**Proceedings of the Day Conference held at London South Bank University in March 2007**

## Contents

#### 1 Is my research a research? Looking at mathematics education research method as a derrida reader

Marcelo Salles Batarce

London South Bank and Universidade Estadual do Mato Grosso do Sul Scholar of Brazilian government – CAPES – Brazil

In this paper I suggest that the labels postmodernism and poststucturalism are not enough to investigate educational research methods from the view of Derrida. I propose a ‘full meaning of research’ as able to grasp the concept of writing in Derrida.

#### 2 Is the tangent line tangible? Students’ intuitive ideas about tangent lines

Irene Biza

Department of Mathematics, University of Athens (Greece)

The results presented in this paper are a part of a doctoral study nearing completion which focuses on students’ intuitive thinking about tangent lines. The study explores the ways in which students who have studied tangents in school in different contexts (Geometry, Analytic Geometry and Calculus): (i) perceive properties that are not generally valid as defining conditions of the concept and (ii) create new, often notvalid, properties out of the fusion of information from across the different contexts. Data was collected through a questionnaire administered to 182 first year mathematics undergraduates in Greece at the very beginning of their studies. Here I exemplify from the data analysis in the course of which several models of the tangent line have emerged based on the above properties.

#### 3 Calculation strategies used by Year 5 children

Alison Borthwick and Micky Harcourt-Heath University of East Anglia

When working on mathematical questions, children choose from a range of calculation strategies. Although the National Numeracy Strategy (NNS) advises that different methods are taught for each of the four operations, this research shows that children often find it difficult to choose the most efficient and effective in order to answer the question. This paper reports on the findings from a sample of Year 5 children who were given questions from a QCA paper and it examines the range of strategies used by them.

#### 4 ‘I would rather die’: attitudes of 16-year-olds towards their future participation in mathematics

Margaret Brown and Peter Brown, King’s College London and

Tamara Bibby, Institute of Education, University of London

Questionnaire responses were analysed from 1997 GCSE mathematics candidates in 17 schools about their expected future participation in AS/A level mathematics, their reasons for this and their attitude to mathematics. The data was gathered as part of a larger study but was analysed separately. The analysis supports findings from previous studies in demonstrating that lack of confidence and perceived difficulty are the major reasons for students not continuing with mathematics, and that dislike and perceived lack of relevance are also factors. The study shows a clear relation between these factors and predicted GCSE grade, and a lesser relationship with gender. When these were corrected for, school participation rates still varied, with enjoyment differentiating schools with high and low participation rates.

#### 5 Graphing and graphing calculators in examinations, trends over time

Roger Brown

Visiting Research Fellow, University of Bath

The paper outlines the initial findings of an analysis of the impact of the graphics calculator on questions in two country’s end of secondary school ‘high stakes’ mathematics examinations. The questions considered were those in which a student response incorporating graphing was expected. The approaches taken by the question writers’ range from requiring the use of the graphics calculator to draw a graph to excluding the graphics calculator from a question where a graphics calculator solution is possible.

#### 6 Primary trainees’ reflection-in-action

Julie-Ann Edwards

School of Education, University of Southampton

This paper explores some of the reflective writing undertaken by trainees on a Primary PGCE course following small-scale classroom-based research as part of their work towards Masters level credits. Types of reflection evident are categorised and the frequency of these categories related to the overall grade achieved for the research undertaken. Questions are raised about the nature of these reflections in relation to what is described by Schön as ‘reflection-in-action’ by professionals. Some of the writing is examined in the context of the use of the language about reflection on both personal and professional development which is promoted throughout the PGCE course.

#### 7 A systematic review of the role of ICTs in learning algebra

Maria Goulding and Chris Kyriacou

University of York

This paper focuses on a systematic review of studies on how different ICT tools can be used to develop understanding of functions. ICT tools included the use of different software (e.g. spreadsheets and graph plotting software) and different hardware (e.g graphics calculators, computers used by pupils and computers used by teachers with the whole class). There was evidence of gains in understanding in particular aspects of functions, evidence of some difficulties in interpreting screen displays, and evidence of productive ways of working.

#### 8 Approaches to a circle-theorem task by a novice group of secondary school pupils

Dietmar Küchemann

Institute of Education, University of London

A group of four Year 10 pupils were observed during a mathematics lesson as they attempted to solve a GCSE question involving circle theorems. The pupils were relatively inexperienced problem solvers and their knowledge of circle theorems was far from ‘fl uent’. This lack of experience cast a useful light on the challenges involved in solving geometric tasks which we as teachers might regard as quite routine.

#### 9 Contexts for pure mathematics: an analysis of A-level mathematics papers

Chris Little and Keith Jones

University of Southampton

While there has been some research into the use of context in mathematics assessments pre-16, little, if any, work exists on the role of context in post-16 mathematics. For A- and AS-level mathematics courses in the UK, assessment schemes are required to include questions that test candidates’ abilities to apply mathematical models to real-life contexts, and to translate real-life contexts into mathematics. This paper explores the ways in which context occurs in ‘pure’ mathematics questions and, through this, suggests a framework for analysis that encompasses issues of accessibility, realism and authenticity.

#### 10 Coding strategic behaviour in mathematical problem solving

Andri Marcou

London South Bank University

The crucial role that strategic behaviour plays in achieving mathematical problemsolving success has been well documented by research into learning mathematics. Strategic behaviour is also important for self-regulation, a goal for mathematical problem solving (MPS). A coding scheme that consists of cognitive, self-regulatory, resource management and task strategies allocated at each stage of MPS was developed to code and analyse primary students’ self-regulated MPS behaviour. The coding scheme was piloted after three studies which involved carrying out clinical interviews with students of year 4, 5, and 6 while working on word mathematical problems. A coded transcript of a clinical interview is presented as an example to illustrate the applicability of the coding scheme.

#### 11 Looking for mathematics

Heather Mendick, Marie-Pierre Moreau

Institute of Policy Studies in Education, London Metropolitan University

Debbie Epstein

School of Social Sciences, University of Cardiff

We use data from our research on maths and popular culture to investigate the question: ‘What is maths?’ In a survey of Year 10 students asking for examples of maths and mathematicians in popular culture, as well as some perhaps predictable references to things like A Beautiful Mind and The Curious Incident of the Dog in the Night-Time, there were many more surprising or controversial entries, including game shows like Deal or No Deal and even action movies like Mission Impossible. We then carried out group interviews with some of these same students once they reached Year 11. We look at their answers and, in particular, we identify the way that learners overwhelmingly define maths in relation to the presence or absence of number and explore their alternative ideas about what makes something maths.

#### 12 Variations on a theme: Introducing new representations of fraction into two KS3 classrooms

Candia Morgan, Institute of Education, University of London

Two teachers in different schools participated in a research project looking at the use of technology based representations of mathematical objects. Each used the same software, incorporating a novel representation of fraction as a dynamic functional relationship between values on two number lines. They planned together, discussing the characteristics of the software, the educational goals and modes of use as well as sharing resources and ideas about student tasks. In practice, the lessons each taught were very different and the ways in which students made use of the software also differed substantially. Influences on the nature of teachers’ incorporation of new elements into their pedagogic practice are discussed, including consideration of explicit and implicit theoretical frameworks and of institutional and cultural contexts.

#### 13 An examination of the developing mathematics teaching practices of primary teachers from ITE into first teaching posts

Sandy Pepperell

Roehampton University

This is an exploratory paper looking at some early evidence from data which is part of a study following the progress of four primary teachers as they move from a university based Post Graduate Certificate in Education (PGCE) course until the end of their Newly Qualified Teaching (NQT) year. The study looks at how we might theorise the transition of mathematics teaching practices from university course into school. The data in this paper focuses on one participant’s ideas about problem solving. The paper also looks at two publications offering sociological perspectives on ITE and classroom teaching to consider possible readings of the data. One possible area to be developed from the ideas in the publications is that of teacher agency and the role it plays in the process of becoming a teacher of primary mathematics.

#### 14 Exploring pupils’ conceptualisations: What makes something ‘mathematical’?

Damon Vosper Singleton

King’s College London

A report of the findings of a study intended to explore year seven pupils’ perceptions of the characteristic ‘mathematical’. Following a protocol based on the methods of Personal Construct Psychology, participants ranked a set of paintings in terms of ‘how mathematical’ they felt the paintings were, and were then asked to explain their decisions. The exercise was repeated with a set of five activities. Participants were seen to respond with a not inconsiderable uniformity to the tasks, although the individual explanations of what makes an activity ‘mathematical’ provided some intriguing insights which indicate possible further exploration. Implications of this finding in terms of future research approaches are discussed with the aim of understanding what determines whether an activity is described as ‘mathematical’.

#### 15 Issues in identifying children with specific arithmetic difficulties through standardised testing: A critical discussion of different cases

Chronoula Voutsina and Qaimah Ismail

School of Education, University of Southampton

The paper discusses issues related to the identification of children with extreme difficulties who are regarded as potentially having dyscalculia. We present cases of 7 year old children with different approaches to a standardised computer-based test. We present issues that the cases raise and reflect on how such tests can inform those who use them and whether they enable or not the identification of children’s specific difficulties in arithmetic learning.

#### 16 Super-ordinate communities of practice: Crossing boundaries, ‘transfer’ and identity

Peter Winbourne, London South Bank University

Cristina Frade and Selma Moura Braga, Federal University of Minas Gerais, Brasil

The aim of this paper is to discuss a theoretical construct – super-ordinate or overarching communities of practice – to contribute to the discussion of transfer and, more specifically, to reconceptualize what, within the school context, might be thought of in Bernstein’s terms as the transfer of knowledge between two insulated vertical discourses. We describe how this theoretical construct was developed from interdisciplinary work carried out by secondary mathematics and science teachers. We tell some stories about the learning of two fifteen year-old students to ground our ideas. We conclude with some theoretical suggestions of how we might develop and make use of the concept of super-ordinate or overarching communities of practice.

#### 17 Developing a framework for researching professional development in mathematics: NCETM/BSRLM working group

Rosamund Sutherland and Colin Matthews

The aims of the research projects instigated by the NCETM are: a) to investigate “what works” in terms of professional development in mathematics b) to develop a culture of action research being part of CPD by encouraging teachers to become active researchers and supporting them in doing so and c) to develop communities of practice as a result of the research.