Proceedings of the Day Conference held at the University of Oxford, 7th June 2003
Victor Kofi Amoah
Alperton Community School, Wembley
According to the situation cognition perspective, knowledge and thinking are inextricably intertwined with the physical and social situations in which it occurs. The implication is that learning situations should be embedded in authentic problem situations that have meaning for the students. This study investigates the effects of two teaching approaches (or strategies) on students’ conceptual understanding of differential calculus. These approaches were the Unify Model and Situated Cognition Approach.
2 An ICT driven curriculum: developing students understanding ofproof at KS4 with a dynamic geometry package and an interactive whiteboard
Poole High School, Dorset
This short paper will address the teaching and learning of proof in secondary schools with special regard to recent changes to GCSE Mathematics specifications. I will focus on the teaching of the Circle Theorems to Higher Level GCSE Students before summarily developing a generalised model of an ‘ICT Driven Curriculum’ applicable to the teaching of geometrical knowledge and reasoning at either Key Stage Three or Four.
Margaret Brown, Mike Askew and Alison Millett
King’s College, University of London
The Leverhulme Numeracy Research Programme was a five year longitudinal study of children’s learning and the factors which affect it. In addition to five case-study projects, it included a longitudinal survey of two cohorts of children in 40 primary schools. The research design included assessment, lesson observation and teacher interviews in Year 4 in 1997/8, two years before the implementation of the National Numeracy Strategy (NNS), and again in 2001/2, two years after it. Additional funding for an extra year by the Nuffield Foundation allowed us to study changes in
Year 4 attainment, including how the NNS affected different items and different groups of children, and to give tentative explanations for these changes deriving from lesson and interview data.
Graduate School of Education, University of Bristol
David A Reid
School of Education, Acadia University, Canada
Decision-making, taking place without time for reflection in situations that are often too complex for complete analysis even in retrospect, is a central part of teachers’ activity in teaching and students’ activity in doing mathematics. Damasio’s (1996) hypothesis of what he calls ‘somatic markers’ (bodily predispositions that inform our decision-making) accounts for the ability of teachers and students to make such decisions. However, somatic markers are by their nature not directly observable. We have reported (Brown and Reid, 2003) seeing evidence for the development of a new positive somatic marker through the behaviours of a teacher and his students. Here we report on progress made in observing the unseeable through a focus on looking for patterns of behaviour in the use of questioning techniques.
Goldsmiths College, University of London
All primary and secondary Initial Teacher Training (lIT) students, irrespective of their subject and/or age specialism are required to pass the numeracy skills test, which was introduced in May 2000. The test is in two parts: a mental mathematics section and a written section. With this in mind, this paper reports on initial findings from a small support group of 10 year 2 BA (Ed) students who identified themselves as needing support with mental mathematics. In brief, my findings highlight several important factors including the effects of low self- image about mathematics ability and the gap between a student’s subject knowledge and understanding.
Agder University College, Norway
Design Research is a term being used to describe forms of research that ‘design’ classroom activity to enhance learning and study its evolution and outcomes. I have become interested in how design research contributes to teacher learning through teachers’ involvement in the research process. This short paper explores, at a very elementary level, potential relationships between design research and research into mathematics teaching that has resulted in developments in teaching and knowledge about teaching.
University of Plymouth
There is universal acceptance that mathematics learnt in school should be useful to the learner, both in other school situations and away from the educational context. However, despite much advice about how to achieve this, little success has been shown to result from schooling. This article reports the findings of a study describing the phenomenon of knowledge utilisation as primary school children experience it. It provides a categorisation of metaphoric descriptions of their beliefs about mathematics, ranging from those that are unhelpful in promoting mathematical knowledge utilisation to those in which it is central and explicit.
8 A sociological description of changes in the intellectual field of mathematics education research: implications for the identities of academics
South Bank University, London
South Bank University, London
University of Patras, Greece
In this paper we will report on the work of our ESRC funded research project “The production of theories of teaching and learning mathematics and their recontextualisation in teacher education and education research training”.
Tom Macintyre, Ruth Forrester
Edinburgh Centre for Mathematical Education (ECME) University of Edinburgh
Researchers at the Edinburgh Centre for Mathematical Education are currently investigating use of the soroban (Japanese abacus) to develop strategies usedfor mental calculation. The classroom-based project involving year 8 pupils in two schools is funded by the Nuffield Foundation. This paper focuses on the initial assessments of students’ mental computation abilities. Deficiencies, particularly in subtraction of two digit numbers, are striking in the light of recent emphasis on developing mental calculation strategies. The findings have surprised teachers and researchers involved in the project, raising questions about assumptions made of students’ competence in mental calculation.
10 The tale of the tail: an investigation of failing single honours mathematics students in one university
Sheila Macrae, Margaret Brown, Hannah Bartholomew
King’s College, London
University of Leeds
We draw on datafrom an ESRC study: Students’ Experiences of Undergraduate Mathematics (R000238564). The aim of the study is to understand better the reasons why students experience undergraduate mathematics courses in different ways and why some maintain or develop more positive attitudes than others to the subject. In this paper we focus on one group of second year students who were ‘at risk’ of failure. By comparing the ‘failing’ students with the rest of the cohort and with each other, we try to see if they could have been identified earlier. We also suggest ways in which the mathematics department might better support these struggling students.
University of Education, Winneba, Ghana
This paper reports a study that investigated the congruence between the teaching methods presented in Ghanaian primary mathematics official curriculum materials and teachers’ classroom practice. The study involved a range of methods ¬observation of classroom practice, content and discourse analyses of lessons in mathematics. It has provided further evidence to support the supposition that in less developed countries, the official school mathematics curriculum exerts poweiful influence on classroom practice. It was found out that though there was rhetoric in the introduction of the curriculum materials on the use of teaching skills that suggest discovery methods, the analyses indicated that only few learning/teaching activities that would encourage the use of such discovery methods were included in the materials.
University College Chichester
In response to a requirement to identify applicants to ITE who are lacking certain defined qualities, a mathematics task was designed. It has now been trialled for 8 months and indications are generally positive. It has three parts – video-, game- and misconceptions-based. The first part – video-based – is outlined here and some of the emerging illustrative data considered. However there are many questions arising from this task that need to be addressed longer term by the project team. As this is intended to become a longitudinal study with several aspects, these questions will be
further addressed in later papers by the team.
Faculty of Education, University of Plymouth
The National Numeracy Strategy calls for greater use of whole-class, interactive teaching with dialogue and discussion at its heart. However, there is little if any rationale given in the Strategy for using talking and listening as an approach to teaching and learning. This study explores children’s perceptions of interaction and, in particular, the role of talking and listening. It concludes that listening is privileged over talking and that this has important consequences for interactive teaching.
14 Adopted teaching styles of parents as co-educators in mathematics: study in a Canadian elementary school
University of Surrey, Roehampton
This study explores patterns of involvement of parents as co -educators of mathematics. Factors influencing attitudes to mathematics and the teaching approaches adopted by parents at different stages of their children’s education are considered. The teacher’s own perspectives and explanations of varying levels of parental involvement as mathematics co-educators are briefly discussed. Findings indicate that teachers and parents have restricted views of each other’s practices.
Tim Rowland, Anne Thwaites, Peter Huckstep
University of Cambridge
The mathematics subject matter knowledge of primary school teachers has in recent years become a high profile issue in the UK and beyond. This paper reports on one dimension of a videotape study of mathematics lessons prepared and conducted by primary PGCE trainees. The aim of the study was to identify ways in which their subject knowledge, or the lack of it, was evident in their teaching. One significant issue that emerged was the particular examples chosen and used within the lessons. This raises questions about what advice we should be giving such novice teachers in their training.
Narumon Sakpakornkan, Tony Harries
School of Education, University of Durham
This paper presents some key findings concerning pupils’ processes of thinking in simplifying algebraic problems. Thefindings are drawnfrom an algebra test given to 103 English pupils and 186 Thai pupils. This paper focuses on one of the six themes explored during the study. The simplification theme has been split into level one: simplify one variable, level two: simplify two variables, level three: simplify two variables with brackets, and level four: simplify two variables of second order with brackets. The pupils’ processes in simplification were categorised from their written responses. English and Thai pupils used the same processes to simplify the level one question. The differences were increased when they faced the harder items. The main difficulties were dealing with negative signs and multiplying out the brackets.
Leida Salway, Jan Winter
Graduate School of Education, University of Bristol
The Home School Knowledge Exchange Project is part of the ESRC Teaching and Learning Programme. The project has three strands, of which one focuses on Numeracy in Key Stage 2. We are working with teachers in four schools, two in Cardiff and two in Bristol to develop activities which will support knowledge exchange between pupils’ homes and schools. We have found parents were initially interested in learning more about the mathematics curriculum and how it is taught, while teachers were concerned to inform parents of similar issues. Over the course of the project the range of knowledge exchange has broadened and we have focused on trying to find ways to bring the pupils’ home and out of school experiences into their school learning.
University of Oxford
This paper explores one approach to describing learning mathematics as participation in practice. Greeno’s articulation of affordances, constraints and attunements appears to provide a unified view which can be applied to mathematics learning at several levels. This framework can be useful in thinking about mathematical tasks and activity, although there are some characteristics of mathematical activity which are not well treated by it.
Olwen McNamara, Julian Williams
In response to the Smith Inquiry’s change of remit, and in particular with regard to the proposal for National Network/Centre for Excellence in mathematics teaching, the BSRLM executive called a group together at its Oxford Conference to discuss research related issues, with a view to making this, a further submission to the inquiry.