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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 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.</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)