Thinking Mathematically 2nd Edition by J. Mason ISBN 0273728911 978-0273728917

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Product details: 

ISBN 10:  0273728911

ISBN 13:  978-0273728917

Author:  J. Mason

Thinking Mathematically is perfect for anyone who wants to develop their powers to think mathematically, whether at school, at university or just out of interest. This book is invaluable for anyone who wishes to promote mathematical thinking in others or for anyone who has always wondered what lies at the core of mathematics. Thinking Mathematically reveals the processes at the heart of mathematics and demonstrates how to encourage and develop them. Extremely practical, it involves the reader in questions so that subsequent discussions speak to immediate experience.

Table of contents: 

Cover……Page 1
Thinking Mathematically……Page 2
Contents……Page 6
Introduction to First Edition……Page 9
Introduction to Second Edition……Page 12
Specializing……Page 18
Generalizing……Page 25
Writing yourself notes……Page 26
Review and preview……Page 38
Reference……Page 40
Phases of work……Page 41
Three phases……Page 42
The Entry phase……Page 43
Entry 1: What do I KNOW?……Page 44
Entry 2: What do I WANT?……Page 47
Entry 3: What can I INTRODUCE?……Page 49
The Attack phase……Page 52
The Review phase……Page 53
Review 1: CHECK the resolution……Page 54
Review 3: EXTEND to a wider context……Page 55
Practising Review……Page 57
Review summarized……Page 59
The three phases summarized……Page 60
Reference……Page 61
Being STUCK……Page 62
Summary……Page 73
What is conjecturing?……Page 75
Conjecture: backbone of a resolution……Page 79
How do conjectures arise?……Page 87
Discovering pattern……Page 90
Summary……Page 93
Structure……Page 95
Seeking structural links……Page 99
When has a conjecture been justified?……Page 103
Developing an internal enemy……Page 107
Summary……Page 111
Reference……Page 112
Still STUCK?……Page 113
Distilling and mulling……Page 114
Specializing and generalizing……Page 116
Hidden assumptions……Page 118
Summary……Page 120
References……Page 121
Developing an internal monitor……Page 122
Roles of a monitor……Page 123
Emotional snapshots……Page 125
Getting started……Page 126
Getting involved……Page 128
Mulling……Page 129
Keeping going……Page 131
Insight……Page 132
Being sceptical……Page 134
Summary……Page 135
On becoming your own questioner……Page 137
A spectrum of questions……Page 138
Some ‘questionable’ circumstances……Page 139
Noticing……Page 144
Obstacles to a questioning attitude……Page 146
Summary……Page 148
Reference……Page 149
Developing mathematical thinking……Page 150
Improving mathematical thinking……Page 151
Provoking mathematical thinking……Page 154
Supporting mathematical thinking……Page 156
Sustaining mathematical thinking……Page 157
Summary……Page 161
Reference……Page 162
Something to think about……Page 163
References……Page 197
Thinking mathematically in curriculum topics……Page 198
Place value and arithmetic algorithms……Page 199
Factors and primes……Page 201
Fractions and percentages……Page 205
Ratios and rates……Page 208
Equations……Page 213
Patterns and algebra……Page 215
Graphs and functions……Page 219
Functions and calculus……Page 223
Sequences and iteration……Page 227
Mathematical induction……Page 230
Abstract algebra……Page 232
Perimeter, area and volume……Page 237
Geometrical reasoning……Page 240
Reasoning……Page 243
References……Page 247
Natural powers and processes……Page 248
Mathematical themes……Page 253
Mathematical worlds……Page 255
Attention……Page 256
Summary……Page 257
Bibliography……Page 258
Subject index……Page 260
Index of questions……Page 264

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