Proceedings of the Day Conference held at Sheffield Hallam University, Sat 22 Feb 2003.
Contents
Research Reports
1 The function concept: comprehension and complication
Hatice Akkoç, University of Warwick
David Tall, University of Warwick
In this paper, we contrast the mathematical simplicity of the function concept that is appreciated by some students and the spectrum of cognitive complications that most students have in coping with the function definition in its many representations. Our data is based on interviews with nine (17-year old) students selected as a cross-section from 114 responses to a questionnaire. We distinguish four categories in a spectrum from those who have a simple grasp of the core function concept applicable to the full range of representations to those who see only complicated details in different contexts without any overall grasp of the conceptual structure.
2 The role of rhetoric in solving an arithmetic word problem
Richard Barwell, University of Bristol
Work in discursive psychology has highlighted the role of rhetoric in social interaction, including in classroom discourse. Edwards and Potter (1992), for example, highlight a number of rhetorical strategies or ‘devices’ and show how they can be used to strengthen claims, accounts or descriptions of reality and undermine possible alternative versions. In this paper, I take a rhetorical perspective to analyse an extract from a Year 5 lesson, in which the teacher guides her class in solving an arithmetic word problem. The analysis reveals the emergence of two narratives, one relating to the word problem, the other to the solution process.
3 Using an Interactive whiteboard to facilitate pupil understanding of quadrilateral definitions
Ian Davison, Institute of Education, University of Warwick
This paper reports on part of a project examining how the affordances of interactive whiteboards can facilitate conceptual learning. Here the focus is on the teaching of quadrilateral definitions through the use of Cabri Géomètre. It appears that Year 5 pupils can gain a good grasp of the inclusive nature of quadrilateral definitions with suitable teaching that employs Cabri and the interactive whiteboard.
4 Descriptions and Definitions in the Development of the Concept Image of Derivative
Victor Giraldo, Universidade Federal do Rio de Janeiro, Brazil
Luiz Mariano Carvalho, Universidade do Estado do Rio de Janeiro, Brazil
In this paper, we review the notion of Theoretical-Computational Conflict, discussed in Giraldo, Carvalho and Tall (2002). We intend to resume the discussion about the role of computer’s limitations for learners’ concept image of derivative and limit, from a broader theoretical standpoint. Our argument will be supported by a case study with a first year undergraduate student in Brazil.
5 Teachers’ theories and strategies in practice of classroom argumentation
Constantia Hadjidemetriou and Julian Williams
University of Manchester
We examine case studies (in progress) of teachers engaging with reflective practice on argumentation. The data comes from three sources i) audio taped meetings where all the teachers share their work with their colleagues, ii) videotaped lessons and iii) interviews of the teacher after each lesson. The aim is to identify the connection between the teachers’ stated strategies and intentions (or ‘espoused theories’) and their ‘theories-in-use’ (what they actually do). The interviews and the group meetings enable the teachers to reflect on their practice and discuss their ‘espoused theories’ whereas the video taped lessons give us the opportunity to search for instances of their ‘theories-in-use’. In this paper data from one case study will be presented and discussed.
6 Some issues regarding formal algebraic notation
Dave Hewitt
School of Education, University of Birmingham
We examine case studies (in progress) of teachers engaging with reflective practice on argumentation. The data comes from three sources i) audio taped meetings where all the teachers share their work with their colleagues, ii) videotaped lessons and iii) interviews of the teacher after each lesson. The aim is to identify the connection between the teachers’ stated strategies and intentions (or ‘espoused theories’) and their ‘theories-in-use’ (what they actually do). The interviews and the group meetings enable the teachers to reflect on their practice and discuss their ‘espoused theories’ whereas the video taped lessons give us the opportunity to search for instances of their ‘theories-in-use’. In this paper data from one case study will be presented and discussed.
7 Observing subject knowledge in primary mathematics teaching
Peter Huckstep, Tim Rowland and Anne Thwaites
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 describes a videotape study of mathematics lessons prepared and conducted by trainee teachers. The aim was to identify ways in which their subject knowledge, or the lack of it, was evident in their teaching. We set out a framework which has emerged from the data, in which classroom events and episodes can be viewed as representative of one (or more) of four broad categories.
8 Teacher-Researchers: can they change schools?
Kevin Thompson, Notre Dame High School, Sheffield
Following a year-long research project to identify ways of improving numeracy levels in year 8 students I reflect on how the results have changed the way mathematics is taught in my school. I conclude that the process of research changes the researcher and students with consequent changes in the classroom culture which affects outcomes. The results suggest that the changes improved levels of numeracy and helped maintain good levels of interest and motivation without a drop in standards in the general curriculum. However, it was found that there was not an automatic adopting of my recommendations. The Head of Department was supportive of the research but unless senior managers co-own the research and are continually consulted and up-dated they are unlikely to implement change. Resistance to change exists despite positive evidence that benefits would follow.
Working group report
9 Mathematics Education And Applied Linguistics: Working Group Report
Richard Barwell, University of Bristol
Constant Leung, King’s College London
Candia Morgan, Institute of Education London
Brian Street, King’s College London
Continuing one of the themes initiated in earlier meetings, the working group considered the question of what linguistic analytic tools can offer to research in mathematics education. In this session we focused on the place of definitions within mathematical practices. Using extracts taken from a range of mathematical texts, Candia Morgan offered critical discourse analyses of definitions, using grammatical tools drawn from functional linguistics, as a starting point for discussion of issues such as: the relationship between a mathematical object or concept and its definition; roles played by definitions in the practices of doing mathematics; what analysis of definitions presented to learners at different stages can contribute to our understanding of these issues.
10 BSRLM submission to 14+ Mathematics Inquiry
“What have researchers ever done for us?”: a submission from the BSRLM to the ’14+ mathematics inquiry’
Julian Williams, University of Manchester
BSRLM is occasionally, through its Executive, able to respond to inquiries such as this, although its constitution has only just changed to allow it to express opinions on behalf of the membership. This submission was compiled by Julian (Chair of BSRLM) on behalf of the executive and members of the society who attended the discussion at the Sheffield Hallam conference.