Magdalini Kokkaliari 11094464 Practical Research of Education 1 In which ways do mathematics teachers expect homework to contribute to their students’ achievement and what is their parents’/carers’ role? A comparison study of English and Greek post compulsory mathematics teachers Finding an initial area of interest and beginning to explore possibilities I have spent half of my life in schools: initially as a student, later as mathematics tutor, then as a secondary teacher and as a mother too. Especially the last twenty years in this triple role mostly focused on my favourite subject, Mathematics. Since my childhood years, I have been spending hours and hours on learning, teaching, talking about, but mainly doing mathematics alone or with my peers, teachers, friends, colleagues, students, family. In all these phases two where mainly the points which were dominant: first that mathematics was in one way or another present in everybody’s life and second that there should be found effective ways of teaching Mathematics to provide all students opportunities to maximise their potential. My assignment for Issues was an attempt to find out under which conditions is an uninterested in mathematics student’s identity formed. I came to the conclusion that there is not such a consistent identity, but it is just a behavioural reaction, a human being’s defence to difficulties, which can be overcome possibly with the cooperation of all those involved. I had a chance to gain further insight on this interest of mine with online qualitative data assignment for Practical Research Module. I decided to interview (appendix 1) an 18-year- old student, who has finished recently his secondary education and could be characterised as uninterested in mathematics. What I found extremely interesting was his reference to his first
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Magdalini Kokkaliari 11094464 Practical Research of Education 1
In which ways do mathematics teachers expect homework to contribute to their
students’ achievement and what is their parents’/carers’ role? A comparison study of
English and Greek post compulsory mathematics teachers
Finding an initial area of interest and beginning to explore possibilities
I have spent half of my life in schools: initially as a student, later as mathematics
tutor, then as a secondary teacher and as a mother too. Especially the last twenty years in this
triple role mostly focused on my favourite subject, Mathematics. Since my childhood years, I
have been spending hours and hours on learning, teaching, talking about, but mainly doing
mathematics alone or with my peers, teachers, friends, colleagues, students, family. In all
these phases two where mainly the points which were dominant: first that mathematics was in
one way or another present in everybody’s life and second that there should be found
effective ways of teaching Mathematics to provide all students opportunities to maximise
their potential.
My assignment for Issues was an attempt to find out under which conditions is an
uninterested in mathematics student’s identity formed. I came to the conclusion that there is
not such a consistent identity, but it is just a behavioural reaction, a human being’s defence to
difficulties, which can be overcome possibly with the cooperation of all those involved. I
had a chance to gain further insight on this interest of mine with online qualitative data
assignment for Practical Research Module. I decided to interview (appendix 1) an 18-year-
old student, who has finished recently his secondary education and could be characterised as
uninterested in mathematics. What I found extremely interesting was his reference to his first
Magdalini Kokkaliari 11094464 Practical Research of Education 2
negative emotion and change of attitude towards mathematics at the age of 12, when he faced
the transition from arithmetic to algebra, while he moved from primary to secondary
education. ‘I could not do my homework, which was very frustrating and day after day I was
giving up the efforts’ which resulted mathematics, which was his favourite subject during
primary education to be proved uninteresting, hard and, finally, useless. He put the blame on
himself, ‘I had not tried enough, like some peers of mine, who were more persistent in trying,
asking the teacher, or others, whose parents used to help them or find a tutor for them’.
In this case study there were some findings, worth-researching. Homework revealed
to be discouraging in the sense of ‘The emotions expressed during mathematics work may be
linked to mathematics achievement’ (Nicole M. Else-Quest, Janet S. Hyde, and Ahalya
Hejmadi, 2008). Secondly it was mentioned that ‘parental involvement in learning and
children’s homework practices, the social aspects of education’ (Hyde et al., 2006) may result
to student’s better results. The parents can have a central role and ‘a warm and positive
homework interaction might cultivate a struggling student’s interest and perseverance with
mathematics’ (Nicole M. Else-Quest, Janet S. Hyde, and Ahalya Hejmadi, 2008). Thirdly the
teachers’ role seemed to be determining for those who are tenacious, excluding the rest.
The last clue led me to take a second chance with the quantitative data online
assignment for practical research (appendix 2). To gain further insight this time on teachers’
attitudes towards homework, I implemented a ‘mathematics teachers’ beliefs for students’
homework’ survey. The 17 teachers, who respond, some of them teaching in English schools
and other in Greek, stated that they believe that homework has a large contribution on
students’ mathematics learning, although there was a dichotomy between them related to
parents’ role. Some of them would accept a desirable parents’ help in case their children are
not able to do part or the whole of their homework, and others’ view was that students should
Magdalini Kokkaliari 11094464 Practical Research of Education 3
ask only their teachers for help in this case. Surprisingly Jenny Houssart’s, our tutor’s,
comment: ‘Given more time, I think there would be potential to explore this data further and I
was particularly interested in whether there was any difference in the responses from teachers
in Athens and those in London coincided with my own thoughts while I was collecting the
data. I moved to London four years ago to teach mathematics in secondary education and I
was surprised a lot of times of unexpected similarities and differences in every aspect of
teaching mathematics processes. I have the chance to share experiences with Greek and
English teachers, to teach or meet students from both mathematics curricula and those who
transfer from one curriculum to the other, to speak with their parents and compare their skills,
their thoughts, their difficulties. When you live within a bicultural environment comparisons
are unavoidable and not necessarily harmful, hence many times you can draw false
conclusions.
We, mathematics teachers, usually think, even with smugness and sometimes with
arrogance, that we teach a universal subject, we speak an international language and we share
common ideas and practices of teaching and learning. We forget to take into account that
teachers’ didactic practices are culturally determined (Lerman 1998) and teachers operating
in an educational system behave within well-defined norms that differ from those of another
(Stigler, J. W., Gallimore, R. and Hiebert, J. 2000) even if it seems to teach the same things
using the same practices. As a mathematics teacher for many years in Greek secondary
schools I had experience of how ‘Lessons are the daily routine of teaching and learning and
are often organized in a certain way that is commonly accepted in each culture’ (Kawanaka
1999, 91) and now I am surprised to find out differences between aspects of the teaching and
learning processes that look the same and similarities between those that seem to be quite
different. But what is more important is that looking at other cultures helps you understand
your own practices more clearly and to wonder whether you could use alternative ones,
Magdalini Kokkaliari 11094464 Practical Research of Education 4
since, based on different beliefs and different expectations, teachers in other cultures might
have developed entirely different teaching practices. (Hiebert, Gallimore et al 1999)
After all these my research question has emerged: a comparative analysis on Greek
and English secondary education mathematics teachers’ beliefs for students’ homework
and their parents’ role.
Refining the research question
From my previous experiences I am aware that undertaking a research study to find
valid and reliable answers to a question is not an easy thing to do; especially to conduct a
comparative analysis on beliefs/attitudes for homework. To gain insight I tried to find
relative literature:
i. HOMEWORK
Homework is a ‘multifaceted process that involves a complex interplay of factors in
two contexts —home and school—and a range of participants from school-system-level
employees to individual students’ (Pamela M. Warton, 2001). While there is an extensive
research literature on mathematics homework and how ‘well-chosen homework assignments
can reinforce classroom learning, by providing a challenge can encourage students to extend
their understanding of mathematics, allowing students who are having trouble keeping up
with their classmates to review material taught in class’ (Mathematics Benchmarking Report:
TIMSS 1999), the study of mathematics teachers’ attitudes towards homework, is
comparatively limited, especially the one focused on their expectations and parents’ role. It is
obvious that this aspect of pedagogy can have successful results, only if there is consensus,
or, at least, collaboration between the three partners: teacher, student and parents/carers.
Magdalini Kokkaliari 11094464 Practical Research of Education 5
In most countries mathematics homework is an obligatory students’ task, for students
of all ‘abilities’ and the time they spend do not always result to high achievement. ‘Compared
with their higher-achieving counterparts, the lower-performing students may do less
homework, either because they simply do not do it or because their teachers do not assign it,
or more homework, perhaps in an effort to keep up academically’ (Mathematics
Benchmarking Report: TIMSS 1999).
In research literacy every aspect of homework is multi-faceted. Taking as a starting
point the definition of homework, Cooper (1989, quoted in Harris Cooper et al Patall 2006)
defines homework as ‘any task assigned by schoolteachers intended for students to carry out
during non-school hours (study hall, library time, or even during subsequent classes)’, while
Harris Cooper et al (2006) adds (a) in-school guided study (b) home study courses delivered
through the mail, television, audio or videocassette, or the Internet; and (c) extracurricular
activities.
Variations in homework can be classified according to its (a) amount, (b) skill area,
(c) purpose, (d) degree of choice for the student, (e) completion deadline, (f) degree of
individualization, and (g) social context. (Harris Cooper et al 2006).
It is essential and crucial for the research question to identify the teachers’ stated
purposes on designing homework assignments for their students and a long reference is going
to be helpful. Although the different purposes of homework are not mutually exclusive, we
can categorise them as (a) instructional and (b) non instructional objectives, with a lot of
subcategories:
Practical skills: to give students opportunities to practice skills taught in class,
increase speed, demonstrate mastery, retain skills, review work, and study for
tests.
Magdalini Kokkaliari 11094464 Practical Research of Education 6
preparation, to ensure that each student is ready for the next lesson, like
completing unfinished classroom activities, studying and internalising what
was learned in school or stimulating the student for a topic to be taught, or an
exam
participation, increase student’s involvement in active learning, in applying
specific skills and knowledge, and in conducting projects
to foster student personal development such as responsibility, self-confidence,
feelings of accomplishment, to learn to manage their time, to establish work
schedules, to build study skills, and develop research skills. At home, students
may control the amount of time they spend on different skills, the books or
resources they use, and the number of consultations with parents, siblings,
and friends to complete their work, to learn to deal with distractions at home
parent–child relations: to establish communication between parents and
children about schoolwork and how it is used in real-life situations
Parent– teacher communications: to involve parents in students’ curricular
activities, to keep them aware of topics taught in class, of their children’s
progress, of the ways of supporting their children’s work and progress. In
special cases parents can act as tutors under teachers’ precise guidelines or
training.
peer interactions (formal or informal): to encourage students to work together,
motivate, help and learn from each other
policy: to fulfil school or district policies for a prescribed amount of
homework per day or per week
Magdalini Kokkaliari 11094464 Practical Research of Education 7
Public relations: for the school to show that it has a rigorous academic
program and high standards of student work, as the research suggests
homework is essential for schools, teachers and students.
punishment: to try to correct problems with student conduct or productivity
(Epstein, J. L., & Van Voorhis, F. L. 2001, Muhlenbruck et al. 2000, Warton 2001, Como
2000 ).
To have further insight we can go on with the amount of homework, the degree of
choice and individualisation, the social context, the importance, the interaction between
teachers, parents, educators, policy makers and a long list.
ii. Comparative analysis
From my reading (Alan Bryman 2008) I was aware of the form of comparative
research as a kind of cross-cultural or cross-national research. Drawing information from
relevant literature ‘strictly speaking, to compare means to examine two or more entities by
putting them side by side and looking for similarities or differences between or among them.
In the field of education, this can apply both to comparisons between and comparisons within
systems of education’ (Postlethwaite Encyclopaedia of Comparative Education and National
systems of Education 1988: xvii). Although comparative education has a long story, many
faces and goals, (International Comparisons in Mathematics Education by Kaiser, Luna and
Huntley 1999), the last few years it has a tremendous increase. Looking at other cultures
alternative practices discovered in other countries might not transpose readily across cultures,
but they can help to see oneself more clearly, they might also suggest alternative practices
and underscore the idea that classroom practices are the result of choices can be re-examined
in a new light (Hiebert, Gallimore et al 1999).
Magdalini Kokkaliari 11094464 Practical Research of Education 8
Mainly these studies are of two kinds:
Large-scale quantitative studies compare the achievement of learners in one country
with those in others. Such studies are helpful in alerting a system’s participants not only to its
mathematical attainment relative to other systems, but also, by means of test repeats, to
previous performance. For my question research it could not be an advantageous method.
First of all it would be cumbersome and not affordable. Secondly quantitative data are
posivistic, not helpful for analysing individual’s deeper thoughts. Such approaches rely,
essentially, on predetermined categorisations of beliefs/attitudes which not only may miss
subtle variations, but may lead to others that the respondents adopt, only because they are
mentioned and they would not have referred to otherwise. Thirdly they might be useful to
gain insight to the researcher for scheduling the interviews; my previous experiences and
studying the literature were adequate for that.
Small-scale qualitative studies share a common characteristic of seeking insight for
human beings’ beliefs, attitudes and expectations. This is exactly the case for my research
question, hence it is not as easy as it is conceived. Two are the main reasons. The first is that
there may be found too many aspects of similarities and differences for such a research, so it
must be narrowed down properly. The second is teaching and learning processes are not the
same in the classrooms of one country or another ( Knipping, C. 2003). This implies that we
have to find similarities and differences within a certain theme; the next question is what to
do with them. A simple juxtaposition of similarities and differences does not in itself explain.
There is a need for analysis based on certain theoretical frameworks, or in the absence of a
suitable theoretical framework, a need for the establishment of one, based on the differences
and similarities observed. More specifically it argues for the importance of seeking to
understand through cross-cultural comparison the relationship between national context,
Magdalini Kokkaliari 11094464 Practical Research of Education 9
institutional ethos and classroom practices in mediating the development of a learner’s
identity. It makes the case for seeking to understand the lived experiences of pupils and the
effect that such experiences have on their attitudes to teaching and learning. (Osborn, 2004).
Thus the research should identify the broad cultural traditions of the two education
systems of England and Greece. It suggested that ‘the English education system had grown
out of a laissez-faire liberal tradition which had traditionally been associated with
voluntarism, local autonomy and differentiated provision. This promoted an individual, child-
centred pedagogy which has, historically, regarded pupils as having individual needs and
abilities which required different types and levels of schooling.’ (Osborn, 2004). By contrast,
education in Greece has been organised according to the republican ideal, which sees the
state as having a duty to provide a universal education which provides equal opportunities for
all. In particular they are reflected in the balance of emphasis placed on the two central roles
of formal schooling systems, namely the inculcation of knowledge and skills on the one hand
(the cognitive function) and on the other, the shaping of values and attitudes in preparation
for the future role of citizen (the affective function). How, for example, we can compare
teachers’ attitudes towards students in English homogenous classrooms (setting) to the Greek
heterogeneous ones? How valid and reliable could be the data? How could we overcome
these difficulties? What are the researchers’ experiences and suggestions? Can comparative
and cross-cultural research be successful under these constraints? Can it be useful and if yes,
for whom?
Their later book (Crossley & Vulliamy, 1997) demonstrates by example how detailed
qualitative case studies can provide significant comparative insights. Cross-cultural studies of
teaching provide information about different systems of teaching and different ways in which
the basic ingredients of teaching can be configured. Comparative findings can help
Magdalini Kokkaliari 11094464 Practical Research of Education 10
researchers construct more informed hypotheses about the ways different instructional
practices might influence learning. These hypotheses can then form the basis of future
research that specifically seeks to determine what matters. If cross-national achievement
differences are tied to cultural variations in teaching, we may discover ways of teaching that
work better than the ones our society routinely deploys. (Stigler et al. 2000)
Undoubtedly homework plays a significant role for students, teachers, parents, school.
Since the researchers state that we can take advantage of the experience of others all over the
world, who share similar goals, at least in the domain of mathematics achievement, and from
whom we can learn what alternatives are possible’ (Stigler et al. 2000), we can go on
planning our research on homework (although the central variable in this research is not
relevant as it is a cross-cultural research, we can define homework as central). The most
responsible to speak for this are the teachers, themselves, who design and decide their
students’ homework assignments. Let ‘purpose on homework’ be the independent variable
with values as defined before: practical skills, preparation, personal development,
participation, public relations, policy, peers interaction, parents-child, parents teacher,
punishment. We can collect data for teachers’ beliefs, for how this influences on student’s
achievement in mathematics, on parents’ engagement and the effect on students’ attainment.
To gain insight on mathematics teachers’ views on all above aspects, for further research on
homework: which one they consider as more important, in what sense, what its role on
students’ academic (in mathematics, or else) development, what are their expectations from
their students’ parents/carers, especially from those, whose children are not consistent with
their homework, which are their difficulties and to what extent and finally to identify the
similarities and differences between Greek and English mathematics teachers, I would collect
qualitative data by semi-structured interviews with open questions.
Magdalini Kokkaliari 11094464 Practical Research of Education 11
For all the reasons I explained above, there is a problem with the reliability and
validity of collected data. Validity means that correct procedures have been applied to find
answers to a question; hence reliability refers to the quality of a measurement procedure that
provides repeatability and accuracy. To improve my results from these two points of view, I
narrowed it down:
Key stage 5- posy compulsory education; in these years Mathematics is an
optional lesson similar to A Level Maths and classes are similar to the
corresponding English ones.
the sample of teachers chosen is going to be similarly representative with
respect to age, sex, experience
the schools chosen are going to be comprehensive from areas with habitants of
the same socio-economic status
Presenting the final outline plan
Refining the research question resulted in narrowing it further:
In which ways do mathematics teachers expect homework to contribute to their
students’ achievement and what is their parents’/carers’ role? A comparison study of
English and Greek post compulsory mathematics teachers
The theoretical framework of the set of approaches of the final outline plan is to
collect qualitative data by interviews and to research the similarities and differences among
English and Greek post compulsory mathematics teachers’ beliefs for the effect of their
designed homework on their students’ attainment in mathematics
Magdalini Kokkaliari 11094464 Practical Research of Education 12
Given the resources available, I would interview ten English and ten Greek
mathematics teachers who work in comprehensive schools in post compulsory education (16-
18) from districts with similar socio-economic status.
Plan action- Methodology
Pre Interview
I would send them an e-mail explaining who I am and what I am interested in. I would
write in details why I have contacted them and if they would agree to give me an interview
via Skype, suggesting the dates and the times and asking for their permission to create a
video. I would let them know how the research would be reported and when. Finally I would