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u: Research Topic: Literacy & Numeracy &; Inclusion; Pupil grouping and organisation of classes.
Attitude and Achievement of the Disengaged Pupil in the mathematics Classroom (Updated)
Nardi, E. and Steward, S.
University ESRC final report R000223451
Page 1
Are all pupils achieving their mathematical potential? If not, why not?
Many studies have highlighted disaffection in terms of deviant behaviour or truancy. Recent thinking however suggests that there is often a large group of learners who are quietly disaffected and whose mathematical potential has yet to be fulfilled. This study set out to explore the attitudes, beliefs and emotions of Year 9 mathematics pupils based in three Norwich schools. The paper draws mainly from pupil interview data, informed by classroom observation, consultation with teachers and pupil achievement data.
The authors found that the focus group (of quietly disaffected pupils) did in fact engage with mathematical tasks in the classroom, but only out of a sense of obligation and experienced no real enjoyment or satisfaction from these activities. The authors identified a profile of quiet disaffection in the secondary mathematics classroom
and suggest that strategies for re-engaging these pupils may lie in reviewing four key areas: the nature of classroom activities (are they fun?), teaching styles, the role of the teacher, and the hierarchical nature of setting.
Keywords
UK; United Kingdom; teaching and learning; pupils; secondary schools; disaffection; year 9; mathematics; self-esteem; teaching styles; pupil attitudes; pupil participation; pupil alienation; setting; inclusion
Content
Are all pupils achieving their mathematical potential? If not, why not?
Page 1
What did the researchers aim to do? Page 2
In what context did the research take place? Page 3
What do we know about disaffection? Page4
What does this report tell us about the disengaged pupil? Page 5
How might we re-engage pupils in their mathematics studies? Page 6
How did the authors conduct their research? Page 7
Implications Page 8
Where can I find out more? Page 9
Page 2
What did the researchers aim to do?
The researchers sought to identify and explore factors relating to pupils disengagement in the secondary mathematics classroom. In particular, they hoped to use pupil interviews to gain an insight into which specific practices, currently employed by mathematics teachers, were most likely to result in disaffection. By means of further discussion with teachers and pupils, the researchers aimed to establish a platform of 'collaborative reflection'. By exploring the thinking and beliefs which were underpinning current practice, together with the pupils views on its effectiveness, they hoped to identify potential alternative methods of teaching which might be a way of re-engaging these pupils.
The authors also aimed to provide some indicators for further research into the area of quiet disaffection, which would incorporate wider aspects of education.
Page 3
In what context did the research take place?
The research took place in three Norwich secondary schools which had participated in a previous research study by a teacher researcher, Jerry Oakley (click to page 9 Where can I find out more?) for the Norwich Area School Consortium. The schools concerned were over-subscribed successful comprehensives, with mixed socio- economic intake and above average GCSE results in mathematics. The teachers had reasonable confidence in their mathematics and in their teaching and felt they had an unbiased relationship with their pupils. The study involved mathematics teachers and Y9 pupils in middle ability sets. Pupils from these sets were targeted because the authors felt they may have the potential for higher achievement than their projected GCSE grades of C/D.
The authors reported that recent international comparisons in pupils mathematical achievement suggest that performance in the U.K. is at rather unsatisfactory levels.
Their study was intended to inform practitioners and others interested in pupil achievement about issues of attitude, beliefs and emotions and how they might relate to pupil performance.
Page 4
What do we know about disaffection in relation to mathematics?
Previous studies defined disaffection in terms of disruption or truancy, or resulting from special educational needs. Other research concluded that disaffection may be seen as a product of local and family cultures that might be in conflict with some educational expectations.
Although some studies viewed disaffection as resigned acceptance rather than deviant behaviour, the authors suggest that quiet disaffection in the mathematics classroom is relatively under- researched. They use recent studies which have highlighted the concept that pupils attitudes and emotions towards mathematics are closely linked with their performance as the starting point for their study. Factors such as the role of interesting class activities, or the role of teachers attitudes towards error making, have also been found to influence pupils overall mathematical performance. The authors cite a study by Boaler, which suggests that disinterest in mathematics generated by certain pedagogical approaches, seems strongly linked with underachievement. For recent research by Boaler, William, and Brown. into students experiences of ability grouping, linked to disaffection, click here to web digest.
This disinterest was not confined to the field of mathematics education. The authors cite research which suggests that in the later years of their schooling, pupils often become disillusioned with the education process. Students expressed a preference for working with their friends, making and discussing things.
Finally, the authors cite evidence from a recent study in the United States which contends that making difficult content easy to learn is barely enough to improve mathematics achievement. It is more important to ensure that difficult mathematical content is presented in an interesting, attractive and enjoyable way.
Nardi and Steward used these and other research findings to inform their investigation into the experiences of quietly disaffected pupils in Year 9.
Page 5
What does this report tell us about the disengaged pupil?
The authors found that students in the focus group seemed to engage in mathematical tasks out of a sense of duty and obligation towards parents or school, but appeared to find their mathematics work a joyless task. By studying pupil interview data and other evidence from lesson observations, they identified five issues common to the disaffected student:
Tedium: Pupils frequently used words such as boring, citing examples of mathematical tasks and activities that appeared irrelevant and tedious, and offered no opportunity for activity. The skills that were offered were seen by some as an isolated body of non-transferable knowledge, steeped in symbolism and abstract concepts. There were occasions when the students found the use of symbolism alienating, but attempts by teachers to contextualise mathematics through practical activities was not proving effective. In fact some students seemed to feel resentful towards such activities.
Isolation: Mathematics was perceived by the students as offering little opportunity to work with peers in a collaborative style to aid understanding. The students demonstrated a clear preference for this style of working, for both practical activities and textbook exercises. They emphasised the importance of negotiation and explanation, in communicating with their peers, as an efficient means of not only completing tasks, but generating a better understanding of the project. The researchers questioned whether teaching styles were based on the view that mathematics demanded high levels of concentration and that pupils worked better away from the distraction of others.
Rote- Learning: Several students in the study viewed mathematics as a set of rules that provided unquestionable and unique methods to answering problems. Certain students saw memorisation and mimicking of procedures demonstrated by the teacher as an efficient route to achieving better results, but admitted that this was not very satisfying. In contrast, subjects such as art were perceived as less rigid.
The authors suggest that underlying this dissatisfaction with dry mathematics could be a desire for a deeper, more essential understanding of the subject and for a more meaningful engagement with mathematics. Indeed, students expressed strong, positive attitudes towards mathematical concepts that they had a firm grasp of, but were frustrated when lack of time meant tasks had to be completed without this gratifying sense of understanding.
Elitism: Teachers attempts to simplify mathematical thinking through algorithms or formulae could have added to learners confusion. The authors suggested that an algorithm or formula often compressed, and assumed an understanding of, a number of mathematical ideas. So it was possible for teachers to see a task as straightforward and accessible when it was not easily understood by the pupils.
A significant finding in this study was that students seemed to perceive mathematics as a demanding subject, in which only exceptionally intelligent people can actually succeed. Lack of success in mathematics tended to be interpreted by the students as being due to lack of intelligence on their part, which led to overwhelmingly negative feelings about their own mathematical ability.
The authors pointed out that such images of the students' own fragile ability in mathematics may then be further undermined in the current school environment of setting and testing. A small but significant number of students perceived the more capable teachers as being allocated to the higher sets. The authors reported that students in the top set were seen as elitist and frightening. Students appeared to find the system of setting too judgemental and the resulting blows to their mathematical confidence often painful.
De-personalisation: The authors suggested that an inherent hierarchy, based on setting, altered the nature of the classroom experience from one that accommodated the learners needs to one that focused on each learners position within this hierarchy.
The students expressed their feelings of alienation towards this perceived system of status through position in the pecking order and expressed a desire for an alternative learning environment recognising individual needs and achievements.
Individualised learning schemes such as SMILE (School Mathematics Individual Learning Experience) seemed to be appreciated by some students for its attempt to address the issue of learning at ones own pace, but was criticised by others who wanted a more interactive mathematical experience. The authors drew attention to the fact that, although students resented the hierarchical nature of setting, they also acknowledged its value in the allocation of individual work that was suited to learners needs.
The authors used this categorisation (TIRED) to offer a strong message for those involved in mathematics teaching. In the absence of mathematical experiences suited to individual needs and consequent feelings of success and self-esteem, they said that students become alienated from the subject and eventually chose not to study it.
Page 6
How might we re-engage students in their mathematics studies?
The fact that students in the study experienced negative feelings about their own mathematical ability did not dissuade them from participating in mathematical activities. Indeed, most students were able to draw on positive experiences of mathematical learning, when asked to explain their ideas about what constituted effective mathematics teaching. After analysing these responses, the authors grouped them into four main areas of practice:
the nature of classroom activities the notion of fun;
teaching styles;
role of the teacher; and
role of stratification structures such as setting.
The authors proposed that effective re-engagement strategies might lie within these themes. As it was not possible to explore these strategies further within the time constraints of the 12 month study, the authors suggested that a subsequent research priority could be action-research studies where such re-engagement strategies were implemented and evaluated.
Page 7
How did the authors conduct their research?
The focus of the study comprised a group of pupils in the middle ability set, predicted to achieve grades C/D in GCSE in two years time, but who were thought to be capable of higher achievement.
Data collection in the main study consisted of classroom observations over a period of seven weeks and also 27 pupil interviews. Information from classroom observations, together with pupil background data was reported separately. This paper draws mostly on the interview data.
All the pupils from the three classes were interviewed in groups of two to four, or individually, about general attitudes to mathematics and specific disengagement incidents. The semi-structured interviews were audio-recorded and then reproduced as a condensed version on an interview Protocol table, which was based on seven categories of statements: conceptual difficulty, mathematics, performance, teaching, social , school, and methodology.
The interviews were fully transcribed and the audio tapes copied onto compact discs. Responses were then multi-level coded and entered into a spreadsheet from which clusters emerged and the characteristics of the quietly disaffected pupil became evident.
Page 8
Implications
In completing this digest the authors began to ask the following questions about implications for practitioners:
Students in the study seemed frustrated when pressures of time forced them to apply a procedural approach to mathematics that they did not properly understand. To what extent might the teaching of efficient calculation methods gloss over essential stages that could help your students understanding of mathematics? Might it be useful to defer teaching efficient algorithms until students have worked to develop their own approaches to a problem?
The study found that students disliked working alone and valued the opportunity to discuss their thinking with others in a non-judgemental setting. To what extent might teaching students the skills they need to work collaboratively in groups help you to incorporate this technique successfully into mathematics lessons?
The study suggested that teachers of students in ability sets for mathematics sometimes underestimated the variety of students individual needs. To what extent could formative assessment help you to discern the varying learning needs of each of your students?
To see a digest on research into the effects of setting in primary mathematics click here. (Link to HYPERLINK "http://www.standards.dfes.gov.uk/research/themes/pupil_grouping/FriNov11552362002/" http://www.standards.dfes.gov.uk/research/themes/pupil_grouping/FriNov11552362002/ )
In completing this digest the authors began to ask the following questions about implications for school leaders:
The study identified numbers of pupils who were quietly disaffected in mathematics. What strategies have you found useful to identify and monitor students who may be producing acceptable examination results and yet are not achieving their full potential?
Some students in the study believed that the most capable teachers were usually given top sets to teach. What beliefs about teaching and learning underlie decisions in your school about the most productive ways of allocating staff to particular groups?
Page 9
Where can I find out more?
This digest is based on the work reported in: Steward, S. & Nardi, E. (2003), Is mathematics T.I.R.E.D.? A profile of quiet disaffection in the secondary mathematics classroom, British Educational Research Journal. (Vol. 29 No. 3 pp.345-367).
A TRIPS digest of a study of the effects of setting by ability on students motivation: Boaler, J., William, D., & Brown, M. (2000) Students experience of ability grouping disaffection, polarisation and the construction of failure. British Educational Research Journal, Vol. 26, No. 5, pp. 631-648 can be found at: HYPERLINK "http://www.standards.dfes.gov.uk/research/themes/pupil_grouping/FriOct110934232002/" http://www.standards.dfes.gov.uk/research/themes/pupil_grouping/FriOct110934232002/
A GTC Research of the Month based on Boaler, J (2002) Experiencing School Mathematics can be found at: HYPERLINK "http://www.gtce.org.uk/PolicyAndResearch/research/ROMtopics/maths/" http://www.gtce.org.uk/PolicyAndResearch/research/ROMtopics/maths/
Rhinos (really here in name only), a research project about quietly disaffected pupils at Sprowston High School, Norwich. A summary can be found on the GTCe Research of the Month web pages HYPERLINK "http://www.gtce.org.uk/research/romhome.asp" http://www.gtce.org.uk/research/romhome.asp in the case studies used in discussing the book Positive alternatives to exclusion (2000) by Paul Cooper et al.
Dowker A. (2004) What works for children with mathematical difficulties? DfES Research Report 554. HYPERLINK "http://www.dfes.gov.uk/research/data/uploadfiles/RR554.pdf" http://www.dfes.gov.uk/research/data/uploadfiles/RR554.pdf
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