Assignment practical-kokkaliari magdalini-pdf

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


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


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,


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.


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.


 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


 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).


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,


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


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.


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


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

guarantee confidentiality. (Ralph Levinson 2012 Session 2 PRMA)

Interview

I would use semi-structured interviews. My aim is to give teachers the chance to

speak, to tell their stories. I would plan an interview schedule of open-ended questions to

probe them speak free, to offer deeper, sensitive and accurate portrayals of experience. It is a

kind of narrative research and narrative researchers believe that teachers construct stories to

make sense of their professional world (Drake 2006, Swindler 2006 from Paul Andrews

2009). That is, stories, “as lived and told by teachers, serve as the lens through which they

understand themselves personally and professionally and through which they view the

content and context of their work” (Drake et al. 2001, p. 2). Moreover, “these stories are

subject-matter-specific and may differ greatly from subject to subject” (ibid). (Paul Andrews

2009). I need the interview schedule of open questions for one more reason; to ensure that I

have identified the areas that should be discussed. The open questions must be clear, no

leading, in an appropriate language, piloting.

The arranged time and date I would call them and after their permission I would start

interviewing. The interviews would be held over Skype and I would create a video using


Snagit. During the interviews I would try to take notes and not to intervene in any other way

except prompting, if necessary.

Post Interview

Afterwards I would work on every interview separately. The two sets of data, English

and Greek, would be analysed separately to ensure that culturally located differences would

not be obscured. I would look over my notes and keep more than one copy of the interview

data. I would leave the data for a day or two to distance myself from the person and my

memories of interacting with them. I would return to the data to transcribe the audio into a

transcript, trying to immerse myself in data and feel what emerges. (Ralph Levinson 2012

Session 2 PRMA) I would post them their own transcript for agreement as to their content

even if they didn’t ask for it. Most important at this point is how I would analyse the

interviews. Analysing qualitative data means making sense of, and interpreting, the

information in terms of the meaning my interview subjects bring. Through my interpretation,

I should be able to make abstracted connections between the interview subjects. This would

help inform the nuances of my proposed design guidelines. The better way to achieve it is to

structure carefully the code. The best way is to read the transcription carefully and in due

course to read id again to ensure that I would not be influenced –as much as possible- from

previous reading. Then I would re-organise it in the direction of the information it reveals

familiar to me from the whole work I have done planning the research. In Appendix IV I

suggest an initial code–from a sample pair of interviews that I conducted during planning this

research (Appendix III) - which I think could be helpful for analysing the collected data. This

initial code could be done for every single interview and then, the data of every country can

be compared easily since the size of the sample is small. Samples of larger sizes can be


analysed statistically as quantitative data and the correlations of the variables may lead to

more warranted correlation as it is known that large-scale studies are less prone to problems of

reliability.

Structured Questions:
1. Which, do you think, is the contribution of homework on student’s mathematics
learning in secondary education?
2. What do you do if students do not do their homework?
3. And the teacher tries in one way or the other but the student continues not to
respond in a desirable way. Which is the next step?
4. What is the parents’ role in this point, to help a student improve his attainment
with homework?
5. Should the parents help their children with their homework or is homework
something between the student and the teacher?

Ethics

Although I have mentioned some of them in previous paragraphs, I am going to

include all the ethical issues, in an attempt to show how essential they are for me.

First of all my research is going to be conducted within an ethic of respect for: the

person, first I mean the teachers: to guarantee their anonymity, to respect every personality

traits, not to take up too much of their time, to have their informed content. I am going to

change all names and ‘do my best to see that participants cannot be identified in anything I

write and take care that my questions do not leave them feeling unreasonably negative about

their practices. I have to think carefully about the research maxim ‘does no harm’ as it is not

obvious how your research could harm anyone’ (Jenny Houssart 2012). For example, in the

beginning I was wondering whether I should mention the teachers’ names in the

acknowledgements. Later on, I realised that it raises ethical issues and I should send a letter

expressing the teachers my appreciation for their help.

‘Harm can entail a number of facets: physical harm, harm to participants

development, loss of self-esteem, stress and using inducing subjects ‘to perform

reprehensible acts’, as Diener and Crandall (1978:19) put it’ (Bryman 2008).


I should show respect for their students, their parents and the whole community of

their school, their community, country and any possible local ethical issues. In addition I

should guarantee the confidentiality of the data collected; I should try to improve the

reliability and validity of my data, explaining the exact way of drawing my conclusions.

While analysing the data I must try to be as objective as possible and try to exclude any

possibility of my research being harmful for anyone involved or not and show respect for

knowledge and Academic Freedom (quotes from Ethics: BERA guidelines).

Individuals should be treated fairly, sensitively, with dignity, and within an ethic of

respect and freedom from prejudice regardless of age, gender, sexuality, race, ethnicity, class,

nationality, cultural identity, partnership status, faith, disability, political belief or any other

significant difference. This ethic of respect should apply to both the researchers themselves

and any individuals participating in the research either directly or indirectly. Adherence to

this ethic of respect implies the following responsibilities on the part of researchers.

Researchers must make known to the participants (or their guardians or responsible others)

any predictable detriment arising from the process or findings of the research and ensure that

I take steps to minimize the effects of designs that advantage or are perceived to advantage

one group of participants over others (BERA guidelines Ethics 2012)

Conclusion

Comparative study is a quite difficult kind of analysing data. The difficulties were

obvious while I was trying to establish the theoretical framework. In this small-scale research

a lot of significant variable left aside. The curriculum, the examinations, the frequency of

homework, the quality of tasks designed to fulfil a specific purpose, the ability of students,

the number of students per class, the policy of the school are all of them factors that would be

very interesting to see how they interact with the three human factors involved through an

aspect of pedagogy, which is the crossroad where they meet each other. But even in this


inadequate effort, I had the chance to view how many useful conclusions the researcher can

draw from unexpected similarities and differences that appear out of the blue. Especially my

last moment’s choice of post compulsory education, when Mathematics is an optional

subject, chosen by students with high attainment seems to inverse the differences seen before

and make things converge, not necessarily for the improvement of mathematics teaching and

learning in the classroom.

I would be highly interested in conducting a research with two carefully chosen case

studies whom we could observe for a period of time, for example one year, or even a term

and have the opportunity to observe and write down what kind of homework the teachers

give, the frequency, the students’ consistence, the reasons of inconsistency, the teachers’

manipulation, the parents’ attitudes, the peers’ reactions. I am sure that we would draw very

interesting conclusions on how teacher, student and his parents’ interact each other creating a

relationship with more similarities no matter how different the culture is.

,


ACKNOWLEDGEMENTS

I should like to thank most sincerely Ralph Levinson, Jenny Houssart, Fiona Rodger for their

impeccable presence and organisation of all illuminating sessions of ‘Practical Research in

Education’, Jacek Brant, Paul Davies and Candia Morgan, whom I do thank as well, but an

additional huge thank you to Jenny Houssart for her encouraging, prompting comments and

care for her students; attitudes that taught me a lot for my role as a teacher.

MAGDALINI KOKKALIARI

KOK11094464

MMAMAT_04

MA STUDENT

MATHEMATICS EDUCATION

INSTITUTE OF RDUCATION

UNIVERSITY OF LONDON

JUNE 2012

REFERENCES


Paul Andrews. (2007). Negotiating meaning in cross-national studies of mathematics

teaching: kissing frogs to find princes Comparative Education Vol. 43( 4), pp. 489–509

Paul Andrews 2009 Comparing Hungarian and English Mathematics Teachers’ Professional

Motivations Proceedings of CERME

BERA Ethical guidelines for Educational Research 2012

Alan Bryman 2008 Social research methods Oxford University Press

Corno, L. (2000). Looking at homework differently. The Elementary School Journal, 100,

529–548.

Cooper, H. (1989). Homework. White Plains, NY: Longman.

Crossley, M. & Vulliamy, G. (1984) Case study research methods and comparative

education, Comparative Education, 20, 193–207.

Diener and Crandall (1978:19) Ethics in Social and Behavioural Research in Chicago:

University of Chicago Press

Nicole M. Else-Quest, Janet S. Hyde, and Ahalya Hejmadi: Mother and Child Emotions

during Mathematics Homework, Mathematical Thinking and Learning, 10: 5–35, 2008

Epstein, J. L., & Van Voorhis, F. L. (2001). More than minutes: Teachers’ roles in designing

homework. Educational Psychologist, 36, 181–193.

Hiebert, Gallimore et al 1999 Teaching Mathematics in seven countries Results from the

TIMSS 1999 video study Dep. Of Education U.S.A.

Jenny Houssart 2012 Comments on draft of Assignment PRMA

Hyde, J. S., Else-Quest, N. M., Alibali, M. W., Knuth, E., & Romberg, T. (2006).


G. Kaiser, E. Luna & I. Huntley 1999 (Eds.), International comparisons in mathematics

education.

Kawanaka, T., Stigler, J., & Hiebert, J. (1999). Studying mathematics classrooms in

Germany, Japan and the United States: lessons from the TIMSS videotape study.

Knipping, C. (2003). Learning from comparing: A review and reflection on qualitative

oriented comparisons of teaching and learning mathematics in different countries. ZDM,

35(6), 282-293

Ralph Levinson 2012 Lectures for Practical Research in Education Institute of Education

Mathematics in the home: Homework practices and mother-child interactions doing

mathematics. Journal of Mathematical Behavior, 25, 136–152.

Mathematics Benchmarking Reports: How Much of Their Out-of-School Time Do Students

Spend on Homework During the School Week? TIMSS 1999 Eighth Grade

Muhlenbruck, L., Cooper, H., Nye, B., & Lindsay, J. J. (2000). Homework and achievement:

Explaining the different strengths of relation at the elementary and secondary school levels.

Social Psychology of Education, 3, 295–317

Osborn, M. (2004). ‘New methodologies for comparative research? Establishing ‘constants

and ‘contexts’ in educational experience’, Oxford Review of Education, 30(2), 265–285

Stigler, J. W., Gallimore, R. and Hiebert, J. (2000). Using video surveys to compare

classrooms and teaching across cultures: Examples and lessons from the TIMSS video

studies. Educational Psychologist, 35, 2, 87-100.

Swidler, S. A. (2000). Notes on a country school tradition: Recitation as an individual

strategy. Journal of Research in Rural Education, 16, 8-21.


Pamela M. Warton: The Forgotten Voices in Homework: Views of Students Educational

Psychologist, 36(3), 155–165, 2001

APPENDIX I

Two tasks in Practical Research Module


1. Qualitative data (Magdalini Kokkaliari 18/2/2012)

Research Question:

What are ‘uninterested’ in mathematics students’ beliefs, emotions, attitude towards

mathematics?

As a Mathematics teacher, I am highly interested in how students feel about

mathematics, especially those, who are classified by their teachers as ‘uninterested’ in that.

What are their beliefs, their emotions, affect, attitude. To gain insight on the development of

‘attitude’ I conducted a face to face interview with an 18-year-old student, who has just

finished secondary education in an independent school of London. I explained to him the

purpose and the ethics (because of which, I have changed some details), he accepted to be

interviewed and the responses were recorded as audio. The interview took place at the school

(at which I teach and he used to be a student, but not in my classes), it lasted 8.25 minutes

and the design was semi-structured. Hence on the one hand, I had a guide, but on the other, I

was able to conduct an open and fluid interview, giving by prompting my interviewee the

chance to express his emotions and ideas.


1. What are your feelings now that your school life has come to an end?

2. How would you describe your relationship with maths during your school years?

3. Do you remember what you liked/disliked about maths?

4. Do you thing that your teachers could have changed in some way your relationship

with maths?

5. If you started school all over again, would you change anything?


Afterwards I transcribed it and structured the code:

Initial Coding:

 emotions

 the student experiences during mathematics related activities His emotions in

the mathematics class still included both pleasant ‘well multiplications,

additions, subtractions it was fun…..the best time’ and unpleasant ones ‘it

started being a little bit confusing, difficult and could not get it, so

disappointing,’54, 56, 77),

but the balance had clearly changed towards the negative, as he moved from

elementary to secondary school

‘In the primary school maths was my favourite subject, but later I could

not get it, I should work hard without success…... so disappointing’

 the student automatically associates with the concept 'mathematics'

(‘All these letters instead of numbers….and geometry, with all these

proofs…..was so confusing and embarrassing’ )

 beliefs

 utility ‘but then in Year 10-13 you have to learn some advanced maths, which

I don’t think that a lot of people are going to use in their everyday life’

 Peers’ attitude-teacher’s role (‘other students may ask the teacher questions

when they don’t get it. Not me, everybody is looking at you, you feel

embarrassed’)


 self-efficacy (‘my own way is like ‘if you can’t do it……….try a little harder

and if you still can’t get through, then time comes to give up’)

 No change (‘Change anything? Err….To be honest, I don’t know if there is

any other way to do the lesson, because it has been the same way for sixteen

years now, my whole life. If this has been the only way for all these years, I

don’t think that anything could change now.’)

 attitude

The analysis of the interview suggests a multidimensional, interconnected model of

negative attitude towards mathematics, quite useful for teachers as a tool for

constructing an accurate diagnosis for their students’ attitude towards mathematics

and intervenes towards a change of it.

References:

1. Bryman, A. (2008). Social research methods (3rd edition). Oxford: Oxford University

Press.

2. Gathering and analysing data through interviews (2012) MA Practical Research

Presentation by Ralph Levinson

Research Question:


What are ‘uninterested’ in mathematics students’ beliefs, emotions,

attitude towards mathematics?

As a Mathematics teacher, I am highly interested in how students feel about

mathematics, especially those, who are classified by their teachers as ‘uninterested’ in that.

What are their beliefs, their emotions, affect, attitude. To gain insight on the development of

‘attitude’ I conducted a face to face interview with an 18-year-old student, who has just

finished secondary education in an independent school of London. I explained to him the

purpose and the ethics (because of which, I have changed some details), he accepted to be

interviewed and the responses were recorded as audio. The interview took place at the school

(at which I teach and he used to be a student, but not in my classes), it lasted 8.25 minutes

and the design was semi-structured. Hence on the one hand, I had a guide, but on the other, I

was able to conduct an open and fluid interview, giving by prompting my interviewee the

chance to express his emotions and ideas.


6. What are your feelings now that your school life has come to an end?

7. How would you describe your relationship with maths during your school years?

8. Do you remember what you liked/disliked about maths?

9. Do you thing that your teachers could have changed in some way your relationship

with maths?

10. If you started school all over again, would you change anything?


Afterwards I transcribed it and structured the code:

Initial Coding:

 emotions

 the student experiences during mathematics related activities His emotions in

the mathematics class still included both pleasant ‘well multiplications,

additions, subtractions it was fun…..the best time’ and unpleasant ones ‘it

started being a little bit confusing, difficult and could not get it, so

disappointing,’54, 56, 77),

but the balance had clearly changed towards the negative, as he moved from

elementary to secondary school

‘In the primary school maths was my favourite subject, but later I could
not get it, I should work hard without success…... so disappointing’

 the student automatically associates with the concept 'mathematics'

(‘All these letters instead of numbers….and geometry, with all these

proofs…..was so confusing and embarrassing’ )

 beliefs

 utility ‘but then in Year 10-13 you have to learn some advanced maths, which

I don’t think that a lot of people are going to use in their everyday life’

 Peers’ attitude-teacher’s role (‘other students may ask the teacher questions

when they don’t get it. Not me, everybody is looking at you, you feel embarrassed’)

 self-efficacy (‘my own way is like ‘if you can’t do it……….try a little harder and if

you still can’t get through, then time comes to give up’)

 No change (‘Change anything? Err….To be honest, I don’t know if there is

any other way to do the lesson, because it has been the same way for sixteen


years now, my whole life. If this has been the only way for all these years, I

don’t think that anything could change now.’)

 attitude

The analysis of the interview suggests a multidimensional, interconnected model of

negative attitude towards mathematics, quite useful for teachers as a tool for

constructing an accurate diagnosis for their students’ attitude towards mathematics

and intervenes towards a change of it.

References:

1. Bryman, A. (2008). Social research methods (3rd edition). Oxford: Oxford University

Press.

2. Gathering and analysing data through interviews (2012) MA Practical Research

Presentation by Ralph Levinson


APPENDIX II

2. Quantitative data (Magdalini Kokkaliari 4/3/2012)


THE SURVEY

By Sunday 4th March I created a questionnaire using Survey Monkey with 10 questions (it

took no more than a couple of minutes to complete, as I was told by 2 respondents, I sent it

for piloting). These questions were multiple choice and the questionnaire was in the form of a

survey on ‘mathematics teachers’ beliefs for students’ homework’. 17 mathematics teachers

-from London and Athens- responded in the following questions:

1. Are you:

o male

o female?

2. How old are you?

o 20-30

o 31-40

o 41-50

o 50+

3. How long have you taught for all together?

o less than a year

o 1 - 2 years

o 3 - 9 years

o 10 or more years

4. At what

o Key Stages you teach?

o Key Stage 1

o Key Stage 2


o Key Stage 3

o Key Stage 4 (GCSE etc.)

o Sixth Form (A Level, Internatonal Baccalaureate, Cambridge Pre-U)

5. At school was Mathematics the subject

o which you enjoyed most

o in which you excelled most

o at which you worked hardest

o which you thought was the most important

6. Did you have extra tuition in Mathematics outside school?

o Yes

o No

7. On average, how long do you expect pupils in your class to spend on a typical piece

of homework?

o up to 10 minutes

o 11-20 minutes

o 21-30 minutes

o 31-40 minutes

o more than 40 minutes

o I don't give homework

8. What contribution do you think homework makes to student's learning?

o large

o small

o too little

o not at all



o Ask them to do it another time

o Use punishments

o Do nothing

o Call parent/carer

o Other (please specify)

10. If a student is not able to do a part of his/her homework, should he/she ask for help

from

o the teacher only

o parent/carer/friends

THE TOPIC

The topic is very important for research on teachers’ and students’ attitude towards

mathematics and the role of homework. Despite the long history of homework and

homework research, the role that homework plays in enhancing student achievement in

mathematics is, at best, controversial. Mathematics teachers’ beliefs for the contribution

of homework on their students’ learning is highly interesting for further research.

The data I’ve collected were from a representative sample with respect to sex, age,

experience and stage at which teach, as it is shown from the graphs of the four first

questions:


The questions 5 and 6 were aimed at finding out what student’s attitude/emotion belief

towards mathematics determines a mathematics teacher’s career as an adult:

The last four questions were in alignment with my research question:


1. Which topic are you covering?

The data I’ve collected gave me the information that:

 a positive student’s attitude towards mathematics in the sense that it is an enjoyable

subject, easy to excel, without extra tuition (self-sufficient), leads to a career as a

mathematics teacher

 mathematics teachers think that homework (21-30 minutes on average) contributes to

student’s learning, which is expected to be done at least another time, using even

punishments or asking parents’ help, under any circumstances (only one answered

that it depends on the particular circumstances)

 there is a dichotomy among mathematics teachers whether students should ask help

only by their teachers or by parents/friends etc. in case they are not able to do a part of

their homework.


The data answered my survey question that teachers believe that homework

has a large contribution on students’ mathematics learning and I think that these data

addressed the research question I posed. There was a limitation taking answers why

they think that students, who are not able to do part of their work should ask their

parents/friends etc. for help and not only their teacher, although they had experienced

mathematics as students as the subject they enjoy, they excel and they had no need of

extra tuition.


APPENDI III

So I planned to conduct two semi-structured interviews with two mathematics teachers in
secondary education, held over Skype (one English and one Greek). I designed a
questionnaire with open-ended questions to encourage full, meaningful answers using my
interviewees’ own knowledge and/or feelings. I sent them an email (to the Greek one) and a
Facebook message (to the English one) explaining the purpose of my interview. The first one
replied in due course and accepted to be interviewed, in the way I have planned. The second
one replied after a long time, apologising and explaining that he had completely missed that
last message. He added that he was willing to be interviewed at any time I wanted and asked
me to send him the questions.
Although it was late, it was a temptation for me to have a second opinion in the way I had
first planned it, with a little change (Facebook instead of Skype). So I sent the questions and
got the answers in a Facebook message.
6. Which, do you think, is the contribution of homework on student’s mathematics
learning in secondary education?
8. And the teacher tries in one way or the other but the student continues not to
respond in a desirable way. Which is the next step?
9. What is the parents’ role in this point, to help a student improve his attainment
with homework?
10. Should the parents help their children with their homework or is homework
something between the student and the teacher?

APPENDIX IV
Homework
Teacher’s beliefs
 Purpose
o Practical skills
 Parents engagement
o Desirable

Student’s improvement negative
Positive


unchangeable
o Undesirable
Positive
unchangeable

o Preparation
o Desirable

Positive
unchangeable
o Undesirable
Positive
unchangeable
o Personal Development
o Desirable

Positive
unchangeable
o Undesirable
Positive
unchangeable

o Peers’ interaction
o Desirable

Positive
unchangeable
o Undesirable
Positive
unchangeable

o Parents-child

 Subject know Parents engagement
o Desirable

Positive


unchangeable
o Undesirable
Positive
unchangeable
o Parents-teacher’
o Desirable

Positive
unchangeable
o Undesirable
Positive
unchangeable

o policy
o Desirable

Positive
unchangeable
o Undesirable
Positive
unchangeable
o Public relations
o Desirable

Positive
unchangeable
o Undesirable
Student’s negative
improvement Positive
unchangeable
o punishment
o Desirable

Positive
unchangeable
o Undesirable
Positive


unchangeable

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