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Thinking mathematically 2. uppl.

By: Mason, J. Burton, L. & Stacey, K.
Material type: TextTextPublisher: 2010ISBN: 9780273728917.
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Enhanced descriptions from Syndetics:

<p> 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.</p>

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Table of contents provided by Syndetics

  • Introduction to First Edition (p. viii)
  • Introduction to Second Edition (p. xi)
  • 1 Everyone can start (p. 1)
  • Specializing (p. 1)
  • Generalizing (p. 8)
  • Writing yourself notes (p. 9)
  • Review and preview (p. 21)
  • Reference (p. 23)
  • 2 Phases of work (p. 24)
  • Three phases (p. 25)
  • The Entry phase (p. 26)
  • Entry 1 What do I KNOW? (p. 27)
  • Entry 2 What do I WANT? (p. 30)
  • Entry 3 What can I INTRODUCE? (p. 32)
  • Entry summarized (p. 35)
  • The Attack phase (p. 35)
  • The Review phase (p. 36)
  • Review 1 CHECK the resolution (p. 37)
  • Review 2 REFLECT on the key ideas and key moments (p. 38)
  • Review 3 EXTEND to a wider context (p. 38)
  • Practising Review (p. 40)
  • Review summarized (p. 42)
  • The three phases summarized (p. 43)
  • Reference (p. 44)
  • 3 Responses to being STUCK (p. 45)
  • Being STUCK (p. 45)
  • Summary (p. 56)
  • 4 ATTACK: conjecturing (p. 58)
  • What is conjecturing? (p. 58)
  • Conjecture: backbone of a resolution (p. 62)
  • How do conjectures arise? (p. 70)
  • Discovering pattern (p. 73)
  • Summary (p. 76)
  • 5 ATTACK: justifying and convincing (p. 78)
  • Structure (p. 78)
  • Seeking structural links (p. 82)
  • When has a conjecture been justified? (p. 86)
  • Developing an internal enemy (p. 90)
  • Summary (p. 94)
  • Reference (p. 95)
  • 6 Still STUCK? (p. 96)
  • Distilling and mulling (p. 97)
  • Specializing and generalizing (p. 99)
  • Hidden assumptions (p. 101)
  • Summary (p. 103)
  • References (p. 104)
  • 7 Developing an internal monitor (p. 105)
  • Roles of a monitor (p. 106)
  • Emotional snapshots (p. 108)
  • Getting started (p. 109)
  • Getting involved (p. 111)
  • Mulling (p. 112)
  • Keeping going (p. 114)
  • Insight (p. 115)
  • Being sceptical (p. 117)
  • Contemplating (p. 118)
  • Summary (p. 118)
  • 8 On becoming your own questioner (p. 120)
  • A spectrum of questions (p. 121)
  • Some 'questionable' circumstances (p. 122)
  • Noticing (p. 127)
  • Obstacles to a questioning attitude (p. 129)
  • Summary (p. 131)
  • Reference (p. 132)
  • 9 Developing mathematical thinking (p. 133)
  • Improving mathematical thinking (p. 134)
  • Provoking mathematical thinking (p. 137)
  • Supporting mathematical thinking (p. 139)
  • Sustaining mathematical thinking (p. 140)
  • Summary (p. 144)
  • Reference (p. 145)
  • 10 Something to think about (p. 146)
  • References (p. 180)
  • 11 Thinking mathematically in curriculum topics (p. 181)
  • Place value and arithmetic algorithms (p. 182)
  • Factors and primes (p. 184)
  • Fractions and percentages (p. 188)
  • Ratios and rates (p. 191)
  • Equations (p. 196)
  • Patterns and algebra (p. 198)
  • Graphs and functions (p. 202)
  • Functions and calculus (p. 206)
  • Sequences and iteration (p. 210)
  • Mathematical induction (p. 213)
  • Abstract algebra (p. 215)
  • Perimeter, area and volume (p. 220)
  • Geometrical reasoning (p. 223)
  • Reasoning (p. 226)
  • References (p. 230)
  • 12 Powers, themes, worlds and attention (p. 231)
  • Natural powers and processes (p. 231)
  • Mathematical themes (p. 236)
  • Mathematical worlds (p. 238)
  • Attention (p. 239)
  • Summary (p. 240)
  • Bibliography (p. 241)
  • Subject Index (p. 243)
  • Index of questions (p. 247)