Thinking Mathematically

ISBN-10: 0273728911
ISBN-13: 9780273728917
Edition: 2nd 2010
List price: $29.99
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Book details

List price: $29.99
Edition: 2nd
Copyright year: 2010
Publisher: Pearson Education, Limited
Publication date: 5/6/2010
Binding: Paperback
Pages: 264
Size: 6.00" wide x 8.75" long x 0.50" tall
Weight: 0.880
Language: English

Introduction to First Edition
Introduction to Second Edition
Everyone can start
Specializing
Generalizing
Writing yourself notes
Review and preview
Reference
Phases of work
Three phases
The Entry phase
What do I KNOW?
What do I WANT?
What can I INTRODUCE?
Entry summarized
The Attack phase
The Review phase
CHECK the resolution
REFLECT on the key ideas and key moments
EXTEND to a wider context
Practising Review
Review summarized
The three phases summarized
Reference
Responses to being STUCK
Being STUCK
Summary
ATTACK: conjecturing
What is conjecturing?
Conjecture: backbone of a resolution
How do conjectures arise?
Discovering pattern
Summary
ATTACK: justifying and convincing
Structure
Seeking structural links
When has a conjecture been justified?
Developing an internal enemy
Summary
Reference
Still STUCK?
Distilling and mulling
Specializing and generalizing
Hidden assumptions
Summary
References
Developing an internal monitor
Roles of a monitor
Emotional snapshots
Getting started
Getting involved
Mulling
Keeping going
Insight
Being sceptical
Contemplating
Summary
On becoming your own questioner
A spectrum of questions
Some 'questionable' circumstances
Noticing
Obstacles to a questioning attitude
Summary
Reference
Developing mathematical thinking
Improving mathematical thinking
Provoking mathematical thinking
Supporting mathematical thinking
Sustaining mathematical thinking
Summary
Reference
Something to think about
References
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
Powers, themes, worlds and attention
Natural powers and processes
Mathematical themes
Mathematical worlds
Attention
Summary
Bibliography
Subject Index
Index of questions

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