil’s needs, how to cope with new educational contents and how to teach them in a variety of manners. I can now separate her conduct resulting from her distress from the purpose I set for the lesson. I.e., I learned how to “put aside” emotions and see things objectively. Today I regard my ability as a corrective math teacher as better, still – I have a lot top improve.

At the end of school year there is an immense development in the students’ sense of efficacy. All students reported an improvement in their sense of efficacy, excluding one student (no. 10) who claimed not to have developed professionally following the course. That specific student exhibited great resistance during the course, mainly because she has been working with a fourth grade pupil, though she intends to work in junior-high school. She also complained to the management for not letting her work with an older pupil. The rationale for that was that in order to understand the problems of older pupils, one should first experience work with younger pupils having difficulties in math, and in spite of her dissatisfaction, I think she did improve her sense of efficacy, even if less than the other ones. At this stage there shows a significant development of the personal insights regarding meta-cognitive processes in the sense of efficacy. The students regard various aspects of efficacy, identify them and label them. If in mid-year they reported of improved sense of efficacy in a small number of subjects, now they are able to identify various components in all their work and discover new things on their own. They are able to define and analyze situation, as well as make use of professional terms to phrase their ideas. The number of components in the sense of personal and professional efficacy has increased, together with their ability to detect them. They are aware of their various abilities, detect a process, which has developed and tie them to their sense of confidence. On the other hand, they know how much they still do not know, thus they want to improve (daring now to declare that they do not know it all). According to reports, training sessions and observations, the sense of efficacy at the end of the year expressed itself in various areas, as follows:

• Ability to detect pedagogic and emotional needs of the pupil.

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• Ability to plan and organize a personalized curriculum. • Ability to create teaching aids, on their own. • Ability to improvise during unexpected situations. • Ability to teach in a variety of manners. • Ability of teaching efficient learning strategies. • Ability to set boundaries. • Ability to show professional deliberation. • Ability to promote the pupil. • Ability to plan a timetable. • Ability to conduct a lesson. • Ability to change and be flexible, according to needs. • Ability to separate personal frustration, disappointment and anger

from the goal of teaching math (i.e. teach even if you don’t like the pupil, or he/she makes you angry).

• Ability to dare and teach unfamiliar subjects. • Ability to respond to emotional problems.

The number of areas in detecting the sense of efficacy at the end of the year is much larger than at mid year (6 only). It supports what was said in the previous chapter with regard to the sense of confidence expressed by the students of their abilities. The higher the sense of efficacy the better the confidence. Such sense of efficacy consists of various areas of functioning, differing from one student to another, both at the beginning and during their work with the pupil (see table 20). These things cannot be quantified, therefore personal reports are the prime indicators for them. In spite of the difference in expressions, generally, the students’ sense of efficacy expressed itself in a variety of manners, as presented above, in addition to controlling inter personal relations with the pupils (such as empathy, understanding and warmth, at the same time setting boundaries and assertiveness). From all that was said at the end of the year, we can reach a better inclusion of the student’s (teacher) ability to control her inner world, and confidence in her ability to organize her cognitive, emotional and behavioral abilities, required to successfully perform the task – the teaching-learning process.

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3.3. Controlling Teaching Methods of Mathematics In this chapter I will attempt to expose, characterize, describe and record the process of change the students underwent in methods of the math teaching. The tools chosen to describe the change are as follows: Answers to relevant questions, and self-reports by means of the “New Way” and Half Way Through” questionnaires (appendices no 1 and 5) and the reflective summary handed in at the end of the year. In addition we used the personal interviews, training sessions and observations. Beginning of the Year: At the beginning of the year the students were asked about their knowledge of math teaching. In addition to personal interviews, they answered the “New Way” questionnaire (question 6, appendix 1). Table No. 21 represents their answers to that specific question. Table No. 21: Knowledge of Math Teaching Student No.

Do you know how to teach math?

1 I’m not familiar with the various methods of teaching math, but I believe one can use teaching aids from other subjects for math.

2 No. This is why I chose this workshop. 3 I’m not sure. 4 No. 5 No. 6 No. 7 Not very well, and certainly not professionally and

systematically. 8 Not yet. 9 I had a brief training in the past, but I don’t think it’s enough. 10 I hope so. 11 No. 12 I believe and hope I am using the right methods. 13 Not quite. 14 I haven’t tried it yet. 15 No.

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As can be seen, at the beginning of the year 7 students clearly said they did not know how to teach math (No. 8 phrased it as “not yet”, meaning she does not know but refrains from stating it in so many words). 2 other replied “not quite” – an answer implying their lack of knowledge. All other students did not state clearly their knowledge or lack of it, refraining from a clear answer. Their answers implied that they did not have the knowledge. No. 1 admitted to not knowing teaching methods, but believing she could manage with aids from other disciplines to teach math. No. 9 claimed to have gotten short training, which she did not think sufficient, and no. 14 said she just had not tried it yet. We can assume that those who did not admit to not knowing, did so because they thought it would be perceived as weakness. To sum up, we can assume (based on reports at the beginning of the year) that the students did not have the knowledge of teaching math, or at least felt they did not know it, though not all of them declared it specifically. The above- mentioned data support previous reports regarding the sense of confidence and efficacy. In table 6 (regarding the sense of confidence) only 4 students claimed to be confident to work with their pupils on math, whereas all others (11) expressed concern and lack of confidence. The reasons for such lack of confidence (as per table 7) at the beginning of the year, were the result of poor knowledge, poor control of teaching methods and lack of experience. They also match the reports of not knowing how to teach at the beginning of the year. Regarding the sense of efficacy at the beginning of the year, none of the students regarded herself as being able to teach math. On the other hand, all 15 students thought of themselves as able teachers in general, claiming that their problem to assess their ability as math teachers resulted from, lack of experience and knowledge. The reports at the beginning of the year support each other: The students feel they do not know how to teach math, they report about it and of the fact that as a result they feel incapable and unconfident. Observations I did at the beginning of the year proved that most of the students taught math by intuition, in the same methods they were taught. They concentrated more in transferring mathematical contents, in surviving and less in adapting the subjects to the pupil’s needs. Their lesson layouts and summaries showed the lessons to be non-professional as well as difficulties in planning and teaching in a clear varied manner. There was also a gap between the plan and the lesson itself. They did not

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know their pupils well then (apart from preliminary acquaintance and didactic analysis), and they have not yet discovered their own personal abilities as math teachers. Mid-Year: At the beginning of the second semester, following several lessons (8-10) the students were asked to say whether they felt they knew how to teach math. The issue was examined in question 4 of the “Half Way Through” questionnaire (appendix 5). Table No. 22 shows their answers to the question, which was intended to notice the changes in teaching methods, if any, and understand the reasons. Table No. 22: The Level of Knowledge in Teaching Math, and its Reasons Student No.

Do you feel now that you know how to teach math? If so, detail the reasons for that?

1 Not really. 2 I feel more confident in teaching the subject. I also feel I am

learning things I did not know before, and I already know how to teach things I did not know at the beginning of the year.

3 Yes. Of course there is still much to be learned, but the experience at the workshop contributes to my knowledge.

4 Yes. The analysis helped me in understanding the phases the pupil requires to learn and understand math, as well as the work itself, the comprehension and the lessons I had to learn on my own.

5 I feel I know more, but still not really. 6 I feel I can teach better than at the beginning of the year, due to

the acquiring knowledge and acquaintance with math curriculi. 7 In a way, yes. Since I was not trained to teach math, not

professionally anyway, I cannot say I know how to teach math properly, but I feel I am developing my own methods of teaching.

8 I feel now more confident in teaching certain subjects in math. This, due to the experience I have gained, the training and being exposed to various teaching methods.

9 I feel now that I can teach better than at the beginning of the year, but still not perfectly. I still miss the knowledge for certain subjects.

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10 Yes, on a lower level, thanks to the variety of educational aids, training and a constant feedback after each lesson.

11 Not especially, unless I am teaching by a definite clear methods, as was done at school. This can be achieved only with experience.

12 I can teach, though one can always learn more. As a result of the training and exposure to educational subjects.

13 I feel I am beginning to know how to teach math, thanks to my experience with the pupil and the tasks at the workshop.

14 I realize that math is hard to teach, but if you go step-by-steo, the problems dissolve gradually.

15 I feel that the experience in the workshop helps me be more professional in teaching math. My successful experience with the pupil make me realize I am indeed doing it properly.

The data in the table show the improvement in the students’ feeling regarding their knowledge in teaching. 12 of them claimed to feel they are better equipped now to teach math, whereas 2 (no. 11 and 14) still have some reservations and one (no. 1) phrased it as “not really”. Student no 11 said she could teach only by a clear and definite method, i.e. she can teach certain things on certain conditions. No. 14 admitted to having difficulties in teaching, unless she does it step-by-step and gradually. She did not relate to herself, but spoke generally, hinting that she is still apprehensive of expressing her insecurity. The change at mid-year is rather significant, compared to the data in Table 21 (beginning of year) where most of the student admitted to not knowing how to teach math. As per Table 22, the students’ knowledge of math teaching in mid-year expresses itself in several areas:

• Teaching specific subjects. • Independent development of teaching methods. • Acquaintance of math curriculum.

The reasons for the improvement of knowledge in mid-year, as per Table 22 are as follows:

• Experiencing in the workshop. • Doing the analysis in math. • Knowledge of math curriculum • Acquisition of knowledge • The training given in the course.

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• Exposure to various teaching methods. In addition, the very fact that the pupil manages to learn and succeed, serves as positive feedback for the student on her teaching (see student no. 15). Another question the students were asked at mid-year – related to teaching methods – was whether they felt a difference in their teaching methods from the beginning of the year, and if so – how? This is more focused than the previous one, whereas it concerns teaching methods (not just content) for the specific pupil each student has been working with. Table 23 represents the students’ answers to question no. 11 in the “Half Way” questionnaire. Table No. 23: Perceived Change in the Teaching method, and How? Student No.

Do you feel any change in teaching methods, in your work with the pupil, since the beginning of the year? If so, how?

1 Not quite, I don’t feel any significant change. 2 Yes. I do feel the change. Teaching has become less intuitive

and more professional. I know how to transfer certain subjects. I am able to take material from books and adapt it for my pupil.

3 Yes. Lessons are more adjusted to the pupil’s nature and ability than they were at the beginning of the year.

4 Yes. Lessons are better constructed and I am looking for material in books and other people’s advice.

5 I feel more confident in my lessons. 6 I am more confident in my mathematical knowledge, thus more

confident in teaching. I also feel more authoritative and able to set boundaries.

7 Yes. Work is done in a more professional manner, writing down my purposes and application thereof, adjusting teaching aids to the pupil’s difficulties and relating to her needs.

8 Yes. I was exposed to a variety of methods and materials. I have more tools and I know how to construct a lesson adjusted to the pupil’s problems. My methods are less intuitive and more professional.

9 I feel more confidence in my teaching methods, than at the beginning of the year.

10 Yes. Lessons are more varied. 11 It seems my relations with the pupil are closer. I don’t see a

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great change from the beginning of the year. 12 I have changed slightly my methodics. I am more assertive in

my teaching. I give less exercise-sheets. 13 I don’t feel any change in teaching methods. 14 Yes. I am more aware of the pupil’s needs and make my layouts

according to her ability. I play and talk to her. 15 I do feel a change in my teaching method. Today I am using

more arithmetic games, and varied realization aids. A significant change in teaching methods can be noticed in Table 23. Apart from 2 students (1 and 13), who stated no change in their teaching methods, and 2 others (5 and 9) who pointed at a change in their sense of confidence, but did not relate to change in methods - all remaining (11) students stated a change in their teaching methods, expressed as following:

• Teaching is more professional and less intuitive. • Knowledge in transferring specific subjects. • Taking material from books and adjusting it to the pupil. • Showing authority, assertiveness and ability to set boundaries. • Writing down objectives and achieving them. • Adjusting teaching aids to the pupil’s needs. • Diversification during lessons. • Making use of games and realization aids.

As mentioned previously, during the course the students were required to plan and prepare lesson layouts and summaries (see ‘tools’ chapter and appendix 3). From my observations, personal sessions and reading of the written layouts and summaries I could well see the improvement of their knowledge and teaching methods. In addition, the improvement showed also in their ability to plan the lessons. Reading the plans at the beginning of the year I noticed the lessons were not properly planned, time division was un-realistic and there was no understanding of the structure of the subject and how it should be taught. The students faced difficulties mainly in phrasing the components of the plan: Designated targets and vs. operative targets, considerations in choosing activities and aids. In addition to my examination of the papers, notes and feedback, a training session was held with the students. They were asked about what they had written, and I tried to help them re-phrase their thinking and considerations. I.e., It is quite possible that the improvement in teaching

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methods and ability to plan a lesson took place, among others, because of the intensive training adjusted to each student in person. This change was examined at mid-year and the students’ answers regarding their feelings about it and the reasons for it are shown in the following Table no. 24. Table No. 24: Improvement or Change in the Ability to Plan the Lessons, and how it is Expressed Student No.

Do you feel any improvement or change in your ability to plan the lessons, since you started to give them? If so, how?

1 I can feel some improvement, but not a significant one. 2 I feel an immense improvement in preparing activities adjusted

to the pupil’s difficulties. Lessons are less “loaded” than they were at the beginning of the year, and they are more of an experience. Activities are varied and I am using more means of realization and mediation.

3 The lessons are more adjusted to the pupil. 4 Yes. Mainly in putting in writing of the targets and time

planning, and the means I would require – all of which according to the pupil’s needs.

5 Today I find it easier to define my targets and put lesson layouts in writing, as we are expected.

6 Yes. I have better knowledge of the pupil, his work-pace and level. It helps me plan the lesson.

7 Yes, mainly by relating to what is being done actually. Since there are things I cannot apply due to inappropriate time or the pupil’s difficulties, The next lesson will be more planned.

8 I am still frustrated, because I do not always manage to do everything I planned, but I am aware of the gaps the pupil has in various subjects. I learned how to plan a lesson with realization means, and grade the tasks.

9 I can feel the improvement in my planning ability, in seeing things and writing down the targets. I manage to separate between targets and means – something I had difficulties doing at the beginning of the year.

10 Yes. Preparations have become more automatic, demands clearer and the writing makes sense.

11 Not yet. Now, after knowing the pupil things are easier, and I feel more confident, but the lessons are still not planned as I would like them to be.

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12 I can feel the improvement in my ability to plan the lessons, because at this stage I know the pupil and his skills.

13 I feel the improvement in planning the lessons, mainly in the short time it takes to write such plans.

14 There is a change for the better, in my ability to understand the pupil and arrange and organize the lesson accordingly.

15 My ability to plan more structured lessons increases with experience. I feel I know how to plan the time more efficiently that before, which means to use, etc’.

The data in the table clearly show the improvement in the students; ability to plan the lessons, as compared to the beginning of the year. Again, two students (no. 1 and 11) reported either a slight, insignificant, improvement, or improvement, which does not effect the planning of lessons to her satisfaction. But all the other students (13/15) reported a change and/or improvement in their ability to plan the lessons. Not all of then actually detailed the nature of change or improvement (maybe they have not yet identified it). Some of them noted that the change may be linked to their better knowledge of their pupil and his/her needs. Others managed to define the changes and phrase them in propfessional terms. The change and improvement are expressed in the following:

• Activities adjusted to the level of the pupil. • Lessons are less ‘loaded”. • Activity is more diversified. • Lessons are a more enjoyable experience. • Use of realization and mediation means. • Definition of targets and putting them in writing. • Time planning. • Grading of tasks. • Ability to separate targets from means. • More automatic preparation and writing. • Writing layouts in shorter time. • Lessons more orderly and organized. • Preparation of structured lessons.

Mid-year indeed shows a turn in the students’ control of math teaching methods. Reports in Tables 22, 23, and 24 demonstrate a connection between knowledge of math teaching, change of teaching methods and ability to plan the lessons. All these effect and are effected by each other.

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End of The Year: In their reflective summaries at the end of the year, the students referred to various aspects related to teaching methods, as can be seen in the following Table No. 25. Table No. 25: Changes in Teaching Methods at the End of the Year Student No.

Expressions Relating to the Changes in Teaching Methods, at the End of the Year

1 Today I know exactly what material to use. I learned to work by a sequence of layouts, i.e. subject planning. At first the writing took for ages, but now it is much easier. The intelligibility of the layouts contributes to my confidence. I learned how to adjust various aids to the pupil’s needs, how to diversify and adjust the lesson to her mood, too. I learned to break each task down to several small tasks, elaborated my phrasing, and today I can understand the structure of math, which in turn helps me in my teaching methods.

2 At the beginning of the year I thought I had no ideas, did not know how to teach and was not creative enough. The pupil I worked with required creative elements (which I understood after learning about multi-intelligence). I started to prepare games and discovered my creativity. I really surprised myself. In fact, the pupil made me learn how to teach in a creative manner.

3 The lesson layouts prepared ahead helped in focusing on the subject. Thinking how to phrase the targets and how to construct a lesson, graded by a number of tasks, helped me to develop. I learned how to translate my thoughts to operative targets, and developed techniques of teaching specific subjects.

4 I feel now that I am more skilled in math teaching. I know about methods and means, and manage to diversify. Lessons are better planned, there is an improvement in the gap between plan and execution. I learned how to grade the plan and adjust the tasks to the pupil’s ability.

5 I still find it difficult to grade a work-plan, though there is some improvement. The layouts helped me organize each lesson separately. When I arrive with a layout, I know exactly what I have to do, and can deal with any changes that might occur during the lesson.

6 I learned how to use realization means to teach memorizing

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strategies. I was exposed to various methods. I experience success in everything related to dealing with arithmetic, and with my ability to plan and organize the lesson. Writing layouts helped me plan the time and subjects I wanted to teach. A planned lesson is easier to teach.

7 My recent lessons are different in structure. The improvement is mainly in teaching methods. At the beginning of the year I used photocopied paged from books, but with time I learned how to prepare my own exercise pages, and games, discovering I was quite creative. The layouts helped me know before each lesson what I was going to teach. In spite of unexpected changes and alterations – planning ahead makes me confident.

8 Writing layouts helped me in organizing the lesson and being prepared. The form we were given (from a book) helped me in organizing my thoughts and in writing. I think I learned how to grade a work-plan on any subject I taught.

9 During the year I learned how to examine and make a work-plan for arithmetic (a new subject for me). I also learned how to make a diversified lesson, how to match one target with a number of activities adjusted to the pupil’s needs. For the first time since my studies, I learned what corrective teaching is. I was exposed to various teaching methods, to aids I had not known, and dilemmas arising during a lesson. I learned how to make exercise-sheets to match the pupil’s needs. I feel, today, I am ready to teach math and corrective teaching of math. I have additional knowledge.

10 Writing the graded plan helped me focus on the targets I faced, without digressions.

11 At the beginning of the year I found it difficult to phrase the targets, and could not prepare layouts. Everything looked cumbersome and impossible. With time I overcame my problems and managed to plan and write correct layouts, properly phrased. Doing this I saw how they helped me in focusing on contents and time planning. Layouts are a very efficient tool.

12 I learned new teaching methods and a variety of learning subjects.

13 I learned how to prepare teaching aids, adjusted to my pupil’s needs. I also learned how to apply teaching methods, taking into consideration her problems. I learned how to prepare realization means and the written layouts helped me to work systematically.

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14 I learned how to make an experience of success, how to focus on a subject and exercise it in different variations. I learned how to plan lessons that would not be too "loaded". Writing layouts helped me grade the plan and focus my thoughts, so as to know exactly what I want to teach and what I want to achieve. I knew how to plan the time by the targets and understand which way is the best to achieve results.

15 I learned how to grade a work-plan, set learning targets and act accordingly. Writing plans and layouts helped me in organizing the contents and managing the lessons. Now I can anticipate problems ahead and prepare the lesson according to them, I know which exercise sheets would be impossible for the pupil to so, or would frustrate him.

At the end of the school year all15 students reported a significant improvement in their teaching methods. The choice what to report in their reflective summary represents the personal meaning each students gives to her own development. Some reports were similar to those made at mid-year, though elaborated, discovering new things about themselves and reaching new, or additional, insights with regard to the process they went through. Some reports showed far reaching changes. Some students, for example (no. 1 and 13) who reported of no significant changes, or no change at all, at mid-year (tables 22, 23, 24) reported now (table 25) of significant changes, of learning how to apply teaching methods, prepare realization aids and work according to lesson layouts. As already mentioned, all students made great progress in teaching methods, but each expressed it differently, uniquely. I observed all these things during lessons and training sessions, but the fact that the students perceived it is the most significant of all (as I see it). The data in table 25, the personal interviews and my observations, all support the findings at the end of the year, with regard to the sense of confidence and efficacy, as reported by the students, and expressed in many areas connected to math teaching methods. In summary, I can say that based on written reports, training sessions, personal interviews and observations, the changes in teaching methods showed in several areas:

• Adapting aids to the pupil’s needs. • Diversified teaching methods.

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• Separating educational task to sub-tasks. • Understanding the link between understanding the subject and

teaching methods. • Creativity and creative teaching. • Efficient use of educational targets. • Interpretation of thoughts and knowledge into phrased behavioral

targets. • Developing techniques of teaching mathematical subjects. • Improving the skills of teaching math. • Getting acquainted with teaching methods and combining them in

work. • Reducing the gap between planning and executing. • Grading curriculum (teaching) in math. • Adjusting educational tasks to the pupil’s needs. • Organizing the lesson. • Using means of realization. • Transferring efficient learning strategies. • Time planning. • Writing professional lesson layouts. • Preparing games, independently. • Adapting activities to educational purpose. • Focusing on set targets. • Application of teaching methods. • Creating an experience of success.

The last subject in the study is the change in the level of reflection, the findings of which will be presented in the next chapter.

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3.4 The Change in the Degree of Reflection In this chapter I will attempt to describe, expose, record and characterize the changes in the degree of the students’ reflection, that took place during the course. The tools chosen to describe these changes were as follows: Questions no. 8 and 9 in the lesson summary following each lesson; the “half way” questionnaire; the training sessions during the year; the personal interviews at mid and end of the year, and the reflective summaries submitted by the students at the end of the year. In addition to the data in the tables, we have the reflective summaries and personal (open) interviews held with 4 of the students (no. 1, 5, 11, 13). Sentences appearing in the tables were omitted from the personal summaries, to avoid duplication. Beginning of the Year At the beginning of the year, following the didactic analysis and creation of a work plan, the students began to give lessons according their plan. Prior to each lesson, they were required to prepare a written layout for the lesson, as well as a summary after the lesson (appendix 3). The summary was intended to help them understand the process of the lesson, to learn from it and develop reflective thinking. The following table (no. 26) shows the students’ answers to question no. 8: “What have you learned about yourself and about your pupil during the lesson?”, and to question no. 9: “What did you ‘take along’ with you from the lesson, and what are you planning to do next?” These two questions were chosen because they require some reflective thinking, as well as learning and drawing conclusions. The following answers were given after the first two lessons. Table No. 26: What have the students learned about their pupils and about themselves from the first two lessons. Student No.

What have you learned about yourself and about the pupil? What did you “take along” with you, and what are your future plans?

1 I have learned that my pupil is extremely “anti”. She won’t study and won’t face the difficulties. I find it difficult to cope with. She requires attention, personal treatment and incentives. What I “took” is the idea of working through play, an interesting method of work, such as taking breaks between

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activities and reduce tasks. 2 I learned it is important to give many explanations, take breaks

between tasks, and try again and again to incorporate games into the lesson.

3 I learned that I have enough patience to repeatedly explain any subject in different ways. I’ve learned I am coping with the problematic pupil in a mature way, and I know now that it is better to incorporate illustrative means and give the pupil work sheets without any choice questions, to prevent him from guessing.

4 I learned that I could support and encourage the pupil; also, that I am not losing my head, in spite of my initial apprehensions. Regarding my pupil, I understood her need for constant encouragement, so she would believe in herself, despite her problems, and keep going. Regarding the subject taught – I would like to improve my control of addition and subtraction up to 1000.

5 I learned that my pupil did have the knowledge, that he was fast in understanding, and wanted to impress me. I also learned the importance of repetition, even if it seems the pupil knows the material.

6 I learned that the pupil needed many experiences of success. I know I have to cope with his poor concentration and motivation, as well as his verbal problems.

7 I learned that I know how to match the didactic means with the pupil’s level and the purpose of the lesson. In the next sessions I intend to teach her to multiply and divide within the range if 100.

8 I found out that my pupil has difficulties in maintaining his concentration. He gets up frequently, talks about subjects, irrelevant to the lesson, but still has the will to learn and succeed. He still has no faith in me, and we have no personal relations. He is not very disciplined, un-attentive, and should be given short tasks. I “take along” with me his will to learn, and his need for immediate positive feedback.

9 I found out that my pupil has fair control of the subject, but being disorderly and disorganized, she makes mistakes. She is working fast, not paying attention to details. I learned that her motivation increases my will to promote her. I am affected by her emotional state. I will try and make the lessons more interesting, using shorter phases and games. I also think that she should both win and lose the games, so she could learn how to handle both winning and losing.

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10 I found a weak and unmotivated pupil, who should receive positive feedback in order to strengthen his self image.

11 I found a very shy, insecure pupil, but I know that my efforts and my will can encourage him and promote him.

12 I learned that games are a great way to learn – they help the pupil to enjoy his studies, increasing his motivation. As for me – I learned I had to have a more organized and orderly layout to make the lesson more efficient. I will continue to teach by means of work-sheets and games, adding more work-sheets that will be clear, not too long and cumbersome – so as to match the pupil’s range of attention and concentration.

13 I found out that my pupil had great difficulties, which frustrate him. I am planning to teach him some difficult subjects, but will do so by means of games and illustrations – so as not to discourage him.

14 I saw that my pupil has to be encouraged, to increase her confidence in math. I also learned that my own frustration threshold is rather high, even when I cannot make her understand certain subjects. I intend to make the lessons an experience of success for her.

15 I learned that, in spite of my wish to promote the pupil quickly, I had to slow down because of her problems. I intend to equip her with the appropriate tools to cope independently with the tasks, thus increasing her confidence.

From the data in table 26, as well as the observations and training sessions, it seems that all students learned and concluded something - already after two lessons. Their reflection rate is still rather low, but some degree of reflective thinking can be noticed. Some answered the questions generally, not relating to all parts of the question, i.e. talking about what they “took along” from the lesson they meant, in fact, what they learned about themselves or the pupil. Others did just the opposite – reaching conclusions of “taking and planning” by learning about the pupil or themselves. Student no. 12, for example, noted that – regarding herself - she had learned that she had to have a proper organized layout to make the lesson efficient, i.e. understanding the relation between a planned organized lesson and success. She noted it as her own learning. Others answered each part separately. With regard to learning about themselves, some of the students reported realizing their capability to cope with the pupils’ problems (see Table 26:

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no. 3, 4, 14). These students related to their own patience and ability to deal with their own frustration, and their sense of capability. Student no. 1 claimed to have found out about her own difficulty in coping with her pupil’s problems. No. 9 reported that her degree of motivation as teacher is effected by the pupil’s conduct during lesson. Another one (no. 6) said she had to learn how to cope with the pupil’s lack of motivation and attention, but did not specifically state what it meant with regard to her. Student no. 7 noted she had learned she could match the subjects to her pupil’s level, i.e. she had the capability to cope with teaching methods. Seven students did not specifically relate to their learning about themselves (no. 2, 5, 8, 10, 11, 13, 15); one (no. 2) gave a general report, not relating either to the pupil, or herself. At this stage, probably, they did not use reflective thinking, nor did they identify or admit their own part in the process. With regard to learning something about the pupil, some students relate to his/her conduct, or other personal features (no. 1, 8, 10, 11). Some concentrate on the pupil’s knowledge (no. 5, 9, 10), whereas others - already at the beginning of the year - tie the pupil’s conduct and knowledge to what they are doing and coping with, now and in the future, i.e. they are already activating reflective thinking and learning (Table 26, no. 2, 3, 4, 6, 7, 12, 14, 15) All the students answered the “Learning and future planning” question, and all their answers dealt with the applicable part of their work, such as: Combining games and illustration means, breaks, smaller tasks, support and positive feedback. Three students related in this section to the teaching of didactic content (no. 4, 6, 7), and one talked about the pupil’s wish to study and achieve (no, 8). So, in the table we can see that 7 students gave arguments related to the pupil’s performance to explain their learning about themselves and the pupil (no. 3, 4, 9, 10, 12, 13, 15), which shows they have reached insight and reflective thinking. Only one student of that group (no. 3) related to the educational factor: “What I got from the lesson is that the pupil should receive work sheets, without any optional answers, since he/she tends to guess”. I.e., this student is already capable of professional discretion and matching of the tasks with the pupil’s needs. Other students, included arguments, related to the emotional factor:

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- “ The pupil should be encouraged to believe in herself”. - “Positive feedback should be given to increase his self esteem”. - “ I intend to create an experience of success for the pupil”. - “This way will increase her confidence”. - “I intend to teach some difficult subjects, but I will do so with games and illustrations, so as not to frustrate him”. One interesting answer, by student no. 9, shows she had immediately identified the pupil’s emotional problems, made an applicable conclusion and showed high degree of reflection, by deciding to let her pupil win some games, and lose some – so she could learn to deal both with success and failure. To sum up, we could say that already at the beginning of the year some reflective ability exists and is expressed, by deliberating following educational activity. This reflective ability includes: * Understanding the pupil’s educational and emotional needs. * Identifying personal capabilities, as a teacher and human being, both in the educational and emotional areas. * Matching teaching methods with the pupil’s needs. Based on the reports and the observations at the beginning of the year, we can say that some of the students tend to “blame” the pupil, and regard his/her external performance as the main factor in the process of the lesson. There is some ignorance regarding the learners and their features, and difficulty in handling vague situations, in understanding various phenomena and coping with dilemmas during the lesson. I.e., there is some difficulty in identifying problematic situations, in understanding complex situations, and a certain amount of confusion due to this lack of control. These findings support, and are supported by, previous findings related to the sense of capability, both as a person and a teacher, and regarding control of teaching methods. All these areas are linked to each other, effecting and being effected by each other.

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Mid Year At mid year, after 8 – 10 lessons, training sessions and a certain amount of experience, the students’ answers for questions no. 8 and 9 in the summary sheet (appendix 3) were gathered again and put in table no 27. Table No. 27: What have the students learned about themselves and their pupils, from their lesson layouts Student No.

What have you learned about yourself and about the pupil? What did you “take” with you, and what are your future plans?

1 I learned I could contain the pupil’s frustration and still promote her. I learned that she needed support and reassurance, as well as that I should not attempt to change her, but rather accept her and make the most of it. I intend to keep working on multiplication table and verbal problems. I think that if I let her build the table by herself, she would understand it better than receiving it as a set of numbers.

2 I learned that her concentration and attention problems require reduction of activities. Too crowded lessons caused her stress and impaired her performance. I see now that future lessons should be less “loaded”, activities should match her skills, to enhance her motivation.

3 I learned that the pupil’s progress was slower than I expected. His objection and cynicism were a result of his problems. Thus, I should slow down and use illustration means for the verbal part.

4 I learned that I had the ability to strengthen the pupil, and relate to her emotional problems. I learned how to adjust myself to her, rather than the other way round. I know now that once you have varied tasks and illustration means make understanding easier and reduces stress.

5 I learned that I still lack control of teaching certain subjects, such as multiplication table. I intend to keep working on multiplication and division, as well as verbal problems.

6 I learned I had to draw the line and be assertive and consistent with the pupil, since he keeps trying to cross them. I intend to continue teaching him some efficient strategies of problem solving.

7 I learned that my pupil should be given the opportunity to succeed, and be given the chance to progress. I know now, that I have the ability to understand her and match my teaching method to her problems. She should be given the tools, i.e.

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efficient strategies, to overcome her problems, not just to assist her immediately.

8 I learned that I had difficulties in drawing the line and insisting on it, rather than overlooking diverting factors and giving in. Sometimes I get carried away and then I cannot complete my planned lesson. I intend to continue with the verbal problems and try to illustrate the meaning of multiplication and division.

9 I learned to keep my disappointment to myself, and keep encouraging her as if nothing happened. I now that I can handle these problems and make her work hard, in spite of them. I adopted the idea of letting her participate in preparing the games, to enhance her motivation.

10 I did not learn about myself anything I had not known before. I have to keep working with him on one-phase verbal problems, then on the two-phased ones. Also, I acquired the idea of practice by games.

11 I learned that any specific, defined, arithmetic rule should be clear to me first, before I teach it to the pupil. I think that arithmetic rules, used as “crutches” are a good means of teaching. The lessons gave me strength and motivation to continue my work, because I feel that an actual learning process has developed, which I can assess and measure.

12 I learned the importance of a break in teaching new subjects, for the sake of repeated practice of previous subjects. I know I can be more assertive, and so I can manage more in each lesson.

13 I learned that my pupil still tries to cross the lines, and that he needs much support and encouragement. I intend to work on multiplication table.

14 My pupil had difficulties in understanding basic arithmetic functions, but I know now that when she manages to concentrate she can deal with them. As for myself, I now understand her and thus am going in her pace.

15 I learned never to give up, even when things are difficult, and keep encouraging my pupil to overcome her problems, and not the them overcome her.

The table again indicates the fact that all 15 students have learned and drawn conclusions from their work with their pupils. As in the beginning of the year, some relate to each part specifically, whereas others speak more generally. With regard to themselves, some students talked about their ability to contain and cope with emotional and educational difficulties (no. 1, 4, 7, 15). Two students (no. 5 and 8) noted their own difficulties, such as

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lacking control of multiplication table, and finding it difficult to draw the line. Only one (no. 10) admitted not to have learned anything new about herself. With regard to learning about the pupil, some referred to the emotional side (no. 1, 3, 13), whereas other talked about the educational aspect (no. 7, 14). At this stage there was no distinction in their answers between ‘learning’ and “taking something with them”, because they have already acquired some experience and the ability to see the combination of these two aspects. All the students showed clear insight regarding the method of teaching, to match the pupil’s needs. Three (no. 5, 8, 13) referred only to the contents, whereas the rest related to teaching methods. At mid-year there was a significant change in the degree of the students’ reflection, and in their attitude to learning about themselves, about the pupil, and “taking along from the lesson”. The emphasis on learning about their pupil, at the beginning of the year, has shifted at mid-year to learning about themselves. In addition to the quantitative aspect of the ratio between learning about themselves, versus learning about the pupil, there is a change in the qualitative aspect. At the beginning of the year 7 students gave arguments related to the pupil’s performance, whereas at mid-year 11 (no. 1, 2, 3, 4, 6, 7, 9, 10, 11, 12, 15 in Table 27) of them referred to their part as teachers. All of them spoke of teaching methods, using professional considerations and matching teaching methods to their pupils’ needs (not in general, as at the beginning of the year). I.e., at the beginning of the year, the remarks were more general, e.g., the general need to use illustration means. At mid-year the students perceived the problems and learned how to integrate this understanding in their teaching methods. This was a significant reflective act, responsive teaching, understanding of a complex situation, of the learners and their nature, at the same time matching the teaching. These two capabilities are not always there; not always does understanding of the pupil’s nature result in matching the required teaching methods. In addition to the students’ answers in their summary sheets, we will show also their answers to question no. 15 in the “half-way” questionnaire (appendix 5), as per Table 28.

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Table No. 28: Discovering new facts about themselves, during their work with their pupil Student No.

What new things have you discovered about yourself, during your work with the pupil? Please detail.

1 I found that I could adapt myself to her, and match my work program, to her age and level. It was not so clear at the beginning of the year, when the pupil would not do what I had prepared for her, causing me to be frustrated.

2 I found out I could be very flexible and adapt myself to the pupil’s needs. I can teach subjects which seemed difficult at the beginning of the year, and the main thing is – I am not afraid of math any more.

3 I found out I could cope with a pupil, who is not always willing to study, lacks motivation, and whose emotional problems make him respond in an unpleasant way. I am starting to accept him as he is.

4 I discovered my ability to understand my pupil’s didactic and emotional problems, and found ways to cope with them.

5 I discovered I could teach math, in spite of the difficulties, and even enjoy it.

6 I found out I could control my frustration and anger. 7 I discovered I could cope with mathematical subjects, which

scared me as a child. I have now great will to teach the subject. I also found out that I had the ability to understand the pupil’s problems, and make her love the subject.

8 I discovered what I really meant to my pupil, and what power I had as a teacher. In the case of my specific pupil – my encouragement and faith in his ability increased his motivation and made him realize he can do it, in spite of his problems.

9 I found I am very confident in teaching the subject, I am a good listener, I am flexible and could match my teaching to the pupil’s needs.

10 I discovered I had lots of patience, and I’d rather work with older people.

11 I found that even when I did not work by a built in method, I still prepared the teaching subjects on my own, to match his needs.

12 During the course I discovered that the quality of material is as important to me as the quantity.

13 I discovered I could teach math, which has not occurred to me until now. I know I can cope with problems in teaching new

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subjects – unknown and unwelcome – and make it agreeable by using games.

14 I found out I could learn things I had never known before, and do it creatively. I discovered I had the ability to contain.

15 I discovered I had to be determined in my work method with my pupil, and set the limits. It was difficult at the beginning of the year, but when I did so, the bond between us strengthened, as did my authority as a teacher. This allowed me conduct the lesson properly. I also learned that teaching by means of illustration and connection to the pupil’s inner world is very efficient.

The purpose of the above question was to make the students do some soul-searching, and focus on the changes they went through while working with the pupil. The use of the verb “discover” (find out) as opposed to “learn” is meant to intensify the sense of capability and innovation at this stage. In the table we can see a significant change in the degree of reflection. All 15 students specifically indicated things they had discovered in themselves. Twelve of them (no. 1, 2, 3, 4, 5, 7, 8, 9, 11, 12, 13, 15) pointed out discovering in themselves an ability of understanding the pupil’s needs and matching their teaching methods accordingly. Six students said they discovered the ability to cope with disappointment and frustration during their work, as well as their ability to accept the pupil as is. These data support and are supported by the data in Table 18. At mid-year there was a change in the students’ sense of capability to cope with didactic and emotional problems, and they could express their sense of capability as math teachers. Self-discovery is a process indicating high reflective ability, which is rather significant in the teaching process. It takes place following experience and feedback. In the training sessions the students learned to identify and analyze the various factors of the lesson, as well as understand their own ability. Another question included in the same questionnaire, relating to the changes during the lessons, was no. 13 (‘half-way’ questionnaire, appendix 5). It examines the changes in the degree of reflection, though it is less overt. From the students’ answers we can see applicable changes resulting from the degree of reflection, as shown in following table.

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Table No. 29: Making Changes during the lesson Student No.

Do you adhere to the lesson plan, you prepared beforehand, or are you making changes during the lesson? What causes you to change? Please detail.

1 Usually, I try to adhere to the original plan of the lesson, but sometimes, when the pupil is extremely restless, or needs extra practice, I am making changes.

2 Today, I am capable of changing during lesson. I do have the lesson pre-planned, and I know what I am going to teach, but I may change things following the pupil’s difficulties. I can improvise, add or omit items.

3 Usually, my lessons correlate with my plan, only sometimes there may be changes due to unexpected problems in specific tasks. Then, I may teach the subject in a different manner, by different strategies, or do different tasks altogether.

4 Usually, I do not change my plan, unless I notice special difficulties on the pupil’s side. Today, it almost does not happen, because I know her well enough to prepare the tasks according to her level.

5 Usually, I adhere to my original plan. 6 Usually, the changes I am making are a result of my faulty

time-planning. If the pupil faces difficulties, I may change the order of work, or change activities.

7 Yes. I do make changes during lessons, due to lack of time or the pupil’s difficulties.

8 At first, I stuck to my original plan, which often did not suit the pupil. Now, I have learned to prepare several alternatives, so I can be more flexible and retrieve what suits best.

9 Usually, I try to adhere to the lesson plan, and I have learned to adapt it to my pupil’s needs and her level. The changes I am making during the lesson are mainly due to her emotional state.

10 Usually, my lessons are conducted as planned. 11 Usually, I adhere to the activities I planned, but sometimes I

make changes according to my pupil’s needs. 12 In most lessons I stick to the layout, though sometimes I am

reflecting as a result of the ambience and progress. 13 During the lesson I am sometimes changing a little the original

plan, following my pupil’s response to various activities. 14 I make changes according to the time my pupil needs for her

tasks. If I see she understands, I move on to a more difficult task. If there are difficulties and frustrations, I intercept and

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create easier tasks. 15 Usually, I try to conduct the lesson according to my original

plan. But, now and then I make changes, as in certain contents not understood by the pupil.

From the above table we can see that most students admitted to making changes during the lesson. Only two of them (no. 5 and 10) said they adhered to the original plan, and they, too, used the term ‘eventually’ when speaking about making changes. I, too, observed such changes, though rarely. All other students (13/15) said they made changes during lesson. The reasons for making such changes, as per the students, were as follows:

• Unexpected difficulties on the pupil’s side in certain tasks. • Tasks that were too difficult, or too easy to perform. • Faulty time-planning of the student. • Emotional state of the pupil. • The pupil’s state of progress. • The ambience during the lesson. • The pupil’s response to various activities. • Pupil’s frustration. • Shortage of time.

These reasons can be divided into two types: Reasons related to the pupil’s performance, and those resulting from the planning of the lesson. Most students argued that the changes occurred because of the pupil’s performance (too easy or to hard for him/her); only one (no. 6) admitted that sometimes the changes were a result of her own faulty time planning. In spite of the turnabout in the ability to make changes – expressing reflective capability – most students still find it difficult to notice and perceive their central place in the process. Though we might assume that the more adjusted the lesson to the pupil’s needs, the less the need for changes, still the students tend to attribute the change to the pupil, rather than to themselves, i.e., they are still not assuming maximum responsibility to their position as teachers during lesson. Nevertheless, there is some improvement in their planning skills to match the pupil’s needs, and most of them indeed report of having learned to do so.

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These findings support the reports in Table 24, regarding the improvement in the ability to plan the lessons at mid-year. Most students reported then, among others, that the improvement expressed itself in time planning, activities and teaching methods – suitable for the pupil’s needs. In addition to the reported changes, 5 students detailed the type of changes they made (Table 29, no. 1, 3, 6, 8, 14). The changes were as follows:

• Additional explanation, or practice. • Change of task. • Teaching the subject in another manner. • Teaching learning strategies, other than those taught previously. • Changing the order of work during the lesson. • Exchanging activities. • Offering other alternatives. • Mediation (by the student). • Creating easier tasks.

These findings support previous ones. The change in the sense of confidence and capability at mid-year is expressed by the changes in teaching methods and the degree of reflection. In other words – the change in the ability to modify can be attributed to the changes in reflection, expressed, among other, by coping with vague situations, the ability to make decisions during lesson, to be surprised and to deal with unexpected situations. End of the Year In their end-of-year reflective summaries, the students referred to the various aspects of year’s events. The following table shows utterances related to reflective thinking, as expressed at the end of the process, in retrospect. Table No. 30: Reflection at the End of the Year Student No.

Sentences Related to Reflection

1 I learned a lot from my pupil. At first I found it difficult to make contact, but later I managed to that, which pleased me.

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Today I can tell which task will frustrate her, and which will be an experience of success. I focused on strengthening her. I learned that diagnosis at the beginning of the year is not the only parameter, and I understood why her results of the diagnostic tests were worse than the lessons. I saw her difficulties, beyond math, how they affected math teaching, and what I could do. The most important thing I learned, is not to sever the emotional part and work according to her needs. I learned the meaning of success for a pupil, and mainly - how to teach didactic contents, taking all difficulties into considerations.

2 At the beginning of the year I was afraid I did not have the appropriate tools to teach a pupil with problems. Analyzing the diagnosis helped me focus and understand them. I learned how to teach mathematical subjects I had not known before, making use of the assistance given to me by the tutor. At first I gave only work sheets; later, with the help of other students, I started to prepare more creative and varied tasks, which motivated the pupil, as well as myself. The workshop contributed much to my development as teacher and human being. I feel more confident now in teaching math; I know it is possible. Looking back, I would add a personal touch to me relations with the pupil, maybe by the telephone. More involvement in his life, and his difficulties at home would probably be of help.

3 I learned mainly about myself; that I had more patience than I thought, and I can contain even problematic, hard-to-work-with pupils. During the year I have matured, both professionally and personally. I am aware of my capabilities as well as my weak spots. I know that not always one explanation or practice is enough, even if the pupil seems to have understood. Sometimes the road is paved with regressions, and further practice is required. In spite of the problems, the course gave me an experience of success and a sense of capability. I learned to cope with the pupil’s frustrations as well as my own. Looking back, I should have focused more on techniques and less on understanding, to create an experience of success. Only toward the end of the year did I understand how much the difficulty in abstract thinking affects understanding and the ability to do arithmetic manipulations.

4 During the course I found out that I could assist a pupil with

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problems in math. With the help of your counseling, I crossed the barrier, and found out I could cope with didactic and emotional problems. I saw that goals I set at the beginning of the year were less relevant, focusing on didactic aspect alone. The course gave me an experience of success, mainly in coping with my pupil’s emotional problems, though the didactic part scared me more.

5 During the course I have developed, both as a person and as a teacher. I learned I could cope with challenges and goals and stand up to them. Through my pupil I understood some of my own problems, which have accompanied me for years. At first I avoided subjects, which were not clear to me, feeling threatened. Later I was more confidence, learned those subjects and acquired control. For me the course was a corrective experience in math. The pupil’s conduct at the beginning of the year may well have resulted from my own lack of confidence. I had to write down every word I was going to say, and everything I was going to teach. I was very dependent. Later, I prepared layouts, but not literally. I understood and was more confident with the subjects I was going to teach. Now I can understand the feeling of frustration and low self esteem of someone who does not understand the subject, and how important it is for me – as a teacher to children with special needs – to make them understand and increase their confidence.

6 During the year, I learned how to cope with a problematic pupil, matching my teaching methods to his needs. It took me a long time to identify the origin of his problems, and the fact that his manipulative behavior resulted from his difficulties and was not intended to spite me. I became more open, ready to try new things, even if I am not in full control of them, i.e., I dare to take chances. I learned to listen to the pupil’s needs, knowing when to mediate, use illustrations, give up certain tasks or insist on others. All these made me more flexible, realizing the complexity of teaching-learning process. The course was a corrective experience for me. I am more confident now, knowing I don’t have to invent things. I know who to approach, for assistance. I know how hard it is for my pupil in class, and that all his manipulations are a result of his problems. I am less frustrated, knowing the reasons for his refusal. I also know that knowing all that is not enough, and I have to do the maximum to find a

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way to cope with these difficulties. 7 Thanks to my pupil I know myself better. I learned I had the

ability to understand her way of thinking and adjust myself by being attentive to her needs – both personal and didactic. Following the course, I acquired confidence and proved to myself I could handle a subject I was never exposed to previously, and teach it successfully. The course was a place for me to prove my skills as a teacher in general, and as math teacher especially. It showed in preparing lesson layouts, writing down the goals and purposes and creating accessories. I can truly say I succeeded, both personally and professionally.

8 The goals I set for myself were numerous, and created a gap with what I managed to do in fact. This gap resulted from my incorrect assessment of the time needed for each subject. I realized work had to be done slowly, with many repetitions, and each small task may take many lessons to teach. I discovered I did not know how to set clear, unequivocal limits in individual work. I tend to understand, accept and sympathize with moods and inclinations, thus conceding educational requirements. Such concessions, I learned, actually harm the pupil. Being considerate does not mean making concessions, and as a teacher I have always to look from outside to see the picture in full. One cannot teach from a standpoint of pity for the pupil. I realized it was extremely important to make good contact with the pupil, to make a basis for motivation and supportive ambience in class. The pupil taught me the importance of clear means of illustration, the need for systematic teaching, by stages, and the importance of setting clear limits.

9 I have learned that I must take the pupil’s mental state into consideration, and to give him as long a time as required – at the same time meeting the goals I set to myself. I know now how to conduct a lesson within flexible limits. I can recognize an immense development in me, both as teacher and person. I learned to be more flexible, and take my pupil’s needs into account, to see her first, and not just her progress and the lesson’s subject. I learned not to be disappointed when things do not happen the way I hoped, and just go on. The course certainly gave me the experience of success.

10 Pedagogically, I feel I promoted the pupil. But the course itself did not contribute anything to me, personally or professionally. I found the work with the pupil extremely hard; he showed great resistance, and refused to cooperate. I had to literally coax

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him into working. In spite of the problems and my disappointment, I would like to point out your assistance, patience and caring all during the course.

11 I came here, after having difficulties and fears about math for many years. I chose to specialize in the subject as part of my coping with it. I learned that when I understand the subject, I can teach it efficiently and easily. Working with the pupil contributed to my professional development, as I dealt with his cognitive and emotional problems. Writing lesson layouts increased my confidence. I knew what I was going into, at the same time I managed to be spontaneous as per the process of the lesson. The combination of these two is the best contribution for me.

12 During the year, I realized I could and knew how to reflect during lesson. I found out I could be very flexible, not sticking only to the layout sheet, if they did not match the development of the lesson. One of the main things I have learned is that pupils are different, and each should receive a different degree of assertiveness. My pupil required a great deal of firmness, since he tended to distraction. Assertiveness in his case was extremely important to learning, and I was glad I could do it, which I was not so sure of before the course.

13 From the didactic aspect, I managed to achieve most of the targets I set to myself. Emotionally, I created good bonding and trust with the pupil, which were rather important for our work. At first I was mainly task-oriented, but later I understood the emotional problems, their meaning and how to deal with them. I discovered wonderful abilities and skills in my pupil. I started to base the lessons on games and other activities, which contributed to the success and to his motivation. His success increased my confidence in my ability to teach math. I feel that the fact I never liked math helped me in this case to understand my pupil’s difficulties and teach him in a better manner.

14 During the year I learned I had to approach the pupil where she has the most problems, and continue from there. I had to let her express things not strictly related to the lesson, because she saw me as a containing person. At the same time I had to put the limits and return to the lesson’s subject. I know she was very insecure, needed support, and used manipulations to catch my attention; I also realized she was loosing her motivation whenever she encountered difficulties. She, as well as I, went through the same process – we both had to overcome our

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difficulties, not letting them overcome us. Teaching her not to give in on herself made me understand I had the same problem. The course made me understand her inner and emotional world, her needs, way of thinking and her immediate need for repeated feedback.

15 The course made me face many challenges. The process of interaction with my pupil and coping with the teaching, gave me a great deal of insight, regarding myself. I realized I had difficulties in setting the rules and limits, and in being assertive – two extremely important skills in coping with pupils, and life in general. In addition I learned that my innocence made it difficult to deal with a manipulative pupil, as I could not identify her manipulations. Still, I realized I could be very patient, emphatic and attentive for her needs, during her pro9cess of learning. On the personal level, I learned that a clear message is very important for the pupils, indicating the teacher’s status. I learned to deal with manipulations. I feel more confident in my professional skills, too. I know how to think and draw conclusions from the lesson. I can give legitimacy to the pupil’s problems, thus reducing her frustration. Noting down my reflections at the end of each lesson required time and some thinking, but I think it is essential and important for my professional development. It made me think of the processes I had dealt with, draw the conclusions and the moral.

At the end of school year, from the personal interviews and the written reports, a clear picture emerges, demonstrating an extremely high degree of reflective thinking and capability. (In addition to Table 30, some reports and interviews are shown also in appendix no. 8). At this stage, all students are capable of describing and relating to their own process of learning from the course. They express a high meta-cognitive ability, expressed by learning of new knowledge about thinking and teaching. All of them speak from a position of teaching teachers, rather than learning, which is, naturally, more adult and mature. At this stage, the use of professional terms, to describe process and insight, is more apparent, as well as new references dealing with matching the dosage and complexity of teaching to the pupils’ capability. Such an attitude signifies the change in the students’ perception of themselves as teachers, compared to mid-year and certainly to the beginning of the year.

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According to the reflective reports, the personal interviews and observations, at the end of the year, we could conclude that both reflective thinking and reflective skills are expressed in the following areas:

• Understanding the nature of the course, and its importance for their training to be teachers.

• Learning new things about thinking and teaching, combining contents and pedagogy.

• Developing awareness of learning process, both the pupil’s and their own.

• Switching from a state of uncertainty, doubt, confusion and perplexity to feeling of controlling complex situation and satisfaction after coping with dilemmas.

• Making use of various types of knowledge for the purpose of interpretation and thinking.

• Identifying problems, conflicts and difficulties, understanding them and responding accordingly.

• Ability of internal self-assessment. • Understanding of phenomena and the ability to make decisions

before, during and following the lesson. • Insight, without blaming the pupil, but rather understanding the

origin of his problems, thus modifying the teaching method and accessories.

• The ability to deal with unexpected, embarrassing situations. • Using one’s discretion for every activity. • Supplying means of mediation to help the pupil think. • Creating awareness of complex situations, and the ability to see all

their components. • Naming and understanding phenomena and their context. • Relating the individual to the general – understanding and insight

for single events and phenomena. • Exposing the students’ own hidden knowledge. • Thorough knowledge of the pupils and their characteristics.

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Chapter 4 Discussion

The discussion of the findings focuses on the changes that took place during the year among the students, participating in a course for specialized math teaching to children with special educational needs. At the beginning of the school year most students admitted to being rather apprehensive. Their fear resulted mainly from a feeling that they would not succeed in promoting their pupils and cope with their problems. Additional concern resulted from their personal difficulties in math, and their poor control of the subject and the teaching thereof – i.e. their fear was a result of factors related to them both as students and as teachers. Some of them showed a gap between their answers concerning the course and their confidence in working with the pupil on math. The same students admitted to apprehension of the course, at the same time being confident in their work with the pupil on math. Maybe the reason was their difficulty in admitting to lack of confidence in working with the pupil, for fear they would fail. The main reasons to their apprehension, as reflected in their words, were poor knowledge of mathematical subjects, and lack of tools and teaching methods for the same. Their reports about control of math teaching methods at the beginning of the year showed they did not know how to teach math. It should be noted that during their training, all of them took theoretical courses prior to this experiencing course. The courses dealt with all the subjects defined by Shulman (1987), such as: Knowledge of teaching subjects, general pedagogic knowledge, curricular knowledge, content-dependent pedagogic knowledge, knowledge about the pupils and their nature, administrative knowledge and educational philosophy. Among others, the students were trained in teaching methods of math, as well as teaching methods for children with special needs. But, as seen later, this does not assure the ability to make use of this knowledge. Silberstein (1994, 1995) speaks about the fact that usually, professional training program goes from theory to practice, and he suggests the combination these two, claiming that teaching is, in fact, a practical-reflective occupation. Should the training program indeed combine theory and practice from the start, the degree of apprehension would probably not be so high. One should distinguish between actual lack of knowledge and the feeling of lacking knowledge. Most of the students probably knew teaching

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methods in theory, but had never practiced them. That same theoretical knowledge was realized only during practice, and this study exposes the experience and medium that accompanied it. Schon (1983, 1987) argues that the teacher’s knowledge is sometimes invisible. Some theories are hidden and can be exposed only in certain situations. The knowledge lies in what the teacher is doing, without even being aware of it. By reflecting and clarifying, the teacher can understand his own behavior and knowledge of the subject. Often, in training and feedback sessions, and even during observations, I proved to the student she was acting in a correct and efficient manner, without being aware of it. The findings about the feeling of efficacy at the beginning of year, too, indicate low self-esteem, with regard to math teaching. On the other hand, the general sense of teaching efficacy was rather high, as evaluated by the students, relating to various components in their personality, and not to teaching in the sense of imparting knowledge and promoting the pupil. In the term ‘sense of efficacy’, in this study, we refer to the teacher’s efficacy, which is a very specific professional sensation. If it is a cognitive process, during which people are building up their beliefs about their performance skills, on a given level of achievement (Tschnnen-Moran, Woolfoik-Hoy & Hoy, 1998) – then the reports at the beginning of the year show a rather poor belief in their performance skills. Such sensations are linked to the reported sense of insecurity in working with a pupil, and lack of knowledge in math teaching. The fact that the students assessed themselves as being good teachers in general, is supported by the fact that the feeling of “efficacy” is not universal, and anyone can feel capable in one subject and less so in another. Therefore, we should relate to the teacher’s sense of efficacy as consisting of three different performance areas. Cherniss (1993) speaks of three areas included in a teacher’s professional efficacy: The task – the teacher’s efficacy to teach well; relations – his/her ability to retain fruitful and efficient relations with others; organization – his/her ability to make a difference and fit in the organization he/she is working in. Gibson & Dembo (1984) included in the term ‘professional efficacy’ of the teacher the task area only. They related to the technical aspects of the occupation: The teacher’s feeling of having the skills in planning a lesson and conducting it, of good control of the knowledge, correcting the pupils’ performance and enhancing their motivation.

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Recent years studies expand the range of task to the teacher’s ability to promote his pupils socially and emotionally, as well (Soodak & Podell, 1996; Rich, Fuchser & Lev, 1996). In our present study we are relating to both areas: Task and relations. I.e., when the students reported, at the beginning of the year, of a high sense of efficacy as teachers in general, they pointed out factors related to efficacy in relations (whereas the task field was perceived as math teaching). Based on my observations of the students’ work with their pupils, our training sessions and their report summaries, it is obvious that they did not feel capable of promoting the pupils emotionally and didactically. Their work, at that stage, was intuitive, accompanied by stress, insecurity, confusion and perplexity. Some of them approached me with questions during the lesson, mainly due to not knowing how to teach the subject, and how to respond to an uncooperative pupil. Others wanted to have my approval of what they did. In addition, I could note the differences in body language, manner of sitting, style and phrasing. Some students addressed the pupil from an authoritative standing, giving instructions in a form of command (… Count from … to …), whereas others used the ‘sharing’ style (… now, let’s count from … to …). It seems that style and phrasing are related to the level of confidence, and the ‘sharing’ style characterized more relaxed students, and in turn reduced the pupils’ anxiety as well. The students’ performance at the beginning of the year was characterized by a behavior, identified by researchers (Desforges, 1995; Connelly & Clandinin, 1992; Schon, 1988) as typical for novices. Unexpected, confusing situation may shake their confidence and interfere their planned thinking, thus they prefer planned situations and performing by expectations. They are not open for new experiences, and prefer to perceive such experiences that corroborate existing beliefs and standpoints. This argument explains also their adherence to lesson layouts and their inability to change or ‘deviate’, as observed at the beginning of the year. It turns out that at the beginning of the year the degree of reflection was rather low, and most students did not reflect in the process (Schon, 1987, 1988). Most of them had difficulties in identifying and decoding situations of teaching, in quick decision making and in rephrasing the situation – thus the results were not as expected.

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On the other hand, some students decoded and interpreted teaching situations right on start, and managed to respond and act automatically, without any reflection. Upon examining the planning of the lessons, the students faced some difficulty, mainly in diversifying their plan, in time division, in the clarity of the tasks and in their considerations for choosing means and accessories. At the first lessons, all of them wrote generally about activities and accessories, but did not relate to their own pupil and his/her special needs. In their summaries at the beginning of the year, some of which required reflective thinking, we could still see that they did not refer to the complexity of teaching situations and to the connection between things. All their attention was directed to the results of their actions, rather than to themselves (Bengtsson, 1995). The reason they turned out with their difficulties during the lesson, rather than effecting process of reflective thinking (Rand, 1994), was probably a result of their insecurity, anxiety and inexperience. We can see that all students, at the beginning of the year, were in level 1 – the level of reporting – on a scale of five degrees of reflection (Bain-Roy, Ballantyne & Packer, Mills, 1999). On that level of reflection, argue the researchers, the student tells, describes and reports, in the simplest manner. A small part of the students, described already at the beginning of the year as highly reflective, were on level 2 – the level of responding – in which the student uses description, without any conceptualization. His attitude to the events is judging, but without argumentation; asks rhetorical questions with no attempt to answer them or offer an alternative. Also, he reports of feelings, such as anxiety, happiness etc’. The professional model of the students at the beginning of the year can be identified in Fuchs’s model (1995), as the phase of survival, or becoming. It is the first of four phases, in which the teacher copes with basic problems of teaching, accompanied by stress and anxiety. At mid-year, following some experience and training / feedback sessions, all the students went through a huge change, in all areas examined. With regard to the feeling of apprehension, some still claimed to be somewhat apprehensive, mainly because their lack of confidence in teaching method. In spite of a certain amount of experience and action, there still is some uncertainty, which indicates reflection appearing when

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a person is in a state of wondering, confusion, lack of cognitive balance and doubts (Dewey, 1933). At mid-year, the students already regard themselves as teachers and not as students Still learning new things, but performing as teachers. At this stage there are already indications to the fact that the students know the reason for their higher confidence. The reasons for the change in their sense of confidence, they claim, are a result of experience, feedback sessions and training, knowing teaching methods, making contact with their pupil. Additional reasons are the written feedback of the instructor regarding their planning and summaries, the clear targets in their work, their coping with the pupil’s problems and planning the lessons. Al this is supported by their reports about their control of math teaching and lesson planning efficacy. Most students claimed to feel now in that area better than they did at the beginning of the year, and managed to identify the reasons for that. The reasons are similar to those mentioned with regard to the sense of confidence. They are expressed by:

• More professional, less intuitive, teaching; • Knowledge of teaching specific subjects; • Adapting existing material to a specific pupil; • Matching accessories and illustrative means to the pupil’s needs; • Creating a diversified experience in the lesson; • Defining goals in writing and applying them; • Correct time division, organization and order during lesson; • Gradual activities during lessons; • Ability to discern between goals and means.

During my observations I could notice more professional work, focused, planned and suitable for the pupil’s needs. Most students began to make their own material instead of using ready-made stuff. Even when using pre-made stuff, they would adapt them to the pupil’s needs, using their discretion. At the beginning of the year they used to copy work sheets from books, without any criticism, a practice now changed, after they have started to write their reasoned professional arguments for choosing and using activities and accessories for the lesson (difficult and unprofessional at the beginning of the year).

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With regard to writing lesson layouts, they reported now of more automatic writing, requiring less time They also stated their efficacy of showing authority, set the limits and showing assertiveness during the lesson. The above-mentioned findings are all related to their improved sense of efficacy at mid-year. Most students noted at this stage their ability to cope with the pupil’s didactic and emotional problems. Some claimed that the dealing with emotional problems was harder than dealing with the didactic problems, and mentioned the training sessions as being helpful in clarifying many subjects. Their sense of efficacy was also identified as expressed by coping with the pupil’s didactic and emotional problems, and by the ability to change his/her motivation. They also noted their own ability to teach mathematical subjects, match the lesson to the pupil’s needs, and make changes and modifications during the lesson, as well as setting the limits. This can all be supported by Bandura (1977, 1997), who defined efficacy as the individual’s judgment regarding is ability to organize and perform successfully a behavior or set of behaviors leading to the desirable results. Though a rather general definition, it matches the student’s sense of efficacy at mid-year. This sense of efficacy covers several fields, related to being teachers – like a set of behaviors (Bandura, 1977, 1997), each one expresses them in a different manner, but all of them reported of a change. We may assume that such improvement indeed took place following experience and training. At this stage the lessons of experiencing began to take shape and conduct the expectations for the future. The students started to interpret what might have happened, and plan their matching conduct accordingly (Kalekin – Fishman, 1998). The ability to identify the reasons and expressions of change indicates awareness of the contribution of the course and the process they were going through, of relating to various aspects in their work with the pupil and of a developing reflective ability. At this stage some of the students have already reached the reflective process in action. They managed to identify and decode both clear and vague teaching situations, and make decisions during the lesson. Other students reached the reflective process following the action (Schon, 1987, 1988). Of course here were some students who managed to combine these two types of reflection, and others (few) who responded automatically to

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teaching situations, without any reflection at all (Eraut, 1995). But, again, most of them interpreted and responded in a controlled manner, using reflective thinking. At mid-year we could see that several students still remained in the first (reporting) and second (responding) level of reflection, though others reached the third level (relating), (Bain Roy, J.D., Ballantyne & Packer, J., Mills, C. 1999). The student identifies data related to previous experience or insight. He spots the weak or strong points in himself, his mistakes and what he has learned from experience, finds a surface explanation for it all and identifies the things needing to be changed. At the end of the year, many students developed further layers of professional development, and detailed them extensively. The students understood the complexity of teaching and their obligation as teachers in effective learning. Their reference focused on understanding and insight of the need to match teaching methods to the differences between pupils. Their attitudes to their occupation were positive, and deep insight was apparent with regard to the knowledge structure of the subject and its connection to the teaching – learning process. At this stage, most of the students felt extremely more confident (only two claimed to be confident, but not fully so). This sense of confidence is, of course, subjective and depends on self-perception and efficacy. Examining all the fields which correlate between reports of these two students of improved teaching methods, the sense of efficacy and the degree of reflection – student no. 8 appeared to be more ambitious and self-demanding, which might contribute to her feeling. She also missed several lessons due to birth, and may have felt not experienced enough. Student no. 10, on the other hand, expressed her objection to the course, as well as turning out to be of low efficacy in tasks, teaching and human relations, etc’. At the end of the year (just like mid-year) the students identified the reasons for change in their sense of confidence (mainly the experience, counseling and training given during the course). The reasons resembled those of mid-year, but now they were well-established and well thought-out. All their apprehensions – reported during the year – disappeared now. The expressions of their sense of confidence concentrated mainly on teaching methods, knowledge of math, and the ability to cope with both didactic and emotional problems of the pupil.

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They support this sensation by their reports about control of teaching methods at the end of the year. All reported of significant improvement, though in different manner and intensity. All found additional qualities in themselves, and reached new insights regarding the process they have gone through. At the end of the year all could recognize the variety of expressions of the change in teaching methods, which included the mid-year ones, but were more in number. They focused in all factors of planning and organization of a professional lesson, in insights about principles of teaching, and in understanding their significant position as teachers in the didactic and emotional coping. At this stage they expressed their awareness of the processes they had gone through and phrased it professionally. The feelings of doubt and apprehension disappeared, and were replaced by a new feeling of control, intensification and willingness to continue the process of learning. Didactically, we could notice an internalization of principles related to planning teaching units or another broad subject, use of relevant resources, development of didactic activity and built-in knowledge, both the students’ and their pupils’. The students acquired content dependent pedagogic knowledge (Wilson, Shulman & Richert, 1987), including understanding of the nature of teaching a specific subject, and the ways and principles of teaching thereof. At this stage the students internalized the principles of the constructive approach by merging previous knowledge with construction of new knowledge in the process of experiencing. Each student’s experience was different from the others’, and resulted in the acquisition of different knowledge (Von Glaserfield, 1995). At this stage they demonstrated control and responsibility in leading the process of building-in, shaping of knowledge, terms and skills. They knew where to locate the things they had learned, within the mental frameworks, and because application is part of understanding - the knowledge became useful (Birenbaum, 1997). At this stage, the students expressed their faith in their own ability, and their sense of efficacy improved as well. Unlike their sense at mid-year, which was expressed in a rather restricted number of fields (teaching methods, changes, ability, setting limits and increasing motivation), now it included many more components of the teaching – learning process, as well as others related to dealing with their own frustration, anger, dissatisfaction etc’. Gibson and Dembo (1984) divided the teachers’ sense of efficacy into two types: General teaching efficacy, and the teacher’s efficacy. The participants of this study acquired a sense of personal teacher’s efficacy. They felt that thanks to their knowledge, experience

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and skills they could promote their pupils’ achievements. As they see it, it is a sort of professional efficacy, by which he/she can promote his pupils without taking into consideration external obstacles, such as the influence of the pupil’s home. All these things are supported by the students’ reports in their reflective summaries, and in the end-of-the-year personal interviews. I could notice signs of extremely high reflective ability and thinking, expressed in many factors related to self-awareness. I also noticed profound understanding of the pupil’s needs, recognition of various teaching situations, controlling them and coping with them, as well as using professional discretion, understanding of dilemmas and an ability of internal assessment. The students reflected their awareness of the learning procedures they had experienced. They internalized the understanding that the processes during learning are as important as the process of internalizing of contents and skills. As Schon (1988) sees it, at the end of the year the students were considered reflective teachers. They managed to be surprised by their pupil’s words, able to phrase unclear teaching situations, supply mediation, and, in general – they were all the time in a learning process. During the year, by the training and experience, they were led to a new way of thinking, generalization, a different categorization of things and renewed understanding of phenomena (different for each of them). With regard to the scale of reflection, most of them were on level 3 (relating), and some on level 4 (reasoning), apart for no. 10, who remained on level 1 and 2. On level 4 of the scale, the student integrates between data and theoretical terms and personal experience. He proves a high degree of conceptualization, through understanding of the reason for things. He analyzes, examines, looks for answers, considers alternatives and makes assumptions. He attempts to explain his conduct, his – and others’ –feelings, by insight, analogy or previous experience. He tries to link between theories and experience. Not all the students on this level performed all the mentioned ingredients, but they managed part of them, in various doses. Some of the highly reflective students were found to be on level 5 of the scale – the level of reconstruction. On this level, the student demonstrates abstract thinking for the purpose of generalization or application of

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learning, he may reach original conclusions based on his experience, discovers rules, builds his own teaching theory, or take a stand with regard to issues. The student discovers and internalizes, following the reflection, the personal meaning of his future learning. (Bain Roy, J.D., Ballantyne & Packer, J., Mills, C. 1999). We might say that at the end of the year, the students have reached the stage of growing, graded second in Fox’s model (Fuchs, 1995), and the stage of maturity, graded third. They started a process of construction, accumulating knowledge, and their perception of themselves has become acute. They understood the curriculum and the subjects taught, started to find satisfaction in their work, knowing what they were doing and looking for ways to improve. They also acquired self-confidence, an ability to focus on the pupil and his needs, they were more relaxed and open for new ideas. Reflection allowed them to move on from a state of uncertainty and doubt, confusion and bewilderment to a new feeling of being in control of complex situations, and a feeling of satisfaction resulting from coping with dilemmas (Villar, 1994). Dewey (1933) supports it and argues that reflective thinking turns vague and conflicting situations into clear, coherent and harmonious ones.

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Chapter 5 Conclusions

Analysis of the observations, the personal interviews, feedback sessions and the students’ pedagogic diaries shows each one’s personal and unique development. Though all of them made progress in all subjects examined, each one showed development in different aspects and a unique dosage. Identifying the personal patterns of their progress and development, gives us vital information for the planning of further training of each one. Teachers’ training should focus more on the process of teaching, as opposed to the technical performance. It should also concentrate on moving the emphasis to the teacher’s soul searching and continuous coping with himself (Rand, 1992). Courses of this kind should put in the teachers’ disposal contextual, usable knowledge, knowledge of teaching strategies which take into consideration specific fields of knowledge on one hand, and individual pupils’ needs on the other (Silberstein, 1998). This program should include a forming assessment of the students’ performance (Birenbaum, 1997) and planning of the follow up according to the findings. I.e., students who find flexible thinking during interaction with pupils difficult, require accompaniment to assist them in locating such situations, and finding ways to give an appropriate answer. Such assistance can be done by reflective analysis of the student’s teaching, supported by the course instructor. The course has nurtured a culture supporting reflective teaching, room for skepticism and questions, which cannot always be answered, as well as dealing with situations of embarrassment and surprise. Together with the encouraged reflection, the students' reflective ability has grown (Korthagen & Wubbels, 1995). The present course emphasized the practical orientation, which stresses relying on experience and practicality. It also stressed the personal orientation arguing the learning to teach is first and foremost a process of transforming, in which the student changes and reconstructs his ideas of learning and teaching, developing his personal style, beyond the acquisition of knowledge and teaching skills. According to this orientation (Feiman-Nemser, 1990), the teachers understand the development process of their pupils and their behavior, and adapt their teaching accordingly. The students in the course reported of understanding the pupil’s way of thinking and matching the tasks to it. One of the conclusions here is the need to continue the training by

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accompanying and supporting the students, as they experience teaching, so they can make use of their knowledge. Such accompaniment should be directed to develop the ability to respond to various needs of learning, take into consideration their entering points, and shape teaching methods and mediation required for their progress (Darling-Hammond, 1996). Among the students we could find various degrees of reflection (Day, 1993). Some of them can be defined as more reflective than others. La Boskey (1993) claims that reflective students are of a more caring and open personality, and are more philosophically inclined than their less reflective peers. They feel the need to search for “the better”. Reflective students are characterized by the need to pose questions, by the ability to evaluate themselves and express themselves better, both orally and in writing (Korthagen & Wubbels, 1995). Still, a high level of reflection is not necessarily enough to construct new knowledge – this required the mediation of the instructor. During the course, I found that the students have undergone a reflective process in the sequence between teacher-focused teaching and the pupil-focused teaching. This is well supported by the categories describing the focal points of reflection(Bain Roy, J.D., Ballantyne & Packer, J., Mills, C. 1999). Similar findings are reported in Adams’s & Krockover’s (1997) study, reporting of various degrees of teaching by the constructivist approach, among students trained in the same courses by the same teachers. Various degrees in students’ achievements sharpen the need for a flexible support program, suitable for every student and supporting his professional development according to his skills, needs and difficulties. One of the most obvious problems the students had was the gap between theoretical knowledge and their performance skills. These evidences support the differentiation done by Schon (1983, 1987) between the knowledge declared by the teacher and one that is expressed during teaching. This gap between declaration and performance is not surprising, since we are talking about two very different skills, reflecting the difference between “knowing something” and “knowing how to use it”. Teaching, directed to change the knowledge structure of the student in any subject, does not necessarily give him the ability to make actual, rational use of such knowledge. In this aspect, I absolutely agree with the criticism offered by the students, that one major drawback of this course is the absence of theoretical lessons related to teaching methods,

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combined with practical experience. I.e., precisely during practical work, we should combine teaching methods to be linked with practice, rather than taught separately during the previous year, expecting the students to apply it in practice. One could conclude that training program should combine both practical and theoretical knowledge – principles and experiencing cases – (Shulman, 1988), and not as is practiced today by starting with theory and only then moving on to practice. Experience without theories to bind it may lead to conservatism and perpetuation of the present situation. Theory without practice will become distant and incomprehensible (Goodlad, 1988). Putting the lesson layout in writing, making notes and summarizing it (appendix 3) were a rather significant factor in the students’ development. Writing created an inner conversation, which was helpful. Vigotsky (1962) claimed writing to be a sophisticated form of speaking. It helps the learning process because, unlike talking and in spite of the difficulties, it contributes to deeper and clearer thinking (Gregg & Steinberg, 1980), as well as being an assessment tool per se. In spite of the students’ eventual complaints about the writing being a burden, they learned to appreciate its contribution. At the beginning fo the year they found it hard to consolidate their thoughts into written words, but during the year they improved this skill, and writing has become a means of communication and transferring messages for them and me. By writing, the students could phrase their standpoints, analyze and process their ideas – i.e. it directed them to a meta-cognitive reflective thinking process, and reflected their own development (Kaniel, 1997). Observation, as a study tool, was found efficient and significant. It provided information impossible to be obtained otherwise, as well as making me involved and more understanding. Being an open, participating, observation, (Sabar Ben Yehoshua, 1990) it allowed me to assess many factors comprising the situation, take notes in real time and analyze it later with the students. Training and feedback sessions were also extremely important in the turning of the students into reflective teachers. Many things, which did not come up during observations, or were not mentioned in the written summaries (thoughts, taking stand, anxieties, etc’) were brought up then. The students’ awareness of complex situations increased, as well as their ability to relate to specific cases and link them to theoretical ideas. These

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sessions provided the opportunity for activation, assessment and experiencing of procedures and contents – all of which made the reflective thinking (Frenkel, 1988). I helped the students understand what had happened during class, which improved their ability to define and generalize their knowledge, and make the link between spontaneous knowledge and teaching knowledge. These talks provided the framework by which they could get clear answers regarding to their image as teachers. These sessions were a mediation process between experience and field-work, and understanding them, i.e., making the contact between practical knowledge and theoretical aspect. By these talks the students could get significant insight of the parallel processes going on between them and their pupil, who often reflected their own situation. For instance, the student’s anxiety often caused the same for the pupil. On the other hand, enthusiasm and creativity on the student’s side caused the same from the pupil’s side. During the talks the students let me hear their “personal voice”, a means of developing insight and sensitivity of the participants of a learning process (Richardson, 1994). The feedback sessions (Shulman, 1987) helped the students understand the complexity of the situation they experienced, identify and analyze various components and figure out generalities and principles by a single experience or event. Through these talks they managed to understand abstract terms in their concrete meaning. Shulman (1987) argues that the varied academic knowledge of theories and principles, the instructor has, the learning and his personal experience – all make him the most significant mediation means for the training teacher student. The process of internal evaluation the students exercised (appendix 7) was found extremely efficient. Such evaluation is based on numerous dimensions. Gardner (1983) too claims that there are many factors effecting the capability to learn, and the differences between learners cannot be measured by one general standard. A feedback session of evaluation was done following the written assessment. The students participated and had the chance to explain their standpoint. Shafriri and Bozo (1998) argue that in the constructivistic learning perception, in which a person creates in his mind the structure of his personal knowledge, the process of evaluation is part of this learning process. Indeed, the students understood it by experiencing internal assessment. Those who did not do so this way, but rather by external assessment, had difficulties doing so in the first semester.

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Internal assessment is a process, not normative, and the control thereof is in the hands of the pupil. In the course, the students experienced self-assessment, related to the didactic aspect, and they did so after each lesson. The feedback given by me for the summary, and the training sessions which followed their evaluation, developed their reflective skills. Another means applied in this study as an evaluation tool was the use of rubric to summarize the analysis and write down the lesson layout and summary (appendix 2, 4). This is one of the most efficient tools, says Birenbaum (1998), for self- assessment. It includes criteria, which are in fact the conditions to be met by every performer, so he can succeed. The rubric is based on standards intended to note at which level the standards should be met. It is an external tool, so all the students knew from it what they were required to do, though the actual evaluation was done by me. Some researchers (Shafriri & Bozo, 1998; Talbot, 1997; Wolf, 1993, Corno, 1994) speak about the fact, that to develop internal evaluation skills, an external evaluation is required. It will assist in building in of standards and criteria, by which the learner will examine his internal assessment, as well as receive support and encouragement. I.e., the rubric was found to be extremely efficient, as long as it is accompanied by mediation. Otherwise, it may be subject to personal interpretation of the student, thus missing its purpose. External evaluation may expand the student’s perception and enable him reach an understanding, he would not be able to on his own. The process of evaluation was not based on a normative basis. Each student proceeded on her own pace. They participated in the assessment and progress, relative to themselves only, thus reducing their level of anxiety. There was no situation of success or failure, but a process of learning, in which one may try and err, without any competition. This method of learning complies with Levin’s and Nevo’s (1998) conclusions, regarding the development of personal commitment to learning and radical building in of new knowledge – all of which may happen only in an atmosphere as this. Yet another inference, unrelated to content, but rather to the process, is the fact that the researcher is also the instructor of the course. This may stop the participating students from expressing their spontaneous and authentic opinions, knowing they are going to be evaluated by their

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instructor. This may lead to a situation in which they will give answers they know the researcher prefers, thus creating social volition. On the other hand, the closeness and openness between the students and the researcher encouraged them to tell he about many personal things, illuminating their performance in the course, and helped her understand and analyze their behavior. By reflecting, they could experience awareness and connect what they said with what they did. During the personal sessions, the students lapsed sometimes to personal contents, be it by sharing their personal problems with the instructor, or telling her some intimate things. Some of these were identified as manipulations and shunning of the course’s contents, which may be problematic if the instructor does not notice it. Stories are good, but the students should be led to the desired places, so they can make the most of these training sessions. Both the overt and covert stories have to be unveiled, at the same time relating to parallel processes taking place between the instructor and the student. The conclusion is that in a course of this type, involving training, the instructor should be – in addition to an expert on content – an expert in reflective instruction. He should lead the student to himself, and help him understand unknown destinations. Support for this approach can be found in the characteristics of reflective instruction and criteria for personal evaluation, mentioned by Schon (1987, 1988). To sum up, we could say that each student has a different, unique sense of efficacy, knowledge and reflection. The course proved that each and every one of these fields can be developed and improved for the students. During the course, when the students encountered pupils with emotional and didactic problems, they sometimes claimed better results with another, “better” pupil. There is no doubt that each encounter between two persons creates an interaction, unique for that specific encounter and these persons. As an instructor, in retrospect, I can conclude that the student – teacher – has a central role in interaction and leading of the teaching-learning process. The ingredients of the teacher’s personality are the ones enabling him the ability to identify, respond and choose the appropriate strategy of action. The message is that responsibility and commitment are always on the teacher’s side, and he is the one to search and find, what in his interaction with the pupil may change the pupil’s conduct, and what he – as a teacher – can do. With regards to the working model of the course, I can say it increased personal growth, self-guidance, intensity and many other changes among

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the students who participated. Still, the course should be improved and made more efficient. Recommendations, based on the study conclusions, will be brought in the next chapter.

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Chapter 6 Recommendations

One recommendation of this study concentrates on the need to combine theoretical lessons in the students’ work with their pupils. These lessons should refer to emotional and didactic aspects of the pupils, and expose the students to various teaching methods. Even if these things were studied in the past, they should be repeated from a different angle, and tied to the present situation of experiencing. Thus, it will help the students to create connectedness, as argued by Gardner (1991), who claimed there should not be any gap between situations in which the knowledge was acquired, and those in which the student is required to practice this knowledge. The more the situations of knowledge acquisition are closer and similar to those in which this knowledge should be used – the more the chances of creating an active, usable knowledge. Therefore teaching should take place in authentic situations, which will lead the students to professional knowledge which will truly integrate theoretical knowledge and experiencing. It is advisable that during the course, each student shall have the opportunity to work with pupils of different ages, according to his/her interest (unlike this course, in which all the pupils were fourth graders). This way will increase the students’ motivation, and will be more significant and relevant for them. In addition, there is the opposite option: Each student will experience working with different ages, which will increase his experience and prepare him for field-work. The assumption is that not always is it possible to work with ages preferred by the students. We also recommended that reflection be incorporated in the training process. One way to do it is “joint learning” and “peer learning”. In this study the peer learning was rather scarce, and the students presented their work with their pupils only at the end of the year. It is advisable that such joint work be presented more often during the year. Such presentation should refer to the purposes, working method, difficulties and dilemmas raised during work, and the way of coping. By being exposed to individual varied cases, the students will get insight regarding general phenomena, learn from each other, regard problems as legitimate and support each other. There is another possibility, of the instructor selecting specific events of the students’ work (based on observations, summaries or training sessions), to be a starting point for discussions and reflective dialogue.

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A reflective dialogue between several students, guided by the instructor, applies the benefits of joint learning and creates a framework for cooperation. It also exposes the students to various ideas, a joint examination enriching the individual, a platform for personal knowledge, personal extroversion, feedback give-and-take, and support of peers to help them overcome their difficulties. It is another opportunity to raise one’s voice, in addition to the training sessions. During the lessons, it is advisable that the students observe each other, giving feedback on their work, thus every one will get several opinions and feedback, not just the instructor’s. The students may, then, get some insight regarding themselves. According to the constructivist approach, too, acquiring knowledge is a combination of an individual and a social process. This approach argues that the process of learning is well-anchored in social aspects, among which are distribution and sharing of personal knowledge (Hewson et al., 1998), by way of dialogue. The dialogue – as some sort of conversation - allows us to accept variance, mutual respect and open mindedness. It also enables the student to move from an existing level of development, already completed, to a higher level. Such transition depends on learning assisted by social mediation. Vigotzky (1978) argues that the new knowledge is built up within a ”The Zone of Proximal Development”. This area is the range of development between the real level and the potential, higher level, which the students may reach after mediation. Social mediation enables the students proceed in building up their knowledge, with the assistance of others (Penuel & Wertsch, 1995). Joint observation of each other, followed by dialogue, may enable that. We also recommend the use of a video camera during lessons, as a tool to develop reflection and studying of peers. Students should be photographed during their work with pupils. This way, they can watch themselves and their pupils authentically. Following the joint viewing, a fruitful discussion may develop and they could evaluate their work better than just by feedback. Watching the films by colleagues can be very useful, provided it is agreed by all and does not constitute a threat. One can also watch the same film several times, or selected parts of it, which have to be emphasized. Using video filming is also useful when training session are not held immediately after the lesson. The students should keep close contact with the home-class teacher of their pupil. Both teacher and student should be updated and made aware

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of what happens during the lesson. This can be done by a “contact notebook”, telephone, or any other method agreed upon. The same contact should be kept with the pupil’s parents. (one must remember that the course, though combining actual work, is held, in fact, in laboratory conditions, which is not the pupil’s natural environment). This method can be a model for systemic work with the pupil. The teacher works at school jointly with other teachers teaching the same pupil. He also has to be in touch with the parents. All these issues if team work and working jointly with parents are not studied during regular training, and should be studied because of their importance as part of the teacher’s job. These things may be applied already during the course, by holding part of the lessons at the pupil’s own school (instead of the college). Application of this recommendation may be another way of assisting the students in their first steps in teaching. Another recommendation is the need for combining the study (done by students) as part of the theoretical part of the course. Though the work in the course does combine study elements, still, a built in study may increase their awareness of the complexity of the situation, and deepen their knowledge. Experiencing research can increase their curiosity and help in deepening their insight. It may raise subtleties up to the surface, help in using various kinds of knowledge and improve reflective thinking. Research can be a lever for professional growth of the students, as well as teachers. This idea is supported by Alpert (1992) who claims that the teacher is the one who should study and evaluate his own work, rather than outside persons. The culture of research should be nurtured to make teacher-researchers, who will turn research knowledge into public knowledge. Doing the research by students will be both a personal and public contribution. This issue should be looked into in future studies. Finally, we should examine to what extent the attention given during the course is reflected in the student teaching in the long term. This issue, too, should be examined in future research.

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Chapter 7 Summary

Analysis of the students’ pedagogic diaries, the observations, training sessions and personal interviews during the year – all indicate the same tendency of development on the students’ side. The results of the study show that such development was indeed significant, with each one experiencing the process in a different dosage and manner. The students participating in the course started their route from different starting points, proceeded on their individual pace and reached their own finish lines at the end. These findings enable us to identify, expose, characterize and understand their progress in the subjects examined, and comprehend the intervening factors that created the changes, according to the purposes of the study (see ‘purposes’ chapter). All the study assumptions have been confirmed (see ‘assumptions’). Experiencing individual work with a pupil having problems in math, twice a week, combined with training and feedback sessions, as well as written feedback after each lesson, caused the students to change extensively. The study has proven that the way to cope with one’s apprehensions is to touch and deal with their cause. It is a rather significant conclusion, both for the process of training and for the parallel process and the message for the teachers. In addition to the expressed changes observed following the assumptions, other changes took place, as expressed by awareness and profound understanding of complex teaching situations, reflective development and insight. These changes cannot be measured and quantified accurately, since they are qualitative, but they were expressed in the personal reports. By their work with the pupils, and the reflective training accompanied with support and receptive ambience, the students discovered new things about themselves and their abilities. The contribution of the course to the students has been in the cognitive, as well as emotional and practical level. Beyond the natural process of socialization, as described in Fuchs’s (1995) model, the course had a relative advantage of my intervention as instructor, which was significant, just because of the fact that the course dealt with math teaching – a subject causing anxiety and recalling previous failures in the students’ past. The intervention model was efficient, but it should be developed according to the conclusions of the study and its recommendations. We

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should compare whether this intervention model will be effective also in training teachers for other subjects, not as stressful as math. The training in the course emphasized the students’ independence and autonomy, so they managed to gradually move from dependency in me to cognitive, emotional and behavioral independence. The joint training style, carrying the message of respect and mutuality, encouraging the expression of personal voice, created a sense of self-esteem. It also generated exposure of knowledge, increased the ability and skills of dealing with various teaching situations. The mutuality in planning the moves and training goals gave the students a feeling of control over things, and enhanced their motivation and commitment. Such mutuality is even more important in the presence of apprehension and fear, since it can relieve them and enhance the student’s sense of value. The students’ development in the course was gradual. One should take into consideration that training teachers of discretion is a prolonged procedure, especially if they are to be meaningful. The course proved that imparting skills and strategies foreign to the existing repertoire, requires more than just basic teaching and training, or a one-time workshop or lecture. Usually it requires a change of thinking, change of standpoints and the teacher’s customary conduct, (Fuchs, 2002). Gradual training allowed a real, slow growing instead of a sudden turnabout. Our training program was in agreement with both their needs and interest, giving an answer to the differences between them. Each one worked at her own pace and capability, with total approval, because – among others – no pressure whatsoever was put on the students, to teach a specific amount of material. Our training was characterized by the need to respond to individual needs, both in content and strategies. Only this way the students could organize the newly acquired knowledge, events and contents into their basic cognitive structures, giving them the personal relevant meaning. The training also concentrated on self-direction – a mental complexity which enables adults to acquire skills to enable him cope with reality and be effective. The skill of self-direction gives a person control over his learning and development. In order that teachers be independent, effective, self-directed learners, they should learn how to learn (Fuchs, 2002).

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The training in the course kept the balance between support and actual assistance on one hand, and reinforcing the student and her own responsibility and independence. This balance is extremely delicate and requires a great deal of sensitivity on the instructor’s side. Too much help will cause dependency and curb development and independence, whereas a feeling of deprived assistance can weaken and frustrate, thus impair the confidence and self-image. All through the course the students received feedback, which created a motivation to learn and change. In spite of the lack of confidence transmitted by the students at the beginning of the year, I could notice a large amount of knowledge and insight. The constructivist theory was applied during the training so that the students implemented reflective procedures on their activities. We could sum up and say, that the training in the course focused on several emphasized points: The first one is reflection, acknowledging teaching as a practical-reflective occupation, being aware of the possibilities of reflective procedures to cause changes in teaching trainees. Teaching and reflective training enable the trainee to examine critically his experience and experiencing. It is a reactive teaching, in which the teacher is aware and sensitive to the response of his pupils. He is open to surprises. Trying to expose his pupils’ responses and understand them. He examines his own conduct against that of his pupil, looking for the best suited alternative to help him construct new knowledge or correct the mistaken. Increasing the trainee’s awareness to the importance of reflection is imperative, as well as involving him in reflective behavior, and allowing him understand its potential as an integral part of the teaching progress. Another emphasis in training is the developmental one. Developmental training is basically differential and individual-tailored (Fuchs, 2002). It is based on acknowledging the difference between the trained persons, their experience, their ability of conceptualization and the manner in which they grasp themselves. Training puts the teaching trainee in the center of the process, and requires a long time. Assistance and training should be matching to his personality and his level of thinking. In our course, each student was trained according to her own needs and personal level. In addition to the above-mentioned aspects, there was the self esteem aspect, based on the students’ ability to analyze and evaluate her behavior

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with the pupil. This assumption derives from an objective perception of teaching, and from the belief that teaching trainees can identify their efficient teaching, and that systematic self-analysis, together with shaping evaluation, can make changes (Fuchs, 2002). The purpose of this emphasis is to develop the student’s ability to analyze his teaching, in connection to the principles of good teaching, so he could improve his work. The training at the course (by training sessions and lesson summaries) developed the ability of self-evaluation, to identify the strong and weak points – which is a complex skill, demanding of the student high awareness of his teaching behavior. Due to the developmental, emotional and mental difference between the students, this process developed differently for each one, still awarding them knowledge and profound understanding of criteria for quality teaching. The recent trend in teacher training is of inquisitive character, replacing that of skill control. It does not underestimate the control of teaching skills, but rather regards them as a mean and not a target in itself. Models characterizing this trend are based on the assumption that the more the teacher is aware of the origins of his actions and their results, able to examine the effect of the ambience he is acting in, the better his control of teaching skills and his conduct. In addition, there is the personal trend, based on humanistic liberal ideas and peidocentric approach. This approach attempts to increase the psychological ripeness of teaching trainees, as well as emphasize the importance of the students’ system of perceptions, standpoints and beliefs (Fuchs, 2002). During the course’s training, both trends (inquisitive and personal) were integrated, believing that they would help the students fully express their potential, especially when anxiety-causing situations are concerned. In that aspect, the issue of teacher training is undergoing many changes. The search for a training program that will respond to the needs of a third millennium education system, characterizes the system in Israel too, and there is still no agreement about the desirable program. Those who regard teaching in class as an applicable science, strive for a training that will grant extended theoretical knowledge on one hand, and enable vast field experience on the other – thus the trainees will apply the theoretical principles in teaching situations in class. Against them there are those who regard teaching as a practical-reflective occupation, and support the approach of getting the student closer to real situations of using knowledge (Silberstein, 1999). This perception is more prevalent and emphasized these days, by policy makers. In both approaches, training

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occupies a central place in mediating and connecting theory and practice, and in making of reflective teachers (Fuchs, 2002). Thus, there is a need for professional training of teachers in college. These teachers should have high reflective skills. They also have to expand their practical-applicable aspect, and their field experience together with their pupils, so their instruction and accompaniment are significant. Teacher training should focus on the process of teaching, rather than on its technical performance. It is about inserting new elements into the practice of teacher training, by transferring the dominant emphasis to internal observation, and the constant coping with himself (Rand, 1992). There is no doubt that by doing that, we can increase the teacher’s open-mindedness regarding innovative teaching and learning methods, which require sometimes giving up of the sure, familiar way, in favor of the unknown and unexpected. It is, no doubt, a harder way, but in spite of the difficulty – or may be because of it – is holds many chances of great promise of success for the intervention process practiced by the teacher. Furthermore, we can contribute – indirectly but significantly – to the shaping of our pupils as citizens of open mind in the dynamic world we live in, to efficient self-control essential to activate processes of change and maximum efficiency in both personal and social adaptation.

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Chapter 8

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Appendices Appendix No. 1 STARTING ON A NEW WAY … WORKSHOP FOR MATH. TEACHERS October 2001 Liora Givon Student’s Name: ___________________ 1. Have you ever experienced teaching; if so – where, with what population and for how long? ________________________________________________________ 2. Have you ever experienced math teaching for regular children or children with learning disorders? If so, please detail ________________________________________________________ 3. Why did you choose the course: Specializing in Corrective Teaching of Math? Please detail all your reasons ________________________________________________________ 4. Do you have any apprehensions? If so, why and of what kind? ______________________________________________________ 5. Do you feel confident enough to work with pupils and teach math? _______________________________________________________ 6. Do you know how to teach math? ________________________________________________________ 7. Do you feel any objection to the course? If so, why and what kind? ________________________________________________________ Have you ever experienced performing a didactic diagnosing in math? If so, where and who did you diagnose? ________________________________________________________ 9. How much are you motivated to work with pupils having difficulties in math? (During the course, and in general?) _______________________________________________________ 10. How do you assess your skills as a teacher, and a math teacher? ________________________________________________________ 11. Do you like the subject of math? ________________________________________________________ 12. Do you like teaching math? __________________________________ 13. What feelings does this course evoke in you? ________________________________________________________ 14. What are your expectations from this course?

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_______________________________________________________ 15. What, in your opinion, is the most important part of the course?

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Appendix No. 2 The Kibbutz College - School of Education Course of Special Education Information Gathering Rubric for the Pupil; Summary of Diagnosis and an Interference Program Proposal. By: Liora (Karp) Givon Criteria Goal not

Achieved Goal Partially Achieved

Goal Fully Achieved

Background about the pupil (info.)

Relating only to a small part of the criteria given by the “profile” page. Mixing of facts and assumptions.

Partial description of part of the “profile” page criteria. Relation based on impression in judicial terms, facts and no analysis of findings.

Thorough relation to all subjects in the “profile” page, in addition to examples observed. Definition between facts and assumptions and analysis of assumptions.

Summary of Diagnosis in Math:

Pre-Diagnosis Performing part of the task list prior to diagnosis.

Performance of all tasks with no records of the pupil’s performance.

Performance of all tasks, including detailed records of performance, behavior and responses of the child to the tasks to be performed. (as per the required pre-diagnosis tasks in the page).

Basic Arithmetical Tasks

Performing part of the tasks, not writing reasons or rationale for not performing the others.

Performing the tasks, not detailing or recording – i.e. no report of the activities the

Full, or partial performance of tasks, with detailed rationale. Detailed records, including what the

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child was required to perform, and not detailing what he knew, or did not know, and how he acted.

child performed, how, how many out of how many etc’, and relating to quantitative description.

Summary of the Mathematical Aspect

Relating on a judicial level to part of the subjects in the mathematical aspect list, i.e. describing the mathematical knowledge without linking it to the child’s behavior during diagnosis. For example: ‘Knows the four basic arithmetic functions” or “no arithmetic understanding”

Relating to all the subjects on the math. Aspect list; descriptive, rather than qualitative analysis. Relating to strong points, and those to be strengthened, but no explanation, examples or arguments explaining mathematical functioning qualitatively. Such as: “Recognizes the procedures of doing arithmetical exercise.

Thorough, qualitative analysis of all aspects, relating to strong points and those to be strengthened. Linking the findings of the analysis to the level of performance with examples and back-up. Such as: “Familiar with computation procedures and arithmetical laws, which is demonstrated when …”

Summary of Functional - Cognitive Aspect

Relating to part of the subjects in the functional-cognitive aspect. No details.

Descriptive relation to all subjects in the functional-cognitive aspect. No relation to strong points and those to be

Thorough qualitative analysis of all subjects of the functional-cognitive aspect. Relating to both strong points and those to be strengthened.

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strengthened. No linking of difficulties in math to functional cognitive level.

Linking the diagnosis findings to the functional-cognitive area. Assumptive analysis including examples and back-ups. Example: “Significant memory apparent, and expressed when required…”

The aspect of Interference

List of five aspects of interference in he mathematical area (general) and general target in the therapeutic, cognitive or functional aspect.

List of five interference aspects, irrelevant to the child’s profile, needs or the analysis results.

List of five interference aspects, which do express gaps in knowledge, but are not appropriate for the child’s needs.

Relating to five relevant aspects, according to the child’s profile, needs, strong points and those to be strengthened following the diagnosis. The list is well argued and accurately phrased. The purposes, measurements and areas may well promote he child.

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Appendix 3

Lesson Layout Plan

Student’s Name: __________________ Date: _________ Subject of the lesson : _______________ Pupil’s Name: ____________________ No. of lesson: ________ Duration of lesson: ______________ Designated purpose, regarding Math: _____________________________________________________________________ Designated purpose, regarding emotional-therapeutic-functional areas: _____________________________________________ Tasks the child has to perform

Time Division

Considerations in Choosing Activities

Details of Means and Accessories

Considerations for Choosing means and Accessories

Records of activities during performance

Lesson Summary No. _____ (to be attached to the lesson plan) 1. Was the purpose of the lesson – related to mathematics - achieved, and if so, how did you see it? If the purpose was not achieved, what, in your opinion, was the reason? ________________________________________________________ 2. Was the time division appropriate? If so, how did you see it? If not, please try to assume the reason?

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3.Did the accessories and activities match the requirements of the student, and the content of the lesson? Please give your reasons. 4. Was there any gap between the plan and the actual lesson, and if so – why? 5.What difficulties did the student experience, how did they express, and what was your reaction? 6.Did you experience any difficulties or frustrations at the lesson, and if so – what were they and how did you cope with them? 7. Did any special need, on the student’s side, appear during the lesson, how did they express and how did you handle them? 8. What did you learn about yourself during the lesson? 9. What have you “taken with you” from the lesson, and what are your plans for the future? Notes (reflections, emotions and further remarks …)

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Appendix No. 4 The Kibbutz College - School of Education Course of Special Education Rubric for Layout and Summary of Lesson. By: Liora Givon Criteria Goal not

Achieved Goal Partially Achieved

Goal Fully Achieved

Designated goal in the area of knowledge (mathematics)

Designated goal is not clearly phrased, and is not linked to the subject of the lesson and the general target set following the analysis.

Designated goal is linked to the subject of the lesson and to the general target set following the analysis. Target is not clearly phrased and is not measurable.

Designated goal is related to the subject of the lesson and to the general target set following the analysis. It is also measurable and clearly phrased. It indicates what is required of the pupil. For example: To do addition and subtraction exercise, within 1 – 20.

Designated goal of therapeutic nature

Goal is not clearly phrased and is not linked to the general (therapeutic) target set following the analysis.

Designated goal is linked to the general (therapeutic) target, set following the analysis. It is not clearly phrased and is not measurable.

Designated goal is linked to the general (therapeutic) target, set following the analysis. It is clearly phrased and measurable. It indicates what is required of the pupil. For

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example: Write instructions for a mathematical game.

The actions the pupil has to perform and considerations in choosing them

Activities are not linked to the designated goal of the lesson. They are not operatively phrased and not linked to each other. No relation to any deliberation in choosing the activities.

Activities are operatively and clearly phrased. It is clear what is required of the pupil on the behavioral level, but the activities are not derived from the designated goal, and not related to each other. They are also not measurable. Alternatively, the activities are graded, linked to each other, though not clearly or operatively phrased, and not measurable.

Activities are operatively and clearly phrased. Activities are linked to the subject and designated goal of the lesson. They are measurable, linked to each other, and graded in a logical ascending order. The activities match the pupil’s needs and each activity defines what behavior is required from the pupil.

Means and Aids Means and aids are monotonous and not aesthetic. They are inappropriate for the purpose of the lesson and for specific actions the pupil has to perform. No relation to consideration in

Means and aids are linked to the purpose of the lesson and to the specific activities. They are monotonous and unaesthetic. Alternatively they could be aesthetic and varied, but not matching the purpose of the

Means and aids are varied and aesthetic. They can be used to teach contents that match the purpose of the lesson and various activities. They also match the pupils needs. Considerations for choosing

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choosing them. lesson, the specific activities and/or the pupil’s needs. The considerations for choosing means are not clearly phrased and there are no arguments.

them are clearly phrased, detailed and logical.

Planning the time distribution

No time distribution according to the activities the pupil has to perform.

There is some time distribution, but it does not match the activities the pupil is required to perform, such as: Allocating time for time consuming activity.

There is a realistic time distribution, matching the activities the pupil is required to perform. Time distribution matches the performance and needs of the pupil.

Recording of activity as it is performed

No relation to any recording of activities as they are performed.

Partial relations to recording of activity. No detailing or description of how the pupil performs. Partial recording of activities.

Full recording of every activity. The description is clear about the pupil’s performance of activities.

Summary of lesson

Summary is both descriptive and judicial, not detailed and has no reflective observation. Not addressing all the questions in the summary

Detailed summary, but no reflective observation, that will testify to the student’s learning and drawing of conclusions

Detailed summary relating to all questions presented in this section. Demonstration of reflective observation,

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page. regarding the teaching - learning process

relating to teacher’s responsibility in the teaching - learning process. Demonstrating consideration in choosing activities and realization means; learning and drawing of conclusions with regard to the teaching –learning process during class.

No relation to the emotional dynamics of the pupil.

Minimal, judging relation to the emotional dynamics of the pupil, without any analysis of the reasons, such as: Fear, stress (no argumentation).

Detailed relation to the emotional dynamics of the pupil, understanding of his needs, as well as an attempt to analyze performance and behavior during the lesson.

No relation to further work.

Relating to further work in descriptive phrases, but no argumentation for the professional reasons.

Relating to further work by description of future subject/s, with professional arguments supporting it.

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Appendix No. 5 Half Way Through – Workshop for Teachers Specializing in Math - March 2002 Student’s Name: ________________ 1. Do you feel that the diagnosis performed at the beginning of the year has helped you to better understand the pupil’s performance in math. Please answer in detail. ________________________________________________________ 2. Do you feel that putting the diagnosis and purposes in writing have helped you? If so, in what way? ________________________________________________________ 3. At this stage, do you feel more confident in your work with the pupil? What is the cause for this improved confidence? _______________________________________________________ 4. Do you feel now that you know how to teach math? What were the reasons for that? ________________________________________________________ 5. Do you still have any apprehensions regarding the course? What exactly are you apprehensive about? _______________________________________________________ 6. Does putting the lesson program in writing help you? In what way? ________________________________________________________ 7. Do you feel any improvement or change in your ability to plan lessons since you have started to give them? In what manner? ________________________________________________________ 8. Does summarizing of lessons in writing help you? In what way? ________________________________________________________ 9. Does the feedback on the lesson plan and summary help you? If so, how? ______________________________________________________ Do you feel capable of coping with the pupil’s emotional and educational problems, as they arise during the lesson? How do you cope with them? __________________________________________________ 11. Do you feel any change in the way you have been working since the beginning of the year? What are the changes, if any? ________________________________________________________

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12. Can you translate the purpose of your work into applied work with the child? Thanks to what? ________________________________________________________ 13. Are you sticking to the work-plan sheet you have made, or do you change things as the lesson proceeds? What are the reasons for the change? ____________________________________________________ 14. Are the training sessions of any help? In what way? ________________________________________________________ 15. What new properties have you discovered in yourself during your work with the pupil, in the course? Please answer in detail. ________________________________________________________ Please add any other subjects, not mentioned in the above questions. ________________________________________________________________________________________________________________ Carry On and Good Luck ! Liora Givon

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Appendix No. 6 Summing Up the Year! Reflective Summary of the teachers’ workshop specializing in mathematics (June 2002, Liora Givon) What have you learned about yourself during the year? How would you sum up your personal and professional development during this year? How did the workshop contribute? In what manner do you feel you have improved? Have your initial apprehensions disappeared, and if so – why? Did you achieve the educational goals you set for yourself, following the diagnosis at the beginning of the year? What have you learned about the student during the year, and what will you retain for the future? Did the workshop give you an experience of success? Why? How do you evaluate today your skills in corrective teaching of math? Do you feel now more confident in your work with students experiencing difficulties in math. If so, what do you attribute it to? Did the preparation of layouts assist you? Have you learned to grade a work-plan? Looking back, what would you add or withdraw from the workshop? Please add any other notes or remarks you regard as relevant and important, that may improve the process you have gone through.

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Appendix No. 7 Self Assessment Please give yourself a mark, and verbal assessment in the following subjects: Subject Mark Verbal Assessment Info-gathering about the pupil Acquaintance session Summary of diagnosis Feedback for diagnosis Preparing regular lesson layouts Planning lesson layouts (purposes and goals)

Using various means of demonstration, and adapting them to the child

Summarizing the lesson plan Attitude to the pupil and his difficulties

Keeping a “connection” note book

General participation in the lesson

Regular attendance General assessment Notes and remarks:

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Appendix No. 8 Reflective Summaries (Presented in random order, not by the student’s number in the course) Reflective Summary No. 1: I came here at the beginning of the year, without any real professional knowledge of math, or math teaching. For me it was the first time to experience math teaching, in fact – my first acquaintance with the world of mathematics. I was quite apprehensive of the subject, both due to the above-mentioned reasons, as well as my personal traumatic experience with math, as a pupil. With that negative load – I started to work with my pupil. One could say that for me, the first semester consisted of groping in the (almost total) dark, with no knowledge of the path I should take. I was very tense, did not feel I actually knew where I was taking my pupil. In fact, I hardly felt like a teacher – in the sense of showing someone the way. As a result, the interaction between us was rather awkward. I am sure, much of my fears and insecurity was reflected in the relations between us. My pupil, being rather reticent, was aware of my feelings, which resulted in minimal connection. All we talked about was the content of the lesson, and nothing more. This is, more or less, how the first semester looked like, making me feel no progress was being made. On the second semester things started to change, following the understanding and insight I acquired. I began to understand the things I did not understand (after reaching a dead end with my pupil), and soon teaching became easier. I was more relaxed during lessons, I knew what I was going to teach and was more attentive to his problems, I adapted myself to him, changing subjects when he showed signs of tiredness. At the same time, the bond between us increased, he opened up and started to talk more about subjects other than math, feeling more comfortable. I feel I have gone through an important process this year, experiencing, for the first time, the teaching of a subject I had not known well, and feared of. Today, I am less anxious of math teaching. The experience of

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not knowing made me understand better what I really understood and what I did not. I realize I have internalized some very important principles, such as knowing what I know and what I don’t, not to teach what I don’t know and not to be afraid to ask and clarify. Most important – I learned to be attentive to the pupil, to mediate between him and the taught subject and create a relaxed atmosphere to support his learning. Now I know I have the capacity to conduct a good, built-in lesson. I can assess the pupil’s capacities and plan the time correctly. Just as I started to understand all this – the year ended. One of the most important things I have learned, is not to be afraid of difficulties, not to attempt to shove them out of the way, but rather try and tackle them, understand them and see all their aspects. Difficulties are an integral part of any process. I feel that both of us (my pupil and myself) have grown during the process. At first, I was afraid to ask him about his problems, but during the last lessons I ventured to do so. Sharing my own sense of confidence with him made him admit his own difficulties. I feel it is only the beginning of a long journey, called ‘math teaching’, and teaching in general. I still have a long way to go, but I am glad of having chosen the course and of the experience – difficult as it was – which enriched me. There is still much theoretical material to be studied. I had many moments of frustration, about the slow progress, but your approach, claiming it to be a process of experiencing and not something measured in how much I managed to teach, was of great help to me. Even writing of lesson layouts and summaries, which looked rather useless at first, made me see – through feedback – my own doing in a different light, and gave it a meaning. To sum up, Liora, much of it all was thanks to you, your attitude, respect and sensitivity, with which you treated us; and the fact that you made it all legitimate – our fears, apprehensions, and the will to learn. Thank you from the bottom of my heart – may there be more teachers like you!

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Reflective Summary No. 2: It was a year filled with experiences – some good, and others difficult. Working with my pupil was pleasant and easy-going, though sometimes rather exhausting and awkward. I had the privilege to work with a special boy, polite and sensitive, patient most of the time and cooperative – and I enjoyed it extremely. It was, undoubtedly, an important experience, which included personal and professional growth. Since I am aware of my weakness regarding math, and since I wanted to have some additional training, I chose to participate in this course, specializing in math teaching. It seems that in some ways I managed, indeed, to overcome my apprehension of math teaching. I acquired knowledge in math teaching, in dividing the subject into stages, devising presentation methods and strategies. All these enriched me personally and professionally, improving my confidence and enabling me to work with my pupil and instruct him confidently. Every small success of my pupil encouraged me and increased my confidence in the method, I had chosen to work with. I learned a lot from him. I learned to accept his way of thinking, the strategies he was using, his thinking errors, as well as his difficulties – including those he would not admit to. In most cases I managed to help, to propose an alternative way and encourage him with the experience of success. The boy is extremely sensitive and gentle, and at the same time - stubborn. His problems presented a challenge for me, to keep explaining until he understood the subject. Sometimes he would be troubled and sad, which would make me feel quite helpless, watching his distress, which he refused to share with me. I accepted and respected his choice to go on with the lesson, tried to encourage him and make him feel better (even if it required making changes in my original plan). Most of the time he cooperated, complaining only rarely. Though such cases made me feel bad, I was glad I could pull out of them quickly and encourage him to work. Regarding work – the first analysis assisted me in personal and didactic acquaintance, giving me a good picture of his work style, as well as his strong and weak points. It also gave me a good idea of his behavior and ways of coping, allowing me to make an appropriate work plan. Lesson layouts, translating my ideas into operative purposes, helped me to organize my thoughts and focus on the required subjects. With time, my phrasing improved too. The layouts helped me to come to the lesson well prepared, knowing clearly what I was going to do. Later I managed to be more flexible, changing and improvising. The regular feedback

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following each lesson assisted in organizing further work and adapting of the subjects and auxiliaries. Today I realize I proceeded too quickly in problems of two phases. I returned to previous stages only after realizing my difficulty in the subject. I realized that when the pupil is distracted, he relates only to the first phase of the question, having difficulties with the second; or he identifies what is required of him, but has difficulties performing, and makes mistakes. I feel that the level of my understanding is higher now, both of the subject itself and the way it is constructed. I realized I could promote a person and help him see the positive aspects of the subject. I can say now that I really love mathematics. The therapeutic goals I chose to concentrate on were as follows: Nurturing and improving his self-image and confidence, and increasing his span of attention. I tried to give him experiences of success, show him his strong points and encourage him. It seemed to enjoy and internalize them. During the year, I noticed he was more comfortable, and rather proud of his achievements. In order to cope with his short concentration span and interrupted attention, I tried to work in a structured manner, with short tasks and repeated familiar working methods. I took breaks between tasks, and if needed, I verbalized the process helping him re-concentrate. Still, often his thoughts would wander, which would impair his performance and control. I also realized that eventually I had to be more flexible and adapt myself to his needs. Regarding the course itself, I could use more lessons dealing with teaching methods, which would contribute to our work with the pupil, and our future work. Also, The connection with the school should be re-examined. I felt more cooperation would be in place, in order to adjust the subjects taught, and tie them to the subjects taught in class, as well as updating the teachers about the pupil’s emotional state. I see this course as an important experience. In spite of my personal problems in math, I realized I could contribute, promote and help my pupil. I also learned to see his strong points and make him aware of them. Today, I am stronger, having better skills to make an appropriately adapted curriculum, as well as teach it – being strict or flexible, as required.

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Reflective Summary No. 3: I chose this course of math teaching for two main reasons. The first one was my own insecurity about math, following previous failures in math and a feeling of helplessness facing it. The second was lack of orientation in the subject’s aspects, knowing just a few teaching methods, means and auxiliaries, and pure ignorance of what is taught in various grades. At the beginning of the year I was confused and rather helpless, having to decide which subject I wanted to choose, how to chose them and how to adapt them to the pupil’s needs, with regard to the therapeutic purposes. At the beginning I faced new challenges, which were rather hard on me, having had to cope with them for the first time. What made it somewhat easier was the instruction and guidance I received, the accepting atmosphere – allowing experiencing and making mistakes, and realizing that what I was doing was, in fact, the right thing. Professionally, I learned how to set goals, following didactic findings, how to phrase them clearly and matter-of-fact. I learned how to divide the subject I wanted to teach into several phases, including relevant lesson layouts. The more lessons I gave, the easier it became to discern between an operative purpose, means and clear phrasing. Regular feedback helped the process of reflective thinking after each lesson. I would then ask myself if the tasks were suitable to the point the pupil was in – didactically and therapeutically – how I acted and reacted to his manner of learning and what needed to be improved or changed. Also, in working with the pupil and analyzing his coping with the subjects, I learned that each subject is made of many sub-aspects, the control of one of which did not assure control of others. Vice versa – lack of control in one subject did not necessarily indicate problems in others. The more I advanced with the process of learning, the easier it became to separate the areas and check where he has difficulties, strengthening that subject accordingly. At the beginning of the year, I made use of ready, available material, relevant only to the subjects I taught, without any previous examination or control. The feedback from the pupil, together with that of my instructor, and the summary I wrote after each lesson, helped me use my criticism and see whether what I taught was relevant to the pupil’s daily life and his didactic development.

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The individual nature of work was not easy, but gave me the opportunity to examine whether it suited me at all, and how I operated interactively with a single pupil. The rather intensive, “cramped” relations with the pupil were hard on me. I felt his need to “draw a new rabbit from the hat” every lesson. I had to rouse his interest and curiosity, and be interesting, intriguing, creative and original, which made the lesson planning rather long and tiresome. In addition, I felt my individual work with the pupil made me face some crucial aspects in my personality. One of them was my difficulty to allow him make mistakes. I found it difficult to allow him the process of “trial and error”. No doubt, my own self-criticism is the source of the problem. As long as I did not allow it to myself, it was impossible for me to let my pupil know that trial and error is part of the learning process. What I did, by my fear of mistakes, is depriving him of enough opportunities to enjoy self-learning, his own initiative and a sense of confidence. All along the learning process he depended on the “crutches” I offered him, and waited for my approval for everything he did. In spite of the difficulty in individual work, it holds many advantages. The direct effect of the learning process on the pupil’s progress can be easily measured. One can also create an ambience suitable for his needs. The action range is large and allows the use of means and auxiliaries – manageable with larger groups of pupils as well. I feel that the pupil indeed gained something by our mutual learning process. I realize I managed to rouse his interest and curiosity. His progress is evident, both didactically and therapeutically. The large number and variety of means I used, motivated his learning and progress and helped him overcome his own lack of confidence. Another inner struggle I experienced during most of the year was the question of boundaries and limits. Where I should pull the rope and when release it, so as to enable him a larger space. On the one hand he needed lots of affection, acceptance and support, as well as positive experiencing. On the other, I found out he took advantage of every loophole he could, and required clear, strict boundaries to feel secure. The more I progressed with the lessons, the more I realized I found the balance between the two. Toward the end of the course I felt the pupil’s stress – due to the final exam, or maybe just the end of the course and the parting. I, for one, felt rather helpless. I did not want to add additional pressure, not knowing how to help him cope with the situation.

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During the year, I felt I could relay acceptance, support and progress. I could see his will and enthusiasm whenever he came to class. To sum up, I have some proposals of change. It is important that the students share their problems, in developing original and creative devices, and in providing advice and solutions for similar problems. Also, the contact with the pupils’ school and its teachers should be tighter, to help our work with them. I would also like to point out our instructor’s serious and thorough attitude all along the year, relaying respect, openness and acceptance. Her involvement in the process of my own personal development was extremely significant. The focusing, clearing and drawing of attention to thinking processes and action methods – both mine and the pupil’s – helped me understand myself and grow.

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Reflective Summary No. 4: This year was of extreme significance for me in everything related to my professional attitude, my approach to teaching and to math teaching in particular. Until this year I could not imagine myself “venturing” into this subject, in spite of my long studies. In addition, my previous experiences were not a great success. Thus, everything related to personal image, professionally, was rather poor, though I knew I had the potential. This year, almost at its end, a change had occurred, mainly as a result of the course I have attended. I experienced a feeling of success, within a complete process of a year, ending in a good feeling. I had never imagined how significant this way would be for me, with regard to my personal image of a person who could indeed, and was willing to take upon himself everything related to his profession. One thing I was afraid of was coping with emotional problems of the pupil, expressed by her conduct during the process of learning. I had a pupil (girl) who suffered extreme emotional and didactic problems. Looking back, the emotional process in working with a girl proved to be a continuous improvement, but at the beginning of the year things were rather frustrating. I found it difficult to cope with her disobedience, stubbornness, her inclination to talk much during class, about irrelevant subjects, and her lack of concentration. The training sessions helped me see things more professionally than I saw as a student, and naturally the focusing on content helped both me and her succeed in the workshop. At this stage I realized it was both advisable and worthwhile to let her have her choice, despite our talking of setting limits, and my fears of losing control. I was afraid my pupil would not react well to my decision to let her decide, but that is not what happened. It was exactly what she needed to make her trust me. She relied on me and let me navigate the lesson eventually, knowing I was attentive. This dynamic greatly improved our possibility to study and make progress, and I am going to remember this for the future. Later, I still encountered eventual disobedience, but it did not frighten me any more. I learned to be more flexible and creative in dealing with her emotional-behavioral aspects. I enjoyed her communication skills and her sense of humor, which made things easier. Her progress and motivation well effected my own confidence as a teacher. I went through a similar emotional process, and we actually strengthened each other.

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With regard to my own development in math teaching – I learned the importance of building-in and grading of any didactic material, and the importance of practice and repetitions. Lesson layouts helped me in phrasing the goals, leaving me no other choice than practicing and experiencing such phrasing. Only at the middle of second semester did I reach a state where I could actually phrase my purposes. I realized I could keep up with my planning and teach what I had planned. I learned to trust myself and be more confident. Today I feel I have the ability to succeed in math, in spite of all. This sense of capacity is extremely important for me, to advance in other subjects of my life. In spite of all, I am sure I still need more time and studies until I can feel fully experienced and to feel fully confident in math teaching.