**Proceedings of the Day Conference held at Sheffield Hallam University in June 2007**

## Contents

#### 1 Mathematical visual forms and learning geometry: towards a systematic functional analysis

Jehad Alshwaikh, Institute of Education, University of London

Mathematics is a multimodal discourse in which mathematical texts use, at least, three different semiotic systems: verbal language, algebraic notations and visual forms. Beside the research that has been done concerning the verbal components of mathematical texts, there is a need to develop tools to describe the non-verbal components. Based on Halliday’s SF grammar, Morgan’s linguistic approach and multimodality approach. I present a preliminary suggested descriptive framework for analysing geometrical visual forms. My intention is to use this framework in my PhD study which investigates the role of mathematical visual representations in the construction of mathematical meaning. In order to illustrate, aspects of two examples will be analysed using this framework.

#### 2 Using dynamic geometry to introduce calculus concepts: CalGeo and the case of derivative

Irene Biza and Theodossios Zachariades

Department of Mathematics, University of Athens, Greece

CalGeo is a three-year project supported by EU programme Comenius 2.1. Amongst the objectives of this project is the design of an in-service teacher education programme which employs dynamic geometry tools for teaching Calculus in upper secondary education. In this paper we present the project, its main objectives and the produced material; an example of a learning environment/activity designed for the introduction to the notion of derivative at Year 12; and, some results of the application of this activity in a real classroom situation. In this activity we use the tangent line and the property of local straightness to introduce the formal definition of derivative. Several cases of differentiable and non-differentiable functions are discussed through their geometrical and symbolic representations.

#### 3 Mathematics education for the gifted in Egypt

Said G. Elmenoufy, Faculty of Education, Menofia University, Egypt

This article provides a description of the status of the education of gifted students in Egypt in general and especially the education of mathematically gifted students. It explores some differences between world trends and the status of Egyptian educational policy for mathematically gifted students.

#### 4 Paired interviews in mathematics education

Hilary Evens and Jenny Houssart

Open University; Institute of Education, University of London

We consider the advantages and disadvantages of carrying out interviews with pairs of children. Although the Mathematics Education literature contains examples of this method, there is relatively little detailed discussion of the rationale for its use, nor of its consequences. We draw on examples from the literature and from our own taskbased interviews with pairs of ten and eleven year-olds. We develop a simple typology of this type of interview, and we propose that children respond differently in the three different contexts. Researchers therefore need to differentiate carefully between them, and to consider their findings in the light of the exact type of paired interview used.

#### 5 ‘Maths in my way’: Caribbean students’ perspectives on the social role of mathematics

Patricia George, University of Leeds

This paper looks at social views of mathematics expressed by Caribbean students. The students appear to say in their own words points made by Gates & Vistro Yu’s (2003) in their work ‘Is Mathematics for All?’ Encapsulated in the students’ views are issues to do with gender, ability grouping practices and social class, issues made possible in part by the ways in which ‘school’ becomes enacted, and how mathematics is done in those schools. In seeking understandings of the students’ views, questions are raised such as who is mathematics for, what type of mathematics is for whom, and for which group(s) of students does mathematics get in the way.

#### 6 Arithmetical notating as a diagrammatic activity

Ian Jones, Centre for New Technology Research in Education, Institute of Education, University of Warwick

Qualitative data is presented from the trialling of a software-based arithmetical notating task designed to foster engagement with the structure of equality statements. The design rationale is “diagrammatic activity” (Dörfler, 2006) where arithmetic inscriptions onscreen are observed and manipulated according to operational rules. The data suggest that the children’s readings of arithmetical notation were transformed from computation to pattern awareness and substitution making. This afforded the emergence of commutative and partitional meaning making for a + b = b + a and c = a + b syntaxes respectively.

#### 7 Introducing more proof into high stakes examination – towards a research agenda

John Monaghan and Tom Roper, University of Leeds

We raise issues in examining what ‘proof’ is in high stakes examinations and what research issues may be usefully explored in considering ‘proof in high stakes examinations’. Our considerations arise from practical 14-19 curriculum and assessment development work. This article is not a standard academic article but, rather, a collection of issues and ideas.

#### 8 Can maths in a test be ‘functional’?

John Threlfall, University of Leeds

This paper argues that the assessment of functional mathematics as currently being developed at GCSE level should go beyond testing mathematical skills and using word problems. Drawing on the literature about mathematics in the workplace, criteria for functional mathematics assessments are offered, and the constraints of tests considered, before answering the question, with: “Yes, but it won’t be easy”.

#### 9 Developing a framework for researching professional development in mathematics: NCETM/BSRLM working group

Rosamund Sutherland and Jane Imrie

University of Bristol; NCETM

We take as a starting point that CPD for teachers of mathematics is about being stimulated to re-think, to experiment, to make fresh distinctions and to probe those distinctions to see if they are informative in enabling choices related to teaching and learning that influence learners’ mathematical experiences and activity.