3.0 INFORMATION REPORT€¦ · 3.0 . Page | 2 Contents ... I wanted to present my previous employer with a comprehensive overview of the work I had done, but in addition, I also wanted

Martyn Krügel’s INFORMATION REPORT Part 2

3.0

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Contents – Part 2

Introduction Page | 4

Part 1

CHAPTER 1 The Teacher’s Guide Project

CHAPTER 2 New and Improved TEACHER’S GUIDE 2.0

CHAPTER 3 Implementing Content and Language Integrated Learning (CLIL)

CHAPTER 4 Preparatory Work for Conducting the CLIL Experiment

CHAPTER 5 The Pretests and Posttests

Part 2 CHAPTER 6 Year 4 Mathematics and TEACHER’S GUIDE 3.0 Page | 5

CHAPTER 7 Curriculum Implementation Page | 30

Part 3 CHAPTER 8 The Curios Case of Ms. Mejal

CHAPTER 9 A Continuous Improvement

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Foreword

I accidentally stumbled into the field of education when the opportunity to work as a teacher at a bilingual school in Bangkok presented itself to me in 2012. After first working as a teacher for three years, I was then appointed the head of academic affairs of the primary department of that school. In this new role it was my responsibility to put into practice academic and learning theories –as suggested and assigned by the school– with the goal of raising the academic standard and in particular the English proficiency of the students in primary who as bilingual learners, studied the subjects of mathematics, science and social studies in English.

The work I subsequently produced, steered me in the direction of thinking in terms of systems and programs, especially as it pertains to implementing curricula and also because I was being guided and informed by research I conducted. What started off as a few suggestions, I then turned into my own research and development project to create a proper bilingual program –in the very unique context of a Thai bilingual school– based upon my own initiatives but more importantly, in an attempt to address some specific needs that I had identified.

I completed the first edition of this report in November 2017 as an internal report. I wanted to present my previous employer with a comprehensive overview of the work I had done, but in addition, I also wanted a documented record for myself to be put to use in the future. After careful deliberation and also to protect the integrity of the work, I decided that it would be best to continue this work in a more independent capacity. This new second edition is an edited version of the original report –containing only the relevant information– to share some of the insights I have gained on how one could potentially go about in developing a program for bilingual primary school children who are required to learn subjects like mathematics and science in English as the second language. In addition, I also now want this report to serve as an introduction to and sample of my work because a standard résumé would be an insufficient mechanism to convey the experience I have gained. This is in line with my personal philosophy that people who can do, are people who can show.

I called the first edition an INFORMATION REPORT but this was only because I wanted to place a specific emphasis on the concept of INFORMATION in the environment I was working. Perhaps this work would be better described as a case study or research project, but now this label has stuck. Communicating in a multi-cultural environment can at times be quite challenging. In an attempt to address this, I started incorporating lots of tables, diagrams, and pictures in my presentations to convey information visually, but perhaps and on a more interesting note, is that it’s the knowledge of mathematics itself –and here I’m merely referring to primary school mathematics– that has drastically improved my own ability to visualize. Primary school mathematics is rich with wonderful tidbits of mathematical concepts that once digested can be immediately applied in practice. Maybe I’m just an old fool, but after I took a closer look at many different primary mathematics curricula and in particular the Singaporean primary mathematics syllabus, and engaged with the informational content these materials are referring to, I started thinking better. Anyhow, this INFORMATION REPORT is neither a new treatise on mathematics nor a new treatise on education, but an honest account by a concerned outsider who asked a very simple question: What are the children learning?

Martyn Krügel

Bangkok, Thailand April 2018

A few notes on style: I apologize in advance for my long sentences, I blame this on the landscape orientation of my pages. And for me to go and put commas in all the right places, will take me several ages. The bolded and capitalized words were intended to focus attention. The coloring of the tables was done purely for my own amusement. All the “I did this and I did thats”, was the tone of a frustrated

person. And all the “Based on initiatives that work”, well… That was just stating the facts.

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Introduction

8. Since the entire project can be summarized as an attempt to improve the academic standard of bilingual primary school children, it is vitally important to

take the WORK SAMPLES produced by the children and initiated by the teachers into consideration. This section contains numerous work samples, the original pre-and posttests of the Year 4 CLIL experiment, additional administrative tasks

that were completed and also some random bits of research taken into consideration for the development of the project.

7. The purpose here was to display the INFORMATION CONTENT as well as the INFORMATION QUANTITY taken

from the new and updated INFORMATION and LANGUAGE SUPPORT (the merging of the teacher’s guide and language support) from the latest version of the journals in operation

during the first semester of the 2017/18 academic year.

1. The journey started with the TEACHER’S GUIDE PROJECT conducted during the second semester of the 2014/15 academic year. This work served as a foundation for all the work

that followed.

2. The teacher’s guide project then continued into the first semester of the 2015/16 academic year starting with a new

and improved TEACHER’S GUIDE 2. 0 for Year 4 mathematics. A lot of curriculum related research occurred during this stage which was applied throughout the project.

3. During the first semester of the 2015/16 academic year the need for systemic solutions arose since the work started generating huge

quantities of information that necessitated thinking in terms of SYSTEMS.

4. Then the direction slightly shifted with the assignment to IMPLEMENT CLIL which was possible as a result of the previous

research done for the teacher’s guide project and thinking in terms of systems. This resulted in the big CLIL experiment that took place

during the second semester of the 2015/16 academic year.

5. During the 2016/17 academic year and from the insights gained from the teacher’s guide project, thinking in terms of systems and also the big CLIL experiment – I was then able to

produce EIGHT JOURNALS that were in operation during the 2016/17 academic year. During this stage the Singaporean Syllabus for Primary Mathematics came into play which

further produced valuable insights for the development of this project.

6. The COMPLETE CLIL ARTICLE submitted at the end of the first

semester of the 2016/17 academic year shed some light on the project.

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CHAPTER 6: Year 4 Mathematics and TEACHER’S GUIDE 3.0

The work done thus far and as outlined in the first few chapters produced a solid foundation that the subsequent development of the project could be based on. The Year 4 CLIL experiment conducted the previous semester also produced valuable insights, the first of which was that the design of the first mathematics workbooks were too complicated. Also, and as mentioned before, that particular design was based on the requirements as stipulated in the Basic Education Core Curriculum but for the new academic year, I had to take a closer look at the Singaporean Mathematics Syllabus since the materials that the students would be using during the new academic year would be based on the Singaporean Syllabus. As mentioned in my report dated 11th May 2017, the Singaporean Syllabus is based on a different design than the Basic Education Core Curriculum upon which all of my previous work was based:

A workbook (of this design) is an efficient medium to track and monitor exactly what the students have learned and a medium through which a school can obtain CLEAR EVIDENCE that the information as stipulated by the curriculum or syllabus (or any

other academic endeavor) has been processed by the students or not.

As a direct result of having this record of these work samples from the Year 4 CLIL experiment, I was then able to design the new JOURNALS. In the next diagram I will

list a few factors to illustrate how knowledge was gained as a direct result of the Year 4 CLIL experiment of the previous academic year.

The Singaporean Syllabus as indicated here produced a significant shift in the direction and development of my work but the syllabus itself conveys the information that should be taught to the children better (more clearly and

more succinctly) than the B.E.C.C. Some of the topics may be the same but the overall philosophies of the two programs

are different.

However, interpreting the Singaporean Syllabus was relatively easy as a direct result of my efforts to better

understand curricula materials that I continuously researched throughout this project guided mainly by my own initiatives

and ideas.

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This part of the design of the mathematics workbooks used in the CLIL experiment worked well because this section allowed for the teachers and students to work through the content

information.

However, this design was too complicated and needed to be simplified:

The language component as depicted below did not work at all. From approximately 130 workbooks submitted after the experiment, not one single student worked through the

additional language support. The main reason for this had to do with TIME because processing information and working through information and learning something always requires time and effort. It was also inconvenient and not practical to have the language

information separated from the working space which I immediately addressed in the design of the new JOURNALS:

A third valuable insight was gained through the work that Dr. Angel and I did in the pretests and posttests. Through this work, in which I formulated specific questions around key terms and mathematical concepts together with the questions being based on Dr. Angel’s evaluation framework, we gained a better understanding of the exact mathematical language requirements.

All of these factors were taken into consideration and provided valuable insights for the continuation of this project and for the creation of the JOURNALS:

Unit 2: Area Pre-test Unit 2: Area Posttest

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However, before I get to the journals, I would like to explain the whole process in detail before discussing the journals which is only a single component of a bigger system because all of the work has been based on sound educational practices. One of the first things I wanted to do then during the new academic year and that I worked on non-stop throughout the April holiday of that period (and every subsequent holiday period) was to complete and create one complete mathematics program template for one semester and for one year level. If there is one complete program template, then different components of the program can be isolated and completed in a constant effort to always speed things up based on initiatives that work and initiatives that I always and willingly produced. The first component of this complete bilingual mathematics program was my ACADEMIC PLANNER for Year 4 Mathematics for the first semester as depicted below. I also provided adequate information in this ACADEMIC PLANNER for its function and purpose to be understood:

The main reason for taking the Singaporean Syllabus into consideration is purely based on the fact that the new materials in use are all based on the Singaporean Syllabus. However, in this academic planner I also aligned the Singaporean Syllabus topics with the corresponding topics of the B.E.C.C. and this detail shouldn’t lead to confusion with regards to the two different philosophies of the two programs

because the two programs are different. By doing this, and provided the children worked through for example the five lessons indicated here, the school would not only in effect be delivering the content of the Singaporean Syllabus but the school would also be in compliance with the B.E.C.C. All of this is dependent of course on the fact that this content information has to be taught to the children and what evidence can a school provide that a child worked through this information? ANSWER: By taking the children’s work recorded in their journals into consideration. A tick in an administrative box is not

evidence that a child worked through a specific set of information but a child’s actual work sample is evidence that the child worked through the information (or not) which is an essential step on the path to understanding and knowledge.

Observe the Information:

Observe the Information:

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The complete ACADEMIC PLANNER that I created through my own initiative is depicted below. Observe how the ACADEMIC PLANNER the LESSON TOPIC QUESTIONS produce, which is then used to create the new and updated TEACHER’S GUIDE 3.0 and the JOURNAL:

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And once I have deduced the LESSON TOPIC QUESTIONS, only then could I proceed with compiling the TEACHER’S GUIDE 3.0 for that semester’s Year 4 mathematics:

Observe the information that succinctly explains the procedure to be followed:

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And here is a depiction of the theoretical background information across two pages to shed light on the contents in the TEACHERS GUIDE 3.0:

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However, the complete TEACHER’S GUIDE 3.0 for Year 4 mathematics for one semester is a document of a 111 pages. A substantial portion of the theoretical background information that I researched and collected the previous year during the compilation of TEACHER’S GUIDE 2.0 was used in this new TEACHER’S GUIDE 3.0, but it still required additional information that I had to research and find which required a substantial amount of time and effort, but when the job was done, I was pleased because if the teachers based and planned their lessons on this information and delivered this to the children the school would in effect successfully deliver a bilingual mathematics program:

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And only once the TEACHER’S GUIDE 3.0 containing the theoretical background information as depicted on the previous page was compiled, could I then extract the language from the mathematical discourse contained in the TEACHER’S GUIDE 3.0 while simultaneously (and always) referring to the publisher’s materials to ensure that we provide adequate language support and cover the necessary content for the compilation of the LANGUAGE SUPPORT to be presented in the new JOURNALS:

Step 1: In the ACADEMIC PLANNER I refer to the

syllabus and materials to identify the exact content

information to be covered and then I deduce the LESSON

TOPIC QUESTIONS.

Step 2: Once I have the LESSON TOPIC QUESTIONS I

then find the information using the Internet that would answer these questions and this is then

the THEORETICAL BACKGROUND INFORMATION

making up the TEACHER’S GUIDE.

Step 3: Once I have the THEORETICAL BACKGROUND

INFORMATION in the TEACHER’S GUIDE, can I then conduct a proper analysis of

the language and identify the key language terms that is then

presented as the LANGUAGE SUPPORT in the JOURNALS:

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The next step in this process that I developed was to complete the LANGUAGE SUPPORT based on a traditional glossary format because that is what the school was familiar with. Observe the depiction below:

The lesson topic question deduced from closely scrutinizing the curricula and materials.

These keywords or terms (that later developed into key mathematical concepts) were extracted from the theoretical background information in the Teacher’s Guide. An understanding of these keywords would

put a student in a good position to answer the lesson topic question and the ability to understand and answer the lesson topic question means that the

school successfully delivered a bilingual mathematics program.

The objective here is to present information to the students that the bilingual students would be able to

digest and process. The theoretical information contained in the Teacher’s Guide were meant for the

teachers and predominantly I had to research and find and rewrite this information to make it as easy as

possible for the children to understand. This particular process takes a considerable amount of

time and effort to put together. As the project proceeded and as my own mathematical

understanding developed, I kept on refining this part of the system in a constant effort to improve the quality of the information to be presented to the

children that will be clarified throughout this report.

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Completing the LANGUAGE SUPPORT requires a considerable amount of time and herewith a depiction of the LANGUAGE SUPPORT document that would later be used to create the Year 4 Mathematics JOURNAL for the first semester:

Only upon completion of the above, could this document then be sent to a Thai translator for the key vocabulary to be translated.

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And only once all of the aforementioned steps, procedures, components of a system were completed, could I then proceed with compiling the JOURNALS. In the original CLIL article that I submitted (of which a shortened version appeared in the Closer Magazine) I elaborated on the design of the journal when I commented as follows:

“One function of the journal is to provide the students with additional language support that they can rely on during their lessons and in line with the CLIL methodology. A journal is also a medium for recording experiences and observations and to facilitate this, we provided the students with a workspace resembling a blank canvas. Here is the basic template and an example from the Year 4 Science Journal:”

“The journal is also giving the teachers the freedom to let loose the creativity that the children possess and the creativity the students has shown us so far has been absolutely overwhelming:”

“Creativity is important in learning because it stimulates the imagination. When students are successfully engaged in the creative process while learning, they will express themselves in their individual ways because a stimulated imagination produces original ideas.”

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The lesson topic questions provide the students with a sequential scaffolding of the topics also used as the contents of the JOURNALS:

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And herewith is a depiction of the first completed JOURNAL for Year 4 mathematics totaling 82 pages:

The process outlined above is an example of a complete bilingual mathematics program for one semester and for one year level that I created predominantly through my own initiatives and also by taking sound educational practices into consideration. And all of this was continually discussed and corroborated by Dr. Angel.

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Let’s now consider this program in practice by looking at some WORK SAMPLES produced by a teacher who followed and applied this program in Year 4 mathematics. It is also worth taking into account that the WORK SAMPLES produced below, was initiated by a first-time mathematics teacher:

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And if we take a closer look at a singular work sample, we can also address the question regarding evidence. I will use the following work sample from Year 4 Mathematics from Unit 4: Tables and Line Graphs – Lesson 2: What are tables and bar graphs?

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In line with my claim that my work has been based on sound educational practices, let’s start with the ACADEMIC PLANNER in which we can closely scrutinize both the Basic Education Core Curriculum and the Singaporean Syllabus as it pertains to this one individual lesson:

It appears that during this lesson the class collected DATA (the favorite colors of my class 4C) probably

based on an activity the teacher conducted. This DATA was then recorded in a table first, and then that DATA

was then applied for the drawing of this bar graph.

This work sample provides irrefutable evidence that this student worked adequately through the required INFORMATION as stipulated by the B.E.C.C.

In this work sample we can clearly see several instances where data

has been collected and organized.

Here we can see several instances where data (had to be read) for the writing thereof to occur. Children unable to

read and write at this stage of their primary school careers has a tendency to sketch the symbols of the language and

the information they encounter as a whole being placed in the extremely unfortunate position of compensating for not having yet acquired the basic skills of reading and writing. A phenomenon I encountered by taking into consideration the

work of students by analyzing some of the thousands of pages of work samples this academic project produced.

Here we can see several instances where tables and bar graphs were drawn with the content closer aligned to the

Singaporean Syllabus.

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To continue, let’s now consider the topics as stipulated by the Singaporean Syllabus pertaining to this individual lesson:

Observe how by addressing the lesson topic question: What are tables and bar graphs? the work that the teacher in this instance initiated (by having

students first work through a table followed by drawing a bar graph) adequately complies with the

first two topics in the Singaporean Syllabus. This work sample provides irrefutable evidence that this student worked adequately through the required INFORMATION as stipulated by the first two topics in the Singaporean Syllabus.

Again, we can clearly see that this student completed two tables from data.

After the recording of the data in the tables, the student then drew a bar graph in line with the

syllabus topic of “Reading and interpreting tables” because to draw this particular bar graph, the student had to read and interpret the table.

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To continue, let’s now consider the topic of “solving problems” (the THIRD sequential topic) as stipulated by the Singaporean Syllabus:

In my report dated 11th May 2017, I mentioned how topics in the Singaporean Syllabus are

sequenced. The first two topics here are meant to introduce a conceptual understanding of the

subject matter. This is then followed by the third topic of SOLVING PROBLEMS. Again, observe the

logic: First the student should be taught something in terms of gaining a conceptual

understanding and only after that occurred can the emphasis shift to solving problems. There seems to be a logical sequential process presented in the

Singaporean Syllabus that leads to problem solving.

Even though creative teachers can always incorporate problem solving in the journals, the materials (like a

traditional workbook containing mathematical exercises) are specifically designed to address this particular syllabus topic of solving problems preferably AFTER the first two topics has

been adequately covered.

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Let’s now consider the information contained in the TEACHER’S GUIDE 3.0. Specific information retrieved from the Internet through my own research and initiative based on the LESSON TOPIC QUESTION that I deduced from interpreting the Basic Education Core Curriculum and the Singaporean Syllabus:

Here we can clearly see how this first-time mathematics teacher worked through the information presented in the Teacher’s Guide. This is also evidence that this

particular teacher and for this lesson was himself engaged in a learning process (knowledge gained can also be transferred) because this teacher clearly had to absorb

some of the above information in order for the student here to produce this work. The example in the Teacher’s Guide shows a table of a class’ favorite colors (and observe the data) and then a similar table (with different sets of data – perhaps

through a class discussion or activity) was produced by this student.

Can we infer from this work sample that this particular teacher had an adequate understanding of what a bar graph is, and that this student worked through this

information?

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Let’s now consider if we have evidence that we provided this bilingual student with adequate LANGUAGE SUPPORT presented in the JOURNALS. All of this has been mentioned before:

The lesson topic question deduced from closely scrutinizing the syllabus materials.

The objective here is to present information to the students that the bilingual students would be able to digest and process. The theoretical information contained in the Teacher’s Guide were meant for the

teachers who are adults and predominantly I had to research and find or rewrite this information to make it as easy as possible for the students to understand. This particular process takes a considerable amount of

time and effort to put together. As the project proceeded and as my own mathematical understanding developed, I kept on refining this part of the system in a constant effort to improve the quality of the

information to be presented to the students.

These keywords or terms (that later developed into key mathematical concepts) were extracted from the theoretical background information in the Teacher’s Guide. An understanding of these keywords would put a student in a good position to answer the lesson topic question and the ability to understand and answer the

lesson topic question means that the school successfully delivered a bilingual mathematics program.

Translating these ideas into Thai also

takes time and effort and it also requires a willingness to learn

for the sake of continually

improving the quality of the

information to be presented to the

students. Here is a translation done by Ms. Kanyapat who

throughout her involvement in this project showed a

willingness to learn. Ms. Kanyapat was a

tremendous help throughout this

project and a person of integrity and

honesty.

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The LANGUAGE SUPPORT has the appearance of a sterile glossary and as mentioned before, this particular design aspect (not to be confused with the aspect of function) was in fact just based on the normal standard glossaries in use by the school and which I adopted. However, in the complete CLIL Article that I submitted, I did mention (considering now the aspect of function) the following:

This would apply to

the aforementioned

mathematics lesson

and work sample as

well.

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It’s also worth taking into consideration my point of departure on this academic journey. Observe the depiction of a Daily Lesson Plan with which I started this report and compare this mechanism to my idea of what constitutes a proper bilingual mathematics program as presented in this report:

There is no evidence in this document that learning transpired.

There is no evidence in this document that students in fact processed information or whether the information

delivered (if it was) was correct.

There is no evidence in this document that the bilingual students in this class were given adequate language

support.

There is no evidence in this document that support was provided to the teacher like a Teacher’s Guide or better

yet, a complete bilingual mathematics program to be followed.

The document here is an administrative mechanism but an ineffective gauge to determine whether learning

transpired.

However, as mentioned in the opening of this report, from this point onward and guided predominantly by my own

initiatives, I created a complete methodology for creating a proper bilingual mathematics program.

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The preceding pages make clear the locale of the evidence. However, all I basically proved is that during one lesson, one student, guided by one teacher, provided satisfactory evidence that a student was engaged in a learning process because there is a record of information processed. It has also clearly been shown that the correct mathematical information was processed and all of this occurred in English. So, if an entire class produces work of approximately the same standard as the work shown in the example, there would then be evidence that learning transpired in a whole class. If an entire year level can produce work of approximately the same standard, then there would be evidence that a whole year level was engaged in a learning process and so on. To determine if the above example is a fluke, the rest of this student’s work can therefore be analyzed. In the table below the remainder of this student’s work is depicted using small images:

Pages 1 and 2 Pages 3 and 4 Pages 5 and 6 Pages 7 and 8 Pages 9 and 10




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The teacher and student in this particular class were able to complete 30 of the 41 lessons of the program for the first semester. Processing information (a prerequisite in learning) requires time. So for the first 30 lessons there are clear evidence that this particular student processed information stipulated by the B.E.C.C. and Singaporean Syllabus. The Singaporean Ministry of Education stipulates a required five mathematics lessons per week for their Grade 4 students who are not bilingual students. This brings forth another revelation that this work produced and that is that there is a strong correlation between the quantity of information to be processed and time. Only by knowing the exact quantity of the information to be processed for a particular subject in a particular year level, can an adequate amount of time be designated for the learning to occur because anything else would be purely a guess. I have mentioned in meetings before that how the students’ time is managed should be carefully considered. Having said that, since this is a program we can also clearly identify the exact information that this student did not work through as indicated in the following table. Being in a position to clearly identify which sets of information have not been processed by a student is also tremendously helpful because only then, can measures be taken to address this all pervasive phenomenon. This is especially important for the subject of mathematics with its “chained” concepts that I pointed out in my report of 11th May 2017. Here’s the remainder of this student’s journal that gives a precise record of the information not processed by this student during this student’s engagement in this program during the first semester:


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Pages 81 and 82

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CHAPTER 7: Curriculum Implementation The academic work that I produced was based on two main assignments. The first assignment was the teacher’s guide project and the second was the project to implement CLIL. However, the work that I subsequently produced went far beyond and far exceeded these two assignments (in quality and quantity) partly due to the very nature of the work, but predominantly through my own initiatives in addressing the particular needs of a particular learning environment. To illustrate this point, let’s consider the following diagram taken from some of the first work that I produced that illustrates my methodology for putting a curriculum into operation (addressing a particular need) followed by some work samples produced during the CLIL experiment:

Here for example I identified two topics in the B.E.C.C. that were not covered in the Year 4 mathematics materials before my involvement. A very basic understanding of the Standard MA3.2 for example, together with the Indicator of “Use geometric

figures in designing” makes it clear how ability for visualization and spatial reasoning can be developed.

Based on the information presented in the B.E.C.C. I formulated the following 14 questions for a unit in geometry in Year 4 mathematics. These 14 questions produce a COURSE in

geometry. It forms a unique SYLLABUS and it wouldn’t be hard for me to argue that this course is on par or even succeed the Singaporean Syllabus’s unit on geometry for Grade 4

mathematics and the questions were all derived from interpreting the B.E.C.C.

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Work samples produced during the Year 4 mathematics CLIL experiment to illustrate my methodology for implementing a curriculum.

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Here’s an interesting

work sample with

overlaying excerpts

taken from the B.E.C.C.

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The work sample depicted on the previous page is so revealing because this particular work produced by this particular student makes it even clear why a work sample evidence is, and so much so, that it is worth depicting again:

1. Observe this student’s astute observations. 2. Observe Standard MA3.2: This work sample provides clear evidence that “ability for visualization” and “spatial reasoning” and “application of geometric models” was practiced and recorded. 3. Observe Standard MA6.1: Indicator 1: Can we infer from this work sample an application of “diverse methods for problem-solving?” The answer is yes. Indicator 2: Can we infer from this work sample that application of mathematical knowledge for problem-solving in various situations was applied? The answer is yes. Indicator 3: Can we infer from this work sample that suitable reasoning was provided for decision-making and that a conclusion was presented appropriately? The answer is yes. Indicator 4: Can we infer from this work sample that the student accurately used mathematical language to communicate a mathematical concept and that the student presented his findings? The answer is yes. Indicator 5: Can we infer from this work sample that mathematical knowledge was linked with another discipline? The answer is yes. Indicator 6: Can we infer from this work sample that this student was provided an opportunity to think creatively? The answer is yes.

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Please note: I am not taking credit for the ingenuity the student exhibited in the work sample on the previous page. This is purely the work of a naturally talented child and all credit belongs solely to him. A fact that can be further corroborated by taking this student’s pretest and posttest results into account that clearly showed that this student (as an individual) already possessed the mathematical knowledge in question. However, I could argue, and I do argue, that by the mere fact of providing this student with an opportunity to produce the work that he did, there is a clear account of compliance with the Basic Education Core Curriculum. In fact, there seems to be a complete compliance with Standard MA3.2 and a complete compliance of the ENTIRE sixth strand. However, I have often heard people say the Basic Education Core Curriculum is substandard, but which one of the following indicators is in fact substandard in terms of primary school mathematics education? I don’t think there is a conscientious educator who would argue that any one of the following seven indicators is substandard. Isn’t the problem perhaps, putting a curriculum into operation?

Which of the following two standards or seven indicators are substandard?

Consider the sixth indicator of the sixth strand again, “Attaining ability for creative thinking” together with my sentiments expressed in the article I wrote:

A Journal is also a medium for recording experiences and observations and to facilitate this, we provided the students with a workspace resembling a blank

canvas to let loose the creativity that they already possess:

The indicator, “Attain ability for creative thinking” in the B.E.C.C. would be difficult to achieve if a child’s entire mathematics education was dictated by a traditional

mathematics workbook alone. In fact, the entire sixth strand in the B.E.C.C. would be difficult to implement through the use of a traditional mathematics workbook

alone.

If there is no account of, “Attaining ability for creative thinking” in the mathematics classroom and especially reflected in the students’ work, then the claim cannot be

made that the curriculum is being “followed”. To properly “follow” this curriculum, the children should be given the opportunity for, “Attaining ability for creative

thinking” as exhibited in the work sample on the previous page.

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This program can also function as a diagnostic-tool. To only take aesthetically pleasing work samples into account would be a mistake because the evidence I am presenting here pertains to good educational practices and has little to do with pretty work samples but only to do with good educational practices. A truly conscientious educator should be immediately drawn to the work samples in which it can be clearly identified that there IS a problem. In the original CLIL article that I submitted I commented that, “if a problem can be identified, a problem can be addressed.”

Through the work samples shown in the previous pages I have made it clear that the underlying principle of my work is based on putting a curriculum or syllabus effectively into operation with evidence supporting this claim. And it should also be taken into consideration that this particular methodology rose out of addressing the needs of a particular and unique learning environment. Another and different learning environment may well need a different approach, but this particular approach appears to be sound.

A possible counter-argument that could be made would be to say that the Basic Education Core Curriculum is inferior in some or other way (and thereby summarily dismissing all of the evidence I have just presented) but it’s also worth remembering that on the previous page I also made it clear that it would be extremely difficult for a conscientious educator to dismiss any one of seven indicators and the two broader strands encapsulating those indicators appearing in the B.E.C.C. Not only would it be very difficult to argue, for example, that “Attaining ability for creative thinking” (to use just one indicator as an example) is not important, it could not be ethically justified.

Through all of my work, I have very clearly and very intentionally, made provision for curriculum information to be put into practice with evidence supporting this claim, but putting a curriculum successfully into operation is not my burden alone even though the evidence would suggest that I did accomplish that. The Basic Education Core Curriculum is also the foundation of the mathematics taught in Thai. In other words, if we were to consider Standard MA3.2, we should be able to see how this knowledge (that this standard refers to in terms of primary school geometry) was also absorbed by the students in their first language mathematics classroom because it should be easy to track a knowledge of primary school geometry between the first language classroom and the second language classroom because the geometric figures that the students should have drawn to practice their geometry skills (as per the curriculum) should be the same in the Thai classroom.

On the following pages is a table displaying 48 work samples. Ms. Mejal was kind enough to submit 48 complete journals of semester one and a lot more semester two journals totaling thousands of pages of evidence for the 2016/17 academic year. The following work samples were all obtained from page 39 of the Year 5 mathematics journal that Ms. Kanyapat compiled under my instruction and a lesson that Ms. Mejal conducted and I selected this page because this is a geometry based lesson. A group of Year 5 students should have encountered and practiced what the following information in the B.E.C.C. is referring to because this information is applicable to Year 4 mathematics according to the B.E.C.C. There is a record that this information was worked through during the CLIL experiment and evidence as a direct result of the geometry workbook that I designed that at the very least gave the students the opportunity to work through this information and an opportunity to practice some of these skills. But, since this information comes from the Basic Education Core Curriculum, the students should also have had the opportunity to practice the ability to visualize, practice the ability of spatial-reasoning, practice the application of geometric models for problem-solving, and use geometric figures in designing in their Thai mathematics classroom as per the following standard and indicator from the B.E.C.C. :

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Now we can take this information from the B.E.C.C. and we can use it to do a quick analysis of 48 work samples to see if we can establish a general standard in terms of the suggestions put forward in the B.E.C.C. These 48 work samples were randomly selected because Ms. Mejal merely collected any journal she could get her hands on. The purpose of the following impromptu experiment is to show how this program can function as a diagnostic-tool by analyzing and evaluating the work appearing in the JOURNALS. For the purposes of this brief experiment though (also taking into consideration that the images are quite small) it wouldn’t be possible to conduct an in-depth analysis or evaluation of these students’ work, but it should be possible to infer what the general standard is in terms of the specific recommendations in the B.E.C.C. pertaining to geometry as repeated in the following table so let’s now observe:

Let’s observe (at a glance): The ability for visualization.

Let’s observe (at a glance): The ability for spatial reasoning.

Let’s observe (at a glance): The application of geometric models for

problem solving.

Let’s observe (at a glance): The use of geometric figures in

designing.

During this lesson the students did not solve a specific mathematical problem, but the task the teacher

assigned here of designing and then identifying different shapes can be construed as a geometry problem to be

solved.

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If the above pictures are too small then an in-depth analysis and evaluation can be made of the original work samples located here:

So, if we look at these 48 work samples, what can we infer with regards to the following?

The ability for visualization. The ability for spatial reasoning. The application of geometric models for

problem solving. The use of geometric figures in

designing.

I think it is still difficult to conclude what the overall standard of the above work samples is but that is due to a lack of comparison to other sets of work samples which can be resolved by emphasizing the importance of continuously monitoring the students’ work year after year and not just the monitoring of completed answers in a traditional workbook because how would one monitor the ability for visualization and spatial reasoning through a traditional workbook alone, not to mention “Attaining ability for creative thinking” which are all put forth in the B.E.C.C.

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The design of the JOURNALS provides the students with the opportunity to practice and exercise a substantial portion of the recommendations made in the B.E.C.C. as well as the Singaporean Syllabus which would entail the correct implementation of a curriculum. In addition to this, the JOURNALS can also function as a diagnostic-tool by taking into consideration the students’ work. To truly determine whether the B.E.C.C. is in fact being properly implemented, we can take a closer look at the geometry strand and its standards and indicators together with the sixth strand and formulate the following questions to be answered:

Are the students exhibiting an ability to explain two-dimensional geometric figures?

Are the students exhibiting an ability to analyze two-dimensional geometric figures?

Are the students exhibiting a satisfactory level of visualization?

Are the students exhibiting a satisfactory level of spatial reasoning?

Are the students exhibiting a satisfactory level of applying geometric models?

Are the students exhibiting a satisfactory problem-solving ability?

Are the students exhibiting a satisfactory reasoning ability?

Are the students exhibiting satisfactory ability to communicate?

Are the students exhibiting a satisfactory ability to present mathematical concepts?

Are the students exhibiting the linking of various bodies of mathematical knowledge?

Are the students exhibiting the linking of mathematical knowledge with other disciplines?

Are the students exhibiting creative thinking?

These questions should be answered in the context of geometry. The children are very creative but the focus here for this impromptu experiment is to see if

we can detect and track a knowledge of geometry.

As mentioned before, this particular group of students had some exposure of practicing the drawing of geometrical shapes (to use one example) as a result of the CLIL experiment that was based on the B.E.C.C. but we should also be able to

detect a transfer of knowledge since all the mathematical concepts and skills and processes to be practiced should also occur in the students’ first language

mathematics classroom.

My own personal opinion with regards to these work samples is that the standard could probably be a little bit higher and that this could be achieved by allowing the children to adequately work through the mathematical concepts, and to practice the skills and processes (especially the skills and processes of

STRAND 6). These work samples are extremely valuable because here we can clearly see (to be confirmed by a

thorough investigation) that these students need a little bit more support and now measures can be taken to help these students.

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A little earlier I mentioned that it is difficult to conclude what the standard of a set of work samples is if there is nothing to compare it against but the purpose of this brief review in looking at the 48 work samples is merely to see and to get a general sense of a Year 5 group of students’ knowledge of geometry. Ms. Mejal also worked through the same lesson again in the latest 2017/18 academic year with a new group of Year 5 students and during this semester they produced the following work for the same lesson as the lesson used for the 48 work samples. It should be noted that these latest work samples were produced in a new and improved Year 5 mathematics journal that will be elaborated on later in this report. In the following work samples it can be clearly seen how the students are explaining and analyzing (see STANDARD MA3.1) a two-dimensional geometric figure even though this lesson is in the context of a Singaporean Syllabus topic of finding the area of a triangle:

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Observe what the student wrote here. Ms. Mejal was conscientious enough to remark that this little anecdote the student expressed

here was interesting and indeed it is interesting. Probably something the student researched on the Internet and then

presented here. This raises an interesting question: What motivated the student to do this?

And as mentioned before, I cannot take credit for the individual ingenuity, creativity and natural talent that the children possess to

make my case but the very important point here is this: To cultivate creativity, one needs a little bit of freedom. This freedom is

provided to the students through a blank canvas page in the journal that I designed and I am in full accordance with the Singaporean

Syllabus and the B.E.C.C. because Indicator 6 of Strand 6 (and applicable to Thai mathematics as well) states: Attain ability for

creative thinking. The student’s work here also complies with the indicator of linking mathematics with other disciplines.

The journals are overflowing with examples such as these and journals that were in full operation and available for anyone to see

and the only thing being done here is: The implementation of a curriculum.

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End of Part 2.

Part 3 CHAPTER 8 The Curios Case of Ms. Mejal

CHAPTER 9 A Continuous Improvement

Copyright © Martyn Krügel, 2018 All rights reserved

3.0 INFORMATION REPORT€¦ · 3.0 . Page | 2 Contents ... I wanted to present my previous employer with a comprehensive overview of the work I had done, but in addition, I also wanted

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