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El. knyga: Learning and Teaching of Algebra: Ideas, Insights and Activities

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(Weizmann Institute of Science, Israel), (University of Melbourne, Australia), (Utrecht University, The Netherlands)
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Algebra is at the core of secondary school mathematics and it is the basis for most of the mathematics that students will see in future studies. On the other hand, for students who will not pursue mathematics or mathematically intensive careers, the basics of school algebra are an integral part of what is now termed as "mathematical literacy".

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.

The book starts with a description of what today's school algebra is about and what its big ideas are. The core chapters address the issues of teaching and learning where research in recent decades has made a strong contribution to improved understanding. Using mini case studies from research projects, these chapters highlight how children's thinking needs to change, how teachers can monitor the changes, and (in some cases) the nature of teaching that can bring about these changes. Broader issues of teaching and pedagogy are addressed throughout. 'Hot issues' in curriculum design, such as how pre-secondary education can best prepare students for algebra, and how concrete models can be used to teach algebra, are also explained.

All chapters will include many annotated examples of the uses of digital technology in teaching and learning mathematics and the final chapter addresses explicitly how digital technology is changing school algebra, including its curriculum goals, teaching and assessment practices.

The book is aimed at mathematics teacher education students, graduate students in mathematics education and practising teachers of students aged approximately 10 - 20. It is also a valuable resource for teacher educators (at the pre- and in-service levels), curriculum developers, and accessible to all teachers of algebra.

Recenzijos

"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)

Acknowledgments ix
IMPACT -- Series Foreword xi
Preface xiii
1 Algebra---Setting the Scene
1(24)
1.1 Introduction
1(1)
1.2 Algebra---Aims, Actions, and Entities
1(15)
1.3 Why Algebra?
16(3)
1.4
Chapter Summary
19(1)
1.5 Thinking Further
20(2)
1.6 References
22(3)
2 Some Lessons From History
25(23)
2.1 Introduction
25(1)
2.2 Linear Equations in Ancient Egypt
26(5)
2.3 Quadratic Equations in Ancient Babylonia
31(2)
2.4 A Geometric View of Algebra From Arabic Mathematics
33(4)
2.5 Beyond Solving Equations: The Emergence of Algebra in Europe
37(4)
2.6
Chapter Summary
41(1)
2.7 Thinking Further
42(5)
2.8 References
47(1)
3 Seeing Algebra Through the Eyes of a Learner
48(32)
3.1 Introduction---Putting on Teachers' Bifocal Spectacles
48(2)
3.2 What Do Algebraic Letters Represent?
50(3)
3.3 The Process--Object Duality
53(2)
3.4 The Meaning of the Equals Sign
55(1)
3.5 Algebra for Recording and Revealing Mathematical Structure
56(2)
3.6 Transitions From Learning Arithmetic to Learning Algebra
58(6)
3.7 The Procedures of Equation Solving
64(5)
3.8 Functions as Processes and Objects
69(3)
3.9
Chapter Summary
72(1)
3.10 Thinking Further
73(4)
3.11 References
77(3)
4 Emphases in Algebra Teaching
80(26)
4.1 Introduction
80(1)
4.2 Teaching Algebra in Context
81(6)
4.3 Productive Practice
87(3)
4.4 The Reconciliation of Routine and Insight
90(5)
4.5 Exploiting Student Mistakes
95(4)
4.6 Proofs in Algebra Teaching
99(2)
4.7
Chapter Summary
101(1)
4.8 Thinking Further
102(2)
4.9 References
104(2)
5 Algebra Education in the Digital Era
106(30)
5.1 Introduction
106(2)
5.2 Digital Tools for Algebra
108(10)
5.3 Core Algebra Entities With Digital Means
118(9)
5.4 Teaching and Learning Algebra With Digital Means
127(3)
5.5
Chapter Summary
130(2)
5.6 Thinking Further
132(2)
5.7 References
134(2)
Epilogue 136(4)
Index 140
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.
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