Proceedings of the Day Conference held at Sheffield Hallam University, February 1996
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Contents
1 Struggling for Survival: The Production of Meaning
Romulo Campos Lins
State University of Sao Paulo Rio Claro, Brazil
In this paper I present a view on meaning production which departs both from the usual notion of “communication” andfrom realist and objectivist approaches to it. To make such a view operational. an account is given of why meaning production does not “go wild”-something any relativist approach should provide-showing the notion of interlocutor to be central in that process. indeed a constitutive part of cognition.
2 Language and Strategies in Children’s Solution of Division Problems
Karen Newstead, Julia Anghileri and David Whitebread
Homerton College, Cambridge
Year 5 and 6 children have been videotaped while solving a variety of written division problems. We have examined their strategies and found that children with more flexible strategies are often more successful at solving these division problems than children who use only one or two strategies to solve them.
Using examples on video, we shared some findings of this ongoing research aimed at examining the development of these strategies and the use of language over a period during which children meet division formally in school.
3 Towards Practical Mathematics: An Examination of Real World Geometry and Mensuration in Nigeria
Isa A Ochepa
A.T.B. University, Nigeria
The undesirable weak performance of students in mathematics, especially at the post-primary school level is a global issue. Many factors have been associated with this weakness. The most popular of the numerous factors available in literature include students’ attitude towards mathematics, the nature of mathematics and the curriculum. In Nigeria, varied efforts have been made in the past by researchers in the educational institutions, professional associations like the Mathematical Association of Nigeria (MAN), the Science Teachers Association of Nigeria (STAN) and the Federal Ministry of Education (FME) to encourage and promote mathematics education. For instance, in the seventies such efforts led first to the introduction of Modem Mathematics and later to the scrapping of it from Nigeria secondary schools in 1977 and in its place is the current mathematics curriculum produced by the Federal Ministry of Education. However, with the new curriculum in operation for over fifteen years, examination results from the West African Examination Council (W AEC), a body which is responsible for conducting certification examination for secondary school graduates in the whole of West Africa, reveals that the situation is still bad.
4 Constructing Meaning for Number
Declan O’Reilly
University of Sheffield
There is now an accumulated body of research both here and abroad (Brown, 1981; Carpenter et aI., 1981; Foxman et aI, 1985) which demonstrates that children lack meaning for decimals. There is also a recognition of the difficulties which children encounter with directed numbers (Bell, Costello and Kiichemann, 1983). The challenge for this study was to investigate how programming their own number line would mediate primary school children’s understandings of both decimals and directed numbers. In what follows, the programming, or construction, stage is omitted. Each of the episodes illustrates children’s interactions with the fully operational number line.
5 Investigating Estimation in the Classroom
Christopher Pike and Michael Forrester
University of Kent
Research into the relationship between language and mathematics in the classroom tends to adopt either the ‘language as aformal object’ view or a discourse analytic perspective. In our presentation we considered what might be gained from adopting the ethnomethodologically inspired conversational analysis approach, specifically by looking in detail at how estimation is taught and learned in primary school. Beyond highlighting the principles which underpin this approach, the results articulate a number of interesting aspects regarding the ways in which mathematical ideas are transformed into accountable procedures for action in the classroom.
6 Writing the Thesis in Mathematics Education
Tim Rowland
Homerton College, Cambridge
In this paper, I share some reflections on the recent experience of writing a doctoral thesis. Readers who anticipate the task with as much apprehension as I did, may find encouragement, and even some assistance, in my account. At the same time, it is evident that their experience may not be the same as mine.
7 Is This A Sign Of The Times? A Semiotic Approach To Meaning-Making In Mathematics Education
Adam Vile
South Bank University
This paper is intended to promote discussion around semiotics as a context for discourse in empirical and theoretical aspects of mathematics education. Semiotics is the study of the nature and action of signs and sign functions; the mathematics register consists of complex signs and should therefore be open to semiotic analysis. This paper introduces the basic elements of semiotics and discusses, in general terms, the possible implications of the application of a semiotic perspective to the context of mathematics teaching and learning. A number of examples from student’s work in solving linear equations are included in order to illustrate some of the ideas put forward in this paper and to promote further discussion.
8 Is the Gap between GCSE and A-Level Bigger in Mathematics than for Other Subjects?
Dylan William
King’s College, London
An analysis of the grades obtained by the age-18 cohort who took A-level examinations in 1994, matched with their results obtained at GCSE two years earlier, supports the idea that the ‘gap’ between GCSE and A-level is larger for mathematics thanfor English, except at the highest levels of attainment. Approximately one-third of students who get a grade A in a subject at GCSE and who go on to A-level get a grade A, whatever the subject. However, to have at least a 50% chance of getting a grade ‘D’ or better at A-level, one needs a grade ‘B’ at GCSE in mathematics, but only a grade ‘C’ in English. As afirst approximation, the gap between GCSE and A-level is the same size in mathematics and Englishfor candidates who attain A-level grade A; one-half of a grade bigger in mathematics than in Englishfor candidates who attain A-level grades Band C; and one grade bigger in mathematics than in Englishfor candidates who attain A-level grades D and E.
9 Democratic Education – Does it Exist – Especially for Mathematics Education?
Derek Woodrow
Manchester Metropolitan University Crewe School of Education
This paper explores the concept of democratic education; taking issues concerned with democratic citizenship in modern democratic societies and ways of teaching which reflect democratic values. Can individualistic teaching and over-respect for individual rights be consistent with democracy? In modern media-power can democracy even exist or are we all just manipulated? Does the autocratic authority imbued in mathematics allow for democracy anyhow?
10 Interviewing – A Support Group
Laurinda Brown
University of Bristol
At this meeting Kerry Cripps, a PhD student from Sheffield Hallam University shared with us her methodology through working with us on transcripts from her research and talking about her thoughts and feelings and how they were changing over time. We had intended to compare and contrast this methodology with that of Stephen Hegedus from Southampton University but his work will now form the basis of the next meeting of the Interviewing Support Group at Loughborough in May, 1996.
11 Geometry Working Group
Isa Ochepa and Abubakar Tafewa
Balewa University, Nigeria
Peter Winbourne
South Bank University, London
Brian Hudson
Sheffield Hallam University
Munder Adhami
King’s College, London
There were two contributions to this Working Group. One was by [sa Ochepa who talked about his work on real world geometry and mensuration in Nigeria. The other was by Peter Winbourne who discussed the distinction between the perception of pattern and classification of pattern, in relation to the use of dynamic geometry software. [sa considered Nigerian students’ largely negative attitudes towards mathematics and their view of it as an abstract subject. Peter’s starting point was that it seems that it is no more necessary for the creation of patterns to have an understanding of their underlying mathematical structure (whatever that means) than it isfor someone to understand the operation of gravity when throwing a ball. As soon as we wish to engage in some kind of classification however (in this case mediated by their construction using dynamic geometry systems), the construct of the underlying structure needs to be addressed.