Proceedings of the Day Conference held at the University of Sussex, November 2004.
Graduate School of Education, University of Bristol
In my work as a teacher educator, teaching on a PGCE secondary mathematics course and as a mathematics teacher in a classroom, I am interested in how students learn in situations where they, initially, do not know what to do. What is the process of coming to know? For the ICMI Study Group 15 – The professional education and development of teachers of mathematics – I have submitted a short, distilled paper on the theoretical principles underlying my practices. I report here on the explorations of those ideas – purposes, basic-level categories and metacommenting – that occurred within the group of teachers and teacher educators attending the session at the University of Sussex BSRLM day meeting.
School of Education, University of Southampton
This paper examines an aspect of collaborative group work arising from a study of peer talk in secondary school mathematics classrooms. The study focused on the extent to which ‘exploratory talk’, defined as the type of talk which indicates reasoning, occurs in these collaborative groups. One feature of this study, which became evident in transcripts of peer talk and in subsequent interviews with students, was the extent to which friendship groupings supported mathematical learning. Evidence from transcripts of peer talk which indicates this type of support is discussed.
School of Education, University of Birmingham
This paper originated from an interest in issues relating to traditional formal notation and viewing a video two years after it was recorded of three boys working with a computer program manipulating arithmetic equations and being surprised about my role as I worked with them. So my interest is in two areas: the learning of formal written algebraic notation, and analysing my role as teacher within a particular framework. I consider issues relating to who or what might explain, question and tel!, and when that might be done.
University of Nottingham
This paper presents findings, and raises questions, from a series of small studies of the socialisation and distribution of new secondary mathematics teachers. These studies have been carried out over the last two years and seek to explore the emerging positions of teachers, both on a pedagogic landscape and sociogeographically to their first teaching appointments. The first of these studies has been reported elsewhere (Noyes, 2004)but here I build on this and try to develop the issues from my teacher-educator perspective in the East Midlands.
University of Bristol
This paper describes an ll-week teaching project with six low achieving year 6 children done as part of my doctoral research (Pendlington 2004). lfocused on three mathematical research questions and one connected to self-esteem. This fourth question is the focus of this paper. The paper traces the development of specific affective strategies (affective scaffolding) through the description and analysis of six critical incidents and considers them in the context of the National Numeracy Strategy. The findings suggest that affective scaffolding is important in maintaining engagement and increasing mathematical competence.
6 Developing collaborative approaches: a secondary mathematics regional partnership, spanning pre-ITE and within-ITE provision
Adrian Pinel, University College Chichester
Maria Dawes, University of Portsmouth
Carol Plater, University of Brighton
A significant and sustained level of collaboration has developed across three neighbouring universities spanning secondary mathematics pre-ITE and within-ITE course provision. Given the usually competitive framework within which such universities operate, this is an interesting socio-culturaI phenomenon. Therefore the ways in which the collaboration has developed are explored by the authorparticipants, including analyses of inhibiting and enabling factors, and these draw upon documentary evidence provided by four key professionals who have been observers of the process. The central research questions addressed are about the viability of such a collaboration, and its nature and evolution to date. Strong inhibiting factors exist as a barrier to initial collaboration, but once breached diminish, and equally powerful enabling / sustainingfactors come into play. Sustainability remains an open question.
This paper considers how reflection on practical activities can lead to meaningful embodiment of mathematical concepts in a way that integrates practice and theory. In particular, it focuses on how an action such as translating an object on a table can be conceptualised as a mathematical concept-in this case a free vector-by shifting the focus of attention away from the actions themselves to the effect of the actions. The practical theory that arises has wide applications in mathematics involving processes that are symbolised and then conceived as mathematical concepts.
Bill Domoney and Alison Price
Westminster Institute of Education, Oxford Brookes University
This paper describes an exploration of algebraic thinking about early number operations with students on our primary Initial Teacher Training (ITT) programmes. While the ITT curriculum expects students to engage with algebraic ideas that ultimately relate to early number concepts, the students themselves did not appear to link what they are learning to the teaching of Numeracy in schools. We therefore devised a teaching session, which worked with generalised arithmetic ideas in depth and assessed its effectiveness in helping the students make sense of the underlying mathematical ideas. This is very much ‘work in progress’, but early findings show that students are able to make the links, but that there are differences in students’ understanding of the relationship between early number and algebra according to the type and stage of their training.
Stuart Rowlands, Ted Graham and Peter McWilliam
Centre for Teaching Mathematics: University of Plymouth
Throughout its twenty five year history, the conceptual change literature assumed student misconceptions of force are formed prior to instruction. We argue that it may well be the case that misconceptions are not formed until the student considers force and motion in a scientific context for the first time. This has obvious implications for research methods. We are in the early stages of developing a research method for investigating conceptual change in mechanics. To illustrate this method, we have taken examples from one-to-one Socratic tutoring to show how the characteristics of misconceptions can be explained with respect to strategic questioning.
10 Studying change processes in primary school arithmetic problem solving: issues in combining methodologies
Chronoula Voutsina and Keith Jones
University of Southampton
In studying changes to children’s successful strategies while solving arithmetic tasks with primary school children, two methodological approaches were combined: the microgenetic method and the clinical method of interviewing. This paper discusses the ways in which these approaches were combined in supporting the realisation of the project. The paper presents outcomes which illustrate the type of changes observed at the various levels of children’s problem solving activity within a specific type of addition task, and argues that the particular methodological combination is suitable and effective in studying the process of procedural and conceptual change in mathematics problem solving.
Keith Jones, University of Southampton
Sue Pope, St Martin’s College Lancaster
This paper reviews some of the issues related to beginning as a researcher in mathematics education. It looks at what helps, and at what might be some of the pitfalls. One key issue that emerges is the role of reflexivity in developing as a researcher – reflecting on how your own background, values, perceptions and behaviour can influence the research you carry out. Advice and illustrative stories are included which may be useful to those new to mathematics education research, especially those newly appointed as tutors in initial teacher education.