Proceedings of the Day Conference held at the Lancaster University, November 2005.
Paul Dickinson and Frank Eade
Manchester Metropolitan University Institute of Education
This article provides an outline of the initial stages of the implementation of a project exploring the use of Realistic Mathematics Education (RME) in English secondary schools. The paper explores some differences in the approaches used by the RME pupils and those taught under the National Strategy. We conjecture that teaching under RME encourages pupils to refine and develop their informal strategies.
Tadcaster Grammar School
John Monaghan, Louise Sheryn
University of Leeds
How does a plumber determine what his/her hourly rate should be, or a hairdresser determine how much to charge for a haircut? If they go to a bank for a loan, then the manager will want some assurances that the rates charged will keep the business afloat. We describe the work some Year 9 and 10 students did as they engaged in these activities and set up their own virtual business and discuss aspects of the work.
University of Bristol
The nature and role of explanation in mathematics classrooms has been investigated from a variety of different perspectives. In this paper, I consider a possible approach derived from discursive psychology. This approach sees explaining as a situated, discursive practice and seeks to understand how explanations are locally accomplished in interaction. Analysis seeks to uncover the structure of explanations from the participants’ (rather than analysts’) perspective. By working on an example of mathematics classroom interaction I explore how this perspective could be useful for research in this area.
Nigel Calder, Tony Brown, Una Handley and Susan Darby
University of Waikato, Manchester Metropolitan University
This paper is concerned with how both children and pre-service teaching students engage in mathematical investigation using spreadsheets. It examines how mathematical phenomena are shaped by the pedagogical medium through which they are encountered. It considers how the nature of pedagogical support influences different styles of social interaction, and how this interaction contextualises and hence conditions the mathematical ideas. A particular focus is on how alternative pedagogical media promote varying discourse networks that influence the approach to the forming and testing of informal conjectures. How these approaches might differ will also be examined.
Kathryn Fox and Sue Pope
St. Martin’s College, Lancaster
Part of the provision for members of the government funded National Academy for Gifted and Talented Youth (NAGTY) includes two week summer schools hosted by various higher education institutions across the country. In this paper we explore the responses of young people on a mathematics summer school for 11-16 year olds held at Lancaster University and tutored by mathematics educators. Two main areas are considered: the students’ attitudes towards being labelled as ‘gifted and talented’ and their mathematical experiences during the summer school.
School of Education, University of Leeds
This paper seeks to explore the association, if any, amongst mediational means, cultural capital, and students’ approaches to mathematics in a Caribbean setting. On a macro-level, student outcomes in mathematics by school type (a crude indicator of social class) suggest that there is a link between these outcomes and social class (itself an indicator of cultural capital). Micro-level analysis via the lens of an algebra question showed some variation in how students made use of rules in attempting the question, and this along the lines of school type. It is posited that the way rules are used as mediational means in mathematics is structured in part by students’ cultural capital, and that this, cultural capital, provides an explanatory model in this context for the observed differences in mathematical achievement.
Dyscalculia, although officially acknowledged, is controversial. It is particularly problematic for mathematics educators, involving evidence from non-educational paradigms and raising issues about inclusion, mathematics and learning. There are implications for research and the prevention of mathematics difficulties.
Una Hanley, Susan Darby, Nigel Calder and Tony Brown
Manchester Metropolitan University, University of Waikato New Zealand
With the introduction of any new initiative into the mathematics classroom, there is often an assumption that it will produce measurable effects in teaching approaches and pupil progress. Our intention is to examine how teachers from a small project in progress are trying to interpret what a new scheme requires of them and how by engaging with it, they re-describe both their pedagogic understanding and classroom practices relationally to earlier approaches. We focus on the key term ‘discussion’ and examine the way in which it serves to anchor the teachers’ conceptions of themselves during this transition. By using a theoretical framework derived from some neo-Marxist writers we consider these discursive shifts and how they can be seen as relevant to attempts at curriculum change.
Alice Hansen and Liz Jackson
St. Martin’s College, Lancaster
Over recent years, the DfES has directed teachers to integrate Information and Communications Technology (ICT) across the curriculum. Teachers have all been encouraged to attend New Opportunities Fund training (at an approximate cost to the government of £450 per teacher) (Fox, 2000) and Initial Teacher Training institutions have been required to address the QTS standards (DfEE, 1998, TTA, 2002). In light of this, ICT has been a particular focus of our Undergraduate and Postgraduate Primary Mathematics Curriculum courses over the last seven years. The aim of our study was to review trainees’ perceptions regarding how well they felt their college experiences within mathematics had prepared them to use software in their primary mathematics teaching.
Department of Education, University of Gloucestershire
This paper reports on the findings of a small study exploring primary trainee teachers’ experiences and perceptions of the mathematical subject knowledge audit carried out during their training. Many trainees described the exercise as a form-filling waste of time, although the institution is required to gather evidence of trainees developing their subject knowledge for inspection amongst other purposes. Through a combination of questionnaire responses and written reflective comments gathered from across the ITT programmes, some views appeared to be commonly held by trainees about the nature and purpose of the audit process. This paper examines the data with a view to modifying the mathematics subject knowledge audit for future cohorts of trainees.
11 The tension between teacher beliefs and teacher practice: the impact of the institutional context
M. Kerem Karaagac
University of Leeds
This paper presents part of my research on teachers’ beliefs and practices in state schools and privately owned exam preparation schools in Turkey. Extracts from an interview with a teacher who uses a technique that he disapproves of will be reported, revealing a tension between the teacher’s beliefs and his classroom practice. This will be complemented by results of three questionnaire items. The results indicate that certain practices are associated with institutional context and thus institutional context can be an important parameter in understanding and teachers’ professional developments.
Andreas Koukkoufis and Julian Williams
The University of Manchester, School of Education
This study attempts to better understand how children learn integer operations after the ‘dice games’ approach of Linchevski and Williams, through Radford’s semiotic analyses of the means of objectification. In this paper we analyse of pilot study data from an ongoing research. Following a short review of Radford’s account of the semiotic processes, it is argued that in the dice games approach factual generalization can be analysed as a three stage semiotic process of reification. Hence, connections between Sfard’s theory of reification and Radford’s semiotic analyses of the means are made.
Chris Kyriacou and Maria Goulding
University of York, Department of Educational Studies
This paper reports the emerging findings of a systematic review of the literature looking at the following question: What strategies can raise motivational effort in Key Stage 4 mathematics amongst pupils in the mid-below-average to average range of mathematical attainment in England? The review has identified four key areas: (i) grouping; (ii) pupil identity; (iii) teaching for engagement; and (iv) innovative methods.
University of Cambridge
This paper describes some initial findings of a study focusing on the way in which teachers draw on their knowledge of mathematics and mathematics pedagogy in their planning and teaching. The first year, of this four year study, entailed the observation and discussion of mathematics lessons taught by trainees during their final placement. Lessons were analysed in terms of the ‘Knowledge Quartet’. One theme that arose from these discussions was, that when questioned about why they taught in certain ways, trainees responded that if they had no restrictions they would have done things differently. Teachers observed in this study seemed to hold firm to their beliefs about good practice but felt they had to conform to the curriculum and teaching methods they thought to be the policy of the mentor, school or government.
This paper reports one finding from the first year of a longitudinal study into the ways in which teachers knowledge of mathematics and mathematics pedagogy, as revealed in their planning and teaching, may be developed through reflection and the use of a particular framework for observation and analysis.
15 Mathematics assessment for learning and teaching: an overview of the age standardisation model ages 5-14
Julian Williams, Lawrence Wo and Sarah Lewis
School of Education, University of Manchester
The MaLT project, by the University of Manchester with Hodder Murray, researched and developed a new set of standardised diagnostic assessment. Data was collected in February and March 2005 from a nationally representative sample of 12591 pupils aged 5-14 from 111 schools. The tests for each year group were vertically equated using Rasch methodology and the scores were then age-standardised and matched against National Curriculum levels using teacher assessment. Single year and three year sub-sample scores enabled comparisons to be made between maturation (within-year) and year-group (between year) effects: progress appears to decline with age, and plateau at Key Stage 3, and particular features at year 2 and year 6 are notable. We suggest these findings have implications for policy.