Thinking Mathematically

Description

Cover Title: Thinking Mathematically, Second Edition ISBN 9780273728917 Contents Introduction to First Edition Introduction to Second Edition 1 Everyone can start Specializing Generalizing Writing yourself notes Review and preview Reference 2 Phases of work Three phases The Entry phase Entry 1: What do I KNOW? Entry 2: What do I WANT? Entry 3: What can I INTRODUCE? Entry summarized The Attack phase The Review phase Review 1: CHECK the resolution Review 2: REFLECT on the key ideas and key moments Review 3: EXTEND to a wider context Practising Review Review summarized The three phases summarized Reference 3 Responses to being STUCK Being STUCK Summary 4 ATTACK: conjecturing What is conjecturing? Conjecture: backbone of a resolution How do conjectures arise? Discovering pattern Summary 5 ATTACK: justifying and convincing Structure Seeking structural links When has a conjecture been justified? Developing an internal enemy Summary Reference 6 Still STUCK? Distilling and mulling Specializing and generalizing Hidden assumptions Summary References 7 Developing an internal monitor Roles of a monitor Emotional snapshots Getting started Getting involved Mulling Keeping going Insight Being sceptical Contemplating Summary 8 On becoming your own questioner A spectrum of questions Some ‘questionable’ circumstances Noticing Obstacles to a questioning attitude Summary Reference 9 Developing mathematical thinking Improving mathematical thinking Provoking mathematical thinking Supporting mathematical thinking Sustaining mathematical thinking Summary Reference 10 Something to think about References 11 Thinking mathematically in curriculum topics Place value and arithmetic algorithms Factors and primes Fractions and percentages Ratios and rates Equations Patterns and algebra Graphs and functions Functions and calculus Sequences and iteration Mathematical induction Abstract algebra Perimeter, area and volume Geometrical reasoning Reasoning References 12 Powers, themes, worlds and attention Natural powers and processes Mathematical themes Mathematical worlds Attention Summary Bibliography Subject index Index of questions