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Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12
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Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12
A Resource for the Mathematics Teacher

Second Edition


March 2008 | 280 pages | Corwin
This updated edition presents ten strategies that are effective tools for teaching students how to solve problems, both in mathematics and in real-life situations. The authors demonstrate how the strategies can be used to solve a wide range of problems and provide about 200 examples that illustrate how teachers can include these techniques in their mathematics curriculum. In many cases, the methods presented make the solution of a problem easier, neater, and more understandable-and thereby more enjoyable. This new edition includes references to current standards, revisions and clarifications throughout the text, and a number of new problems that can be used to teach the different strategies.
 
Preface
 
About the Authors
 
1. Introduction to Problem-Solving Strategies
 
2. Working Backwards
The Working Backwards Strategy in Everyday Life Problem-Solving Situations

 
Applying the Working Backwards Strategy to Solve Mathematics Problems

 
Problems Using the Working Backwards Strategy

 
 
3. Finding a Pattern
The Finding a Pattern Strategy in Everyday Life Problem-Solving Situations

 
Applying the Finding a Pattern Strategy to Solve Mathematics Problems

 
Problems Using the Finding a Pattern Strategy

 
 
4. Adopting a Different Point of View
The Adopting a Different Point of View Strategy in Everyday Life Problem-Solving Situations

 
Applying the Adopting a Different Point of View Strategy to Solve Mathematics Problems

 
Problems Using the Adopting a Different Point of View Strategy

 
 
5. Solving a Simpler Analogous Problem
The Solving a Simpler Analogous Problem Strategy in Everyday Life Problem-Solving Situations

 
Applying the Solving a Simpler Analogous Problem Strategy to Solve Mathematics Problems

 
Problems Using the Solving a Simpler Analogous Problem Strategy

 
 
6. Considering Extreme Cases
The Considering Extreme Cases Strategy in Everyday Life Problem-Solving Situations

 
Applying the Considering Extreme Cases Strategy to Solve Mathematics Problems

 
Problems Using the Considering Extreme Cases Strategy

 
 
7. Making a Drawing (Visual Representation)
The Making a Drawing (Visual Representation) Strategy in Everyday Life Problem-Solving Situations

 
Applying the Making a Drawing (Visual Representation) Strategy to Solve Mathematics Problems

 
Problems Using the Making a Drawing (Visual Representation) Strategy

 
 
8. Intelligent Guessing and Testing (Including Approximation)
The Intelligent Guessing and Testing (Including Approximation) Strategy in Everyday Life Problem-Solving Situations

 
Applying the Intelligent Guessing and Testing (Including Approximation) Strategy to Solve Mathematics Problems

 
Problems Using the Intelligent Guessing and Testing (Including Approximation) Strategy

 
 
9. Accounting for All Possibilities
The Accounting for All Possibilities Strategy in Everyday Life Problem-Solving Situations

 
Applying the Accounting for All Possibilities Strategy to Solve Mathematics Problems

 
Problems Using the Accounting for All Possibilities Strategy

 
 
10. Organizing Data
The Organizing Data Strategy in Everyday Life Problem-Solving Situations

 
Applying the Organizing Data Strategy to Solve Mathematics Problems

 
Problems Using the Organizing Data Strategy

 
 
11. Logical Reasoning
The Logical Reasoning Strategy in Everyday Life Problem-Solving Situations

 
Applying the Logical Reasoning Strategy to Solve Mathematics Problems

 
Problems Using the Logical Reasoning Strategy

 
 
Afterword by Herbert A. Hauptman
 
Sources for Problems
 
Readings on Problem Solving
 
Index

“The authors have provided a uniquely strategy-focused resource supported by a wealth of engaging examples that mathematics teachers can readily use to help students develop a more purposeful, systematic, and successful approach to problem solving.”

Howard W. Smith, Superintendent
Public Schools of the Tarrytowns, Sleepy Hollow, NY

"This terrific resource helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. In very simple terms, the authors present and illuminate the strategies that are the backbone of mathematics instruction. This indispensable material is useful at all levels, from basic stages to advanced student work to the development of top problem solvers."

Daniel Jaye, Principal
Bergen County Academies, Hackensack, NJ

"Each chapter covers a different strategy and includes problems that could be solved using that strategy. This would be a great resource for any secondary mathematics teacher and a wonderful resource for the mathematics teacher educator."

MAA Reviews, July 2008
Mathematical Association of America

Sample Materials & Chapters

Preface

Chapter 1


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