Thinking Mathematically
by Mason, J; Burton, L.; Stacey, K.Edition: 2nd
Format: Paperback
Pub. Date: 2010-05-06
Publisher(s): Pearson
Other versions by this Author
-
This Item Qualifies for Free Shipping!*
*Excludes marketplace orders.
List Price: $139.99
Buy New
Usually Ships in 8 - 10 Business Days.
$139.85
Buy Used
Usually Ships in 24-48 Hours
$104.99
Rent Textbook
Select for Price
Rent Digital
$71.99
How Marketplace Works:
- This item is offered by an independent seller and not shipped from our warehouse
- Item details like edition and cover design may differ from our description; see seller's comments before ordering.
- Sellers much confirm and ship within two business days; otherwise, the order will be cancelled and refunded.
- Marketplace purchases cannot be returned to eCampus.com. Contact the seller directly for inquiries; if no response within two days, contact customer service.
- Additional shipping costs apply to Marketplace purchases. Review shipping costs at checkout.
Summary
Thinking Mathematicallyis 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 Mathematicallyreveals 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.
Author Biography
John Mason is Professor Emeritus at the Open University and a Senior Research Fellow at the University of Oxford. Kaye Stacey is Foundation Professor of Mathematics Education at the Melbourne Graduate School of Education, University of Melbourne.
Table of Contents
| Introduction to First Edition | p. viii |
| Introduction to Second Edition | p. xi |
| Everyone can start | p. 1 |
| Specializing | p. 1 |
| Generalizing | p. 8 |
| Writing yourself notes | p. 9 |
| Review and preview | p. 21 |
| Reference | p. 23 |
| Phases of work | p. 24 |
| Three phases | p. 25 |
| The Entry phase | p. 26 |
| What do I KNOW? | p. 27 |
| What do I WANT? | p. 30 |
| What can I INTRODUCE? | p. 32 |
| Entry summarized | p. 35 |
| The Attack phase | p. 35 |
| The Review phase | p. 36 |
| CHECK the resolution | p. 37 |
| REFLECT on the key ideas and key moments | p. 38 |
| EXTEND to a wider context | p. 38 |
| Practising Review | p. 40 |
| Review summarized | p. 42 |
| The three phases summarized | p. 43 |
| Reference | p. 44 |
| Responses to being STUCK | p. 45 |
| Being STUCK | p. 45 |
| Summary | p. 56 |
| 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 |
| 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 |
| Still STUCK? | p. 96 |
| Distilling and mulling | p. 97 |
| Specializing and generalizing | p. 99 |
| Hidden assumptions | p. 101 |
| Summary | p. 103 |
| References | p. 104 |
| 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 |
| 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 |
| 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 |
| Something to think about | p. 146 |
| References | p. 180 |
| 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 |
| 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 |
| Table of Contents provided by Ingram. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
Digital License
You are licensing a digital product for a set duration. Durations are set forth in the product description, with "Lifetime" typically meaning five (5) years of online access and permanent download to a supported device. All licenses are non-transferable.
More details can be found here.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.