Proceedings of the Day Conference held at the Institute of Education, London, November 1996
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Manchester Metropolitan University Crewe School of Education
Homerton College, Cambridge
The interplay between generalisations and particular instances – examples – is an essential feature of mathematics teaching and learning. In this paper, we bring together our experiences of personal and classroom mathematics activity, and demonstrate that examples do not always fulfill their intended purpose (to point to generalisations). A distinction is drawn between ’empirical’ and ‘structural’ generalisation, and the role of generic examples is discussed as a means of supporting the second of these qualities of generalisation.
Manchester Metropolitan University
Derrida’ s revolutionary work in the study of language has seriously challenged the way in which we see words being attached to meanings. This paper makes tentative steps towards examining how his work might assist us in understanding the way in which our attempts to describe or capture our mathematical experiences modify the experience itself. In doing this we draw on the work of Derrida and John Mason in locating possible frameworks through which to conceptualise the relationship between language and mathematical cognition. It concludes that mathematical meaning never stabilises since it is caught between the individual’s on-going experience and society’s on going generation of societal norms as manifest in its use of language, in particular, those penaining to society’s view of mathematics. That is, mathematics, language and the human performing them are always evolving in relation to each other.
Nottingham University School of Education
This paper offers a definition of “social justice”, a term which is in great danger ofbeing over used and thus losing any meaning, as well as exploring the models 1 am working with the theorise the issue of social justice in and through mathematics classrooms and mathematics teaching. The paper draws heavily on the work of Rawls (1971) as well as recent workfrom McCarthy (1990), Brandt (1986), and Marion-Young (1990).
University of Hull
University of Warwick
For those who have followed our work over the last few years, this paper may come as a surprise. Our previous work has moved in a clear direction towards developing and using our own theory of learning (Duffin and Simpson, 1995). In this paper, however, we have paused from that goal to reflect on how it is that we are working and in what sense, if any, what we are doing is valid as research.
5 An Analysis of Students Talking About ‘Re-Learning’ Algebra: from Individual Cognition to Social Practice
Brian Hudson, Susan Elliott and Sylvia Johnson
Sheffield Hallam University
In this paper we report on a study with the aim of investigating how afocus on langlloge and meaning can assist students in reconstructing algebraic knowledge. The project is set in the context of ongoing work with students in Higher Education who need to develop their understanding of algebra if they are to make substantial progress within their under/graduate studies. The project is based upon a belief that students’ difficulties with algebra are language-related We have collected extensive data by means of videotaped sessions involving the students talking about their own understandings of algebra. The students involved were drawn from courses in initial teacher education and engineering. This paper presents a detailed analysis of the responses of one student and discusses the ways in which this shifted our attention as researchers from looking at our data from the perspective of individual cognition towards one of informed by social practice theory.
South Bank University, London
It is not my intention in this paper to argue for a socio-cultural perspective on mathematics education (see Lerman, 1996) but to examine some of the problems that one faces in research from that perspective. The international group for socio¬cultural research held its second meeting in Geneva earlier this year (1996) and there is a growing body of research from that group and from its members. In the UK in mathematics education I believe that we have little experience (with some notable exceptions, e.g. Solomon 1989; Nunes & Bryant 1996) and my intention here is to open a discussion about the problems of designing and carrying out socio¬cultural research. By ‘socio-cultural’ I am referring to theories which argue that social and cultural forces are constitutive of human consciousness not merely causative (Smith, 1993, p. 128). In particular, but not exclusively, I will refer to the work of V ygotsky and followers when outlining the theoretical issues that socio¬cultural research attempts to address in mathematics teaching and learning. It is perhaps more appropriate to describe Vygotskian research as historical-cultural rather than socio-cultural in order to emphasise phylogenesis: “The fossilized form is the end of the thread that ties the present to the past” (Vygotsky 1978, p. 64).
Susan Molyneux-Hodgson and Rosamund Sutherland
School of Education, University of Bristol
As a window onto the mathematical practices of science students, a project working alongside people studying vocational science courses (GNVQ Advanced) is currently in progress. Through classroom observation, analysis of course materials, individual interviews and diagnostic tests, a picture of the students work with mathematics-in¬science is emerging. The practice of converting between units of measurement has been analysed in depth. Converting is a critical aspect of science, drawing on several mathematical ideas. In this paper we present a summary of our analysis of students converting practices in a test situation, and describe an episode of converting in chemistry.
Christopher Pike and Michael Forrester
Dept Psychology, University of Kent at Canterbury
This paper presented findings of a study looking at the comparative and combined effects of age and number-sense on children ‘s ability to estimate measures. While evidence was found for a developmental effect of age on children ‘s number-sense, no such effect was found for the ability to estimate either length or area. However, childrens’ ability to use and perceive number relations, together with an understanding of the relative magnitudes of larger numbers, were found to have a significant influence on their ability to estimate area.
Centre for Teaching Mathematics, University of Plymouth
Despite its widespread support, constructivism’s credibility is now under scrutiny. Many constructivists refer to Vygotsky as an authority to substantiate their position; however, the various interpretations of Vygotsky open an interesting element in the constructivism controversy. This paper will argue that the Vygotskian perspective is the attempt to build a psychology structured by the Marxist epistemology of theory and practice, that to know the world it is necessary to change it by our interaction: if we are to explain the mental functions of the student as a developmental process, then we must facilitate the completion of a task that the student cannot do unaided To place the constructivism controversy within the Vygotskian perspective, a parallel will be drawn between the positions taken up in the controversy and the subjective, consensus and objectivist positions that have been adopted in the philosophy of science.
University of Oxford Department of Educational Studies
The word “confidence” was used frequently by teachers in unstructured interviews about teacher assessment of mathematics. The author analyses how it was used andfinds that different relationships are perceived between confidence and achievement. It is conjectured that different relationships lead to different kinds of teacher action or inaction. Lower usage among the secondary teachers than among primary teachers is examined and discussed, the author finding that the secondary teachers used a slightly more subject-specific vocabulary in similar circumstances, seeing links between thinking, hard work and achievement. A lack of specific description of mathematical achievement is a feature of both groups.
Paul Ernest, Exeter University
Adam Vile, South Bank University
This was the first meeting of this group and was very well attended. It is clear by the level of interest in this group just how fore grounded semiotic issues are becoming within our community. The aim of the group is to bring together those mathematics educators with an interest in semiotics in a context in which ideas, approaches and perspectives can be shared and developed. The spirit of this first session was certainly one of discussion and there was clearly a need to make sense of certain theoretical ideas and notions.