The Learning and Teaching of Algebra

The purpose of this book is to provide the reader with both a practical and research-informed introduction to the main issues in school algebra education which nowadays remains one of the core challenges of mathematics education in general. The book will enable readers to:

• identify and emphasize the big ideas of algebra;

• imbue teaching with a sense of purpose (why algebra? what is it for? In which ways does it empower to better understand real world situations and solve interesting problems?);

• understand how students think about algebra and design lessons accordingly;

• critically pursue assessment tools;

• use technology for algebra learning.

  Zusatztext "The book makes a valuable contribution to the existing literature in terms of the teaching and learning of algebra. At the same time it is different, in various ways: one of the differences is that it has been co-authored by three authors, rather than edited, which provides the reader with a more coherent reading." Birgit Pepin, Nieuw Archief voor Wiskunde (Dutch Journal of the Royal Mathematics Society) Informationen zum Autor Abraham Arcavi holds the Lester B. Pearson Professorial Chair at the Weizmann Institute of Science! Israel. He has written about the teaching and learning of algebra for researchers and teachers! led large curriculum development projects! and has been involved in teacher professional development for more than 30 years.Paul Drijvers is Professor of Mathematics Education at the Freudenthal Institute! Utrecht University! The Netherlands. His research interests include the role of ICT in mathematics education! the teaching and learning of algebra! and teachers' professional development.Kaye Stacey is Professor Emeritus at the University of Melbourne! Australia! having held the Foundation Chair of Mathematics Education there for 20 years. She has made major contributions to understanding students' early learning of formal algebra and discovering how information technology can enhance the teaching of algebra and functions throughout secondary school. Zusammenfassung IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include: • Algebra: Setting the Scene • Some Lessons From History • Seeing Algebra Through the Eyes of a Learner • Emphases in Algebra Teaching • Algebra Education in the Digital Era This guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides. Inhaltsverzeichnis Preface 1. Algebra Setting the scene 1.1 Introduction 1.2 Algebra Aims, actions and entities 1.2.1 Aims 1.2.2 Actions 1.2.3 Entities 1.3 Why Algebra? 1.4 Chapter Summary 1.5 Thinking further 1.6 References 2. Some lessons from history 2.1 Introduction 2.2 Linear equations in ancient Egypt 2.3 Quadratic equations in ancient Babylonia 2.4 A geometric view of algebra from Arabic mathematics 2.5 Beyond solving equations: The emergence of algebra in Europe 2.5.1 Some algebraic rules and their explanation 2.5.2 Negative numbers 2.6 Chapter summary 2.7 Thinking further 2.8 References 3. Seeing algebra through the eyes of a learner 3.1 Introduction putting on teachers' bifocal spectacles 3.2 What do algebraic letters represent? 3.2.1 Fruit salad algebra misleading teaching with long term consequences 3.3 The process-object duality 3.4 The meaning of the equals sign 3.5 Algebra for recording and revealing mathematical structure 3.6 Transitions from arithmetic to algebra 3.6.1 Contrasting arithmetic and algebraic problem solving 3.6.2 Fundamental ideas of equation solving 3.6.3 Algebra and creativity 3.7 The procedures of equation solvi...

  Autorentext

  Abraham Arcavi holds the Lester B. Pearson Professorial Chair at the Weizmann Institute of Science, Israel. He has written about the teaching and learning of algebra for researchers and teachers, led large curriculum development projects, and has been involved in teacher professional development for more than 30 years.

  Paul Drijvers is Professor of Mathematics Education at the Freudenthal Institute, Utrecht University, The Netherlands. His research interests include the role of ICT in mathematics education, the teaching and learning of algebra, and teachers' professional development.

  Kaye Stacey is Professor Emeritus at the University of Melbourne, Australia, having held the Foundation Chair of Mathematics Education there for 20 years. She has made major contributions to understanding students' early learning of formal algebra and discovering how information technology can enhance the teaching of algebra and functions throughout secondary school.

  Klappentext

  IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Algebra provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. Areas covered include: Algebra: Setting the Scene Some Lessons From History Seeing Algebra Through the Eyes of a Learner Emphases in Algebra Teaching Algebra Education in the Digital Era This guide will be essential reading for trainee and qualified teachers of mathematics, graduate students, curriculum developers, researchers and all those who are interested in the "problématique" of teaching and learning algebra. It allows you to get involved in the wealth of knowledge that teachers can draw upon to assist learners, helping you gain the insights that mastering algebra provides.

  Inhalt

Preface

1. Algebra Setting the scene

1.1 Introduction

1.2 Algebra Aims, actions and entities

1.2.1 Aims

1.2.2 Actions

1.2.3 Entities

1.3 Why Algebra?

1.4 Chapter Summary

1.5 Thinking further

1.6 References

2. Some lessons from history

2.1 Introduction

2.2 Linear equations in ancient Egypt

2.3 Quadratic equations in ancient Babylonia

2.4 A geometric view of algebra from Arabic mathematics

2.5 Beyond solving equations: The emergence of algebra in Europe

2.5.1 Some algebraic rules and their explanation

2.5.2 Negative numbers

2.6 Chapter summary

2.7 Thinking further

2.8 References

3. Seeing algebra through the eyes of a learner

3.1 Introduction putting on teachers' bifocal spectacles

3.2 What do algebraic letters represent?

3.2.1 Fruit salad algebra misleading teaching with long term consequences

3.3 The process-object duality

3.4 The meaning of the equals sign

3.5 Algebra for recording and revealing mathematical structure

3.6 Transitions from arithmetic to algebra

3.6.1 Contrasting arithmetic and algebraic problem solving

3.6.2 Fundamental ideas of equation solving

3.6.3 Algebra and creativity

3.7 The procedures of equation solving

3.7.1 Process-object distinction in solving simultaneous equations

3.8 Functions as processes and objects

3.9 Chapter Summary

3.10 Thinking Further

3.11 References

Chapter 4: Emphases in algebra teaching

4.1 Introduction

4.2 Teaching algebra in context

4.3 Productive practice

4.4 The reconciliation of routine an…