The Learning and Teaching of Algebra: Ideas, Insights and Activities (IMPACT: Interweaving Mathematics Pedagogy and Content for Teaching)

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. Cover 1 Title Page 4 Copyright Page 5 Table of Contents 8 Acknowledgments 10 IMPACT – Series Foreword 12 Preface 14 1 Algebra—Setting the Scene 16 1.1 Introduction 16 1.2 Algebra—Aims, Actions, and Entities 16 1.3 Why Algebra? 31 1.4 Chapter Summary 34 1.5 Thinking Further 35 1.6 References 37 2 Some Lessons From History 40 2.1 Introduction 40 2.2 Linear Equations in Ancient Egypt 41 2.3 Quadratic Equations in Ancient Babylonia 46 2.4 A Geometric View of Algebra From Arabic Mathematics 48 2.5 Beyond Solving Equations: The Emergence of Algebra in Europe 52 2.6 Chapter Summary 56 2.7 Thinking Further 57 2.8 References 62 3 Seeing Algebra Through the Eyes of a Learner 63 3.1 Introduction—Putting on Teachers’ Bifocal Spectacles 63 3.2 What Do Algebraic Letters Represent? 65 3.3 The Process–Object Duality 68 3.4 The Meaning of the Equals Sign 70 3.5 Algebra for Recording and Revealing Mathematical Structure 71 3.6 Transitions From Learning Arithmetic to Learning Algebra 73 3.7 The Procedures of Equation Solving 79 3.8 Functions as Processes and Objects 84 3.9 Chapter Summary 87 3.10 Thinking Further 88 3.11 References 92 4 Emphases in Algebra Teaching 95 4.1 Introduction 95 4.2 Teaching Algebra in Context 96 4.3 Productive Practice 102 4.4 The Reconciliation of Routine and Insight 105 4.5 Exploiting Student Mistakes 110 4.6 Proofs in Algebra Teaching 114 4.7 Chapter Summary 116 4.8 Thinking Further 117 4.9 References 119 5 Algebra Education in the Digital Era 121 5.1 Introduction 121 5.2 Digital Tools for Algebra 123 5.3 Core Algebra Entities With Digital Means 133 5.4 Teaching and Learning Algebra With Digital Means 142 5.5 Chapter Summary 145 5.6 Thinking Further 147 5.7 References 149 Epilogue 151 Index 155 'The Learning and Teaching of Algebra' provides a pedagogical framework for the teaching and learning of algebra grounded in theory and research. 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 "problmatique" 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 IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of advanced textbooks for teacher education which aims to advance the teaching of mathematics by integrating mathematics content teaching with the broader research and theoretical base of mathematics education. " The Learning and Teaching of Algebra" is a primer for teachers and researchers that 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 and all those who are interested in the "problematique" 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." "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."--Publisher's description