BSRLM Proceedings: Vol 26 No 1 Warwick University 2006

Proceedings of the Day Conference held at Warwick University, February 2006.

Contents

1 Teachers’ Awareness of Dimensions of Variation: a Mathematics Intervention Project

Thabit Al-Murani
Department of Educational Studies, University of Oxford

This paper presents the findings of a 16-month longitudinal teaching intervention exploring how deliberate and systematic variation can be used to raise awareness in teaching and learning situations. The results indicate that intervention teachers attending to variation produce significant learning benefits for their students.

2 The Role of Aesthetics in Mathematics Education

Mojtaba Ammari-Allahyari
Institute of Education, University of Warwick

In this study, I examine appreciation of the relationship between aesthetics and mathematics and mathematics education. In this paper first I tried to give a definition of beauty followed by some natural phenomena. Then I made an effort to show the mathematics behind those phenomena. In the last a discussion on how appreciation of the confluence between mathematics and nature facilitate teaching-learning processes in mathematics education.

3 Analysing Geometric Tasks Considering Hinting Support and Inscriptions

Beth Ashfield and Stephanie Prestage
University of Birmingham

The study was undertaken to determine the features of tasks within the secondary geometry curriculum that inhibit, or promote, access to the mathematics they contain. It was conducted as a part of a PhD research project considering the development of the skills needed to become a good geometer through interactions with resources. The resources considered were the textbook used to teach geometry, the examinations used to assess geometrical knowledge and understanding and dynamic geometry software packages used to underpin the understanding and learning that takes place within the regular lessons.

4 “It’s not just magic!” Learning Opportunities with Spreadsheets in the Financial Sector

Arthur Bakker, Phillip Kent, Richard Noss, Celia Hoyles and Chand Bhinder
Institute of Education, University of London

In the research project “Techno-mathematical Literacies in the Workplace” we have carried out case studies in several industry sectors to characterise employees’ need for functional mathematical knowledge mediated by tools and grounded in the context of specific work situations. We have subsequently designed learning opportunities which we have tested and revised as part of design-based research. This paper gives examples from three financial companies in which we have used spreadsheet-based learning opportunities to support employees in their understanding of the (for them) hidden mathematical models on which pension investments and mortgage illustrations are based.

5 Task Selection and Task Implementation: Seven Constraints Affecting the Teacher’s Instruction

Ibrahim Bayazit
Institute of Education, University of Warwick

This paper examines an experienced teacher’s task selection and task implementation teaching the function concept. There are seven constraints in the teacher’s selection and implementation of the tasks and these factors potentially inhibit his students’ engagement with the notion of function. The evidence suggest that task, by itself, does not grab the students’ attention; it is the teacher’s expertise in creating task conditions, such as establishing connections between the ideas and between the representations, which could promote students’ understanding.

6 Functional Mathematics and its Assessment

Margaret Brown, Diana Coben, Jeremy Hodgen, Ian Stevenson, Hamsa Venkatakrishnan
King’s College London

In this paper we outline our work in the King’s College London / Edexcel project, Developing Curriculum Pathways in Mathematics. This is one of two projects funded by the Qualifications and Curriculum Authority (QCA) to develop possible curriculum and assessment structures for post-14 mathematics as a result of the Department for Education and Skills’ (DfES) response to the Smith and Tomlinson Reports (Smith, 2004; Tomlinson, 2004). We describe our current curriculum model and our approach to Functional Mathematics and its assessment focusing on National Qualifications Framework (NQF) levels 2.

7 A Study of Effective Practice on Inclusive Adult Numeracy Teaching

Diana Coben, Margaret Brown, Valerie Rhodes, Jon Swain, Katerina Ananiadou and Peter Brown
King’s College London, in association with the National Centre for Research and Development in Adult Literacy and Numeracy (NRDC)

This paper reports on one of a suite of projects on adult basic education, combining analysis of quantitative and qualitative data. Adult numeracy teaching was observed in a wide range of settings and involved diverse groups of learners and teachers. Classes made a significant overall mean gain of 9% in attainment, but the range of gains between classes was large. Few correlations between gains in learning or attitude and characteristics of teaching, teachers or learners were found to be significant. This connects with the awareness expressed by teachers of the need to be flexible and adapt their approach to circumstances.

8 Teaching Geometry in Lower Secondary School in Shanghai, China

Liping Ding and Keith Jones
University of Southampton

The teaching and learning of geometry has been the subject of considerable international interest, with many questions remaining about appropriate teaching methods and curriculum design (Mammana& Villani, 1998; Royal Society, 2001). With a view to informing the development of better pedagogical models and instructional strategies in geometry, this paper reports some findings from a study of geometry teaching at the lower secondary school level in Shanghai, China. The analysis is based on observations of geometry lessons, and data on students’ performances in mid-term examinations, at Grade 8 (UK Year 9, students aged 13- 14). The study suggests that an essential teaching strategy used by Chinese mathematics teachers at this Grade level is an approach that aims mutually to reinforce visual and deductive approaches in order to develop students’ thinking, particularly in the transition to deductive geometry.

9 The Views of Older Adults on School Mathematics Past and Present

Jenny Houssart
Centre for Mathematics Education, The Open University

This research presented here considers issues in the teaching of mathematics from the point of view of a group of people aged 75 and over. It draws on written accounts of their use of and attitude to mathematics. Extracts are identified in which they reflect on their own experiences of learning mathematics at school or give their views on more recent mathematics education. Common themes are mental arithmetic and the use of calculators. Most respondents report positive views of their own mathematics education and reservations about more recent systems. Some accounts reveal inaccurate views of current practices in mathematics teaching.

10 Secondary School Pupils’ Approaches to Proof-Related Tasks in Geometry

Dietmar Küchemann and Celia Hoyles

We give an account of two pupils’ attempts to solve two GCSE geometry questions involving circle theorems. We identify some of the characteristics of such tasks, some of the pupils’ emerging strategies and some of the difficulties the pupils encountered, especially with using the givens and extracting information contained in diagrams.

11 The Balance of Power in the Mathematics Classroom

Sandra Pendlington
University of Bristol

Some psychologists see power as a dimension of self-esteem - having power over ones situation maintains high self-esteem. Within the classroom the teacher can be seen to have the power to ‘direct learners’ and be the ‘holder of knowledge’. Learners are’ the directed and the receivers of knowledge’. This papers aims to explore whether these relationships are necessary and unavoidable or in need of change. The paper focuses on low achieving children, who initially presented as powerless. After a 3 month teaching project, analysis indicated a change in this position and indicated some possible reasons for this.

12 Doing Maths or Practising the Finished Product

Stephanie Prestage and Pat Perks
University of Birmingham

This paper considers the teaching and learning of mathematics using the ideas of ‘Adapting and Extending’ (Prestage and Perks, 2001) in comparison with our observations of the use of exemplar materials such as those in the Secondary Strategy, to allow a discussion of the tensions for our ITE students’ planning for teaching. In our test-based culture and the prevalence of national materials do our students have time to do mathematics or is their only strategy to ‘practise the finished product’.

13 Proof, Reason, Abstraction and Leaps: a Cultural-Historical Approach to Teaching Geometry

Stuart Rowlands and Robert Carson
University of Plymouth, Montana State University

Geometry for most learners is ‘shape and space’ without reason, deduction and proof. There seems to be the assumption that deductive geometry is inappropriate, either because it is difficult to learn or that there are no obvious benefits. We take the view that most secondary school learners are capable of engaging with the abstract and rule-governed intellectual processes that became the world’s first fully developed and comprehensive formalised system of thought. This article discusses a curriculum initiative that aims to ‘bring to life’ the major ‘transformative events’ in the history of Greek geometry, aims to encourage a meta-discourse that can develop a reflective consciousness and aims to provide an opportunity for the induction into the formalities of proof and to engage with the abstract.

14 The Role of Pace within Primary Mathematics Lessons

Margaret Sangster
Canterbury Christ Church University

A consideration of the nature and role of pace in the mathematics lessons in primary schools. This is a discussion paper based on observations of student teachers conducting lessons during school experience.

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