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 problematique accessible from the child's world to the mathematical problematique'.
Author(s): R. Sutherland, Teresa Rojano, Alan Bell, Romulo Lins
Series: New ICMI Studies
Edition: 1
Publisher: Springer Netherlands
Year: 2000
Language: English
Pages: 287
Preliminaries......Page 1
TABLE OF CONTENTS......Page 6
1. Approaches to Algebra......Page 10
2. The Historical Origins of Algebraic Thinking......Page 22
3. The Production of Meaning for 52$/3*"......Page 46
4. A Model for Analysing Algebraic Processes of Thinking......Page 70
5. The Structural Algebra Option Revisited......Page 92
6. Transformation and Anticipation as Key Processes in Algebraic Problem Solving......Page 108
7. Historical-Epistemological Analysis in Mathematics Education......Page 130
8. Curriculum Reform and Approaches to Algebra......Page 150
9. Propositions Concerning the Resolution of Artihmetical-Algebraic Problems.......Page 164
10. Beyond Unknowns and Variables......Page 186
11. From Arithmetic to Algebraic Thinking by Using a Spreadsheet......Page 200
12. General Methods......Page 218
Reflections on the Role of the Computer in the Development of Algerbraic Thinking......Page 240
Symbolic Arithmetic vs Algebra the Core of a Didactical Dilemma......Page 258
References......Page 270
Index......Page 282
