Perspectives on School Algebra

1. Front Matter

   Pages i-vii

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2. Approaches to Algebra

   • Romulo Lins, Teresa Rojano, Alan Bell, Rosamund Sutherland

   Pages 1-11

3. The Historical Origins of Algebraic Thinking

   • Luis G. Radford

   Pages 13-36

4. The Production of Meaning for Algebra: A Perspective Based on a Theoretical Model of Semantic Fields

   • Romulo Campos Lins

   Pages 37-60

5. A Model for Analysing Algebraic Processes of Thinking

   • Ferdinando Arzarello, Luciana Bazzini, Giampaolo Chiappini

   Pages 61-81

6. The Structural Algebra Option Revisited

   • David Kirshner

   Pages 83-98

7. Transformation and Anticipation as Key Processes in Algebraic Problem Solving

   • Paolo Boero

   Pages 99-119

8. Historical-Epistemological Analysis in Mathematics Education: Two Works in Didactics of Algebra

   • Aurora Gallardo

   Pages 121-139

9. Curriculum Reform and Approaches to Algebra

   • Kaye Stacey, Mollie Macgregor

   Pages 141-153

10. Propositions Concerning the Resolution of Arithmetical-Algebraic Problems

    • Eugenio Filloy, Teresa Rojano, Guillermo Rubio

    Pages 155-176

11. Beyond Unknowns and Variables - Parameters and Dummy Variables in High School Algebra

    • Hava Bloedy-Vinner

    Pages 177-189

12. From Arithmetic to Algebraic Thinking by Using a Spreadsheet

    • Giuliana Dettori, Rossella Garuti, Enrica Lemut

    Pages 191-207

13. General Methods: A Way of Entering the World of Algebra

    • Sonia Ursini

    Pages 209-229

14. Reflections on the Role of the Computer in the Development of Algebraic Thinking

    • Lulu Healy, Stefano Pozzi, Rosamund Sutherland

    Pages 231-247

15. Symbolic Arithmetic vs Algebra the Core of a Didactical Dilemma

    • Nicolas Balacheff

    Pages 249-260

16. Back Matter

    Pages 261-278

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This book confronts the issue of how young people can find a way into the world of algebra. The contributions represent multiple perspectives which include an analysis of situations in which algebra is an efficient problem-solving tool, the use of computer-based technologies, and a consideration of the historical evolution of algebra. The book emphasises the situated nature of algebraic activity as opposed to being concerned with identifying students' conceptions in isolation from problem-solving activity. The chapters emerged from a working group of the International Group for the Psychology of Mathematics Education. The authors are drawn from an international community and the work highlights the differences in school algebra around the world. The group invited Nicolas Balacheff to write a provocative postscript and he suggests that `there is no possible entrance to the world of algebra without a strong push or guidance from the teacher, because there is no natural passage from the problématique accessible from the child's world to the mathematical problématique'.

• algebra
• curriculum
• education
• evolution
• mathematics
• mathematics education
• problem solving
• proposition
• learning and instruction

• Graduate School of Education, University of Bristol, UK

  R. Sutherland

• Centro de Investigación y de Estudios Avanzados-IPN, Mexiaco City, Mexico

  T. Rojano

• School of Education, University of Nottingham, UK

  A. Bell

• Mathematics Department, UNESP, Rio Claro, Brazil

  R. Lins

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