Proceedings of the day conferences held at Roehampton in November 2000.
1 How many burgers can a human being eat? Writing word problems when english is an additional language
University of Bristol
Last term, as part of my doctoral research, I recorded pairs of English Additional Language (EAL) students as they worked on the task of writing word problems together. What kind of ‘resources’ do EAL learners use when jointly thinking and constructing word problems? In this paper, taking the discursive psychology of Derek Edwards (1997) and others as a basis for examining students’ interaction, I discuss one transcript from the above work. There is evidence that the students are oriented both to the genre of word problems, and to a personal narrative.
2 “I’d be more likely to speak in class if…”: How some year eight student’s experience teacher questioning and discussion strategies
Mark Boylan, Sheffield Hallam University
Peter Lawton, Aston Comprehensive School
This paper reports on some exploratory research with one class of Year Eight students. The students were given the opportunity to express their views on a variety of teacher questioning strategies in whole class interactions. The students’ responses highlight that feeling emotionally and intellectually secure are important factors influencing willingness to participate. A key finding was the importance of having an opportunity to discuss questions for many students. This was particularly true for female students.
3 Do the students learn the teacher or the teacher learn the students? Making meaning out of developing mathematical classroom cultures
University of Bristol, Graduate School of Education
In the academic year 1999/2000, the developing cultures of 4 year 7 mathematics classrooms were explored. Initially 4 teachers shared images of ‘becoming a mathematician’ with their students, particularly stressing ‘asking and answering the question why’. Students were seen as entering a ‘community of inquirers’ within the scheme of work of their teacher’s department. There is now a wealth of interviews, videotapes and observations from which to make meaning. Do Steinbring’s (1999) descriptions of the autopoetic behaviour of mathematical communication offer a way of communicating an interpretation of what has happened over time in these classrooms? Rather than the students learning the teacher or the teacher learning the students there seems to be meaning making within the mathematics itself.
4 Three way interaction: Exploring the impact of a headteacher and a researcher on a novice primary teacher teaching geometry
University of Surrey Roehampton
This paper is based on the analysis of part of the data collected for my PhD research projection this paper the focus is on one teacher who decided to put aside his teaching method of knowledge transmission in order to undertake an experimental teaching session in his classroom. The role of the researcher in the teacher’s decision making as well as the role of the headteacher of the school in inhibiting the teacher’s further explorations of his children’s ideas are discussed.
University of Oxford, UK & The Aga Khan University, Karachi, Pakistan
This study was part of my doctoral research and aimed to study the role of social interactions both, between students and between students and teacher in students’ learning and understanding of mathematics as they did mathematics in small groups. The study was based in two classrooms in Pakistan where students in small groups (10-12 yr.) learnt mathematics.
The methodology was qualitative in nature. Data generation was through observations, which were recorded on videotapes and student interviews, which were conducted under, stimulated recall. Field notes were also maintained of all research activities. Preliminary analysis raised questions and issues about the nature of learning and how it takes place. Of particular significance were questions regarding the socio-cultural and individual psychological elements in learning?
King’s College, University of London
This paper explores aspects of one LEA Numeracy Consultant’s style of teaching teachers. By analysing a brief excerpt from a National Numeracy Strategy training session, I suggest that the Consultant used several discursive tools to vary and strengthen the warranting given to her statements concerning teaching and learning.
Centre for Mathematics Education, Open University
This article is based on interviews with Key Stage Two teachers about how they use number resources. It concentrates on one resource advocated by the Numeracy Strategy, the number line and one resource which now has a lower profile, base ten blocks. Particular attention is paid to the use of resources in teaching calculation. Findings show that most teachers make use of the number line, often to teach calculation. Base ten blocks are used for teaching calculation by some teachers, though about half make no use of them. However, closer analysis suggests that teachers have different levels of understanding both about how number lines might aid calculation and about the place of standard written methods of calculation.
Celia Hoyles and Dietmar Küchemann
Institute of Education, University of London
We report on the performance of four high attaining groups of Year 8 students on two written questions, one in algebra, one in geometry, designed to test mathematical reasoning. Preliminary findings suggest that performance is not always consistent between classes, between questions and compared to an overall measure of mathematical attainment.
9 The importance of premises: From an essentialist to an anti-essentialist view of ICT in mathematics education
Centre for Learning, Knowing and Interactive Technologies
Graduate School of Education, University of Bristol
This paper reports both the talk I gave at the BSRLM Day Conference – Loughborough University – and my reflections after interacting and exchanging views with the ones who attended it. The aim of my original talk was to outline my ongoing PhD project by introducing, through theories of technology, an anti-essentialist view about technology  and a way of viewing computing in educational policy through the same light . Interestingly enough what seemed to be a major focus in the session was the matter of what an essentialist and anti-essentialist view of technology actually means . In this paper I discuss only what was discussed during my talk. The other issues, including the description of my ongoing PhD project, will be described later, in a future paper.
10 Adjusting to the norms of mathematical writing: Short stories on the journey from cipher to symbol
Elena Nardi and Paola Iannone
School of Education and School of Mathematics, University of East Anglia
To cipher is to ‘express, show forth, make manifest by any outward signs, portray, delineate’, to ‘express by characters of any kind’, to engage with a ‘secret or disguised manner of writing, whether by characters arbitrarily invented or by an arbitrary use of letters or characters in other than their ordinary sense, by making single words stand for sentences or phrases, or by other conventional methods intelligible only to those possessing the key’ … (Oxford English Dictionary). Here we draw on a small study of the transition from informal (school) to formal (university) mathematical writing and discuss examples of Year 1 mathematics undergraduates’ written work that illustrate their authors’ variably successful but often endearing attempts at adjusting to the norms of mathematical writing.
Elena Nardi and Susan Steward
School of Education, University of East Anglia
The number of pupils choosing post-GCSE mathematics and achievement in pre-GCSE mathematics are affected by pupils’ attitudes towards mathematics as a school subject and by their experiences in the mathematics classroom. We have been awarded an ESRC research grant to study quiet disaffection in secondary mathematics classrooms and to uncover the reasons for pupil disengagement from school mathematics. Here we review relevant literature on pupils’ attitudes towards the learning of mathematics and on sources of disaffection and under-achievement: in particular, we discuss the effect on pupil achievement of their confidence and interest in mathematics and of the learning environment of the mathematics classroom. We also present examples from our preliminary classroom observations.
Federica Olivero & Rosamund Sutherland
Graduate School of Education, University of Bristol
This paper provides an overview of a project carried out last year with 5 Further Mathematics A-level students. The project centred around introducing the processes of conjecturing and proving in geometry, within the context of a dynamic geometry environment. The students worked on a sequence of designed activities for seven one and a half hour sessions and then worked independently for several weeks on a challenging project. In the paper we shall present some preliminary results which derive from the students’ work in the classroom based sessions with both Cabri and paper and pencil.
Rustington Community Primary School West Sussex
This work has been done in association with Cara Hood Clymping Primary School Liela Upchurch Wickbourne Infants School and Fiona Dowley Arun Vale Infants. (No test results from Arun Vale are currently included in the work)
Adrian Pinel and Jeni Pinel
University College Chichester, Independent Researcher
This paper is about a study of 48 pupils aged 4 to 14 years, within a ‘pyramid’ of 15 schools engaged in the early stages of a numeracy improvement project. The purpose of the study was to confirm or challenge judgements made by key teachers [primary heads /co-ordinators, middle school subject leaders, upper school KS3 co-ordinator]. The longer term objective was to create realistic benchmarks for pupil achievement throughout the pyramid. The paper describes the basis upon which the study was carried out, its findings, indicating the nature of the benchmarks that came from it.
15 Ethnomathematics: A liberation from the yoke of eurocentrism or the biggest disaster that could befall mathematics education
Stuart Rowlands and Robert Carson
University of Plymouth and Montana State University
Based on a review of the literature from practitioners in the United States, the introduction to this session will argue the latter.
University of Surrey Roehampton
In 1994/5 the Royal Society and Joint Mathematical Society set up a joint working group on the teaching of algebra in schools and as a result published a Report “Teaching and Learning Algebra pre 19” (Royal Society, 1997). The report was the catalyst for my research for my Masters dissertation into high attainers’ understanding of symbols. I have used classic errors and misconceptions to inform my research which involved students from years 10, 11, 12 and 13. In this paper I briefly explore some of the implications for teaching which have emerged from part of the research.
Chronoula Voutsina and Keith Jones
University of Southampton
The aim of this study is to determine the pathway of changes that occur in the problem solving strategies of 5-6 year old children when they are engaged in solving a specific form of addition task. Karmiloff-Smith’s model of Representational Redescription (RR) suggests that higher conceptualisation and control of the employed strategy develops both before and after the achievement of an efficient solution. Evidence from data reported in this paper tends to support this hypothesis.
University of Oxford
In this paper I am going to look at the roles and uses of unison response in the teaching and learning of mathematics. This work is based on a collection of field-data from mathematics classes in Cape Town. Although the context of the data is important, the issues which arise may be universal but this paper is too short to give anything but a brief introduction. A longer paper is in preparation.
British Society for Research into Learning Mathematics Geometry Working Group
Convenor: Keith Jones, University of Southampton, UK
A report based on the meeting at the University of Loughborough, 6th May 2000 by Keith Jones, University of Southampton, UK
The successful teaching of geometry depends on teachers knowing a good deal of geometry and how to teach it effectively. This report provides a review of what is known about teacher knowledge in geometry, how the knowledge develops and how this knowledge development can be supported by professional development .The available evidence suggests that attention could usefully be paid both to the initial and continuing education of teachers of mathematics in terms of their background and understanding of geometry.