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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

Afterword by Nobel Laureate Herbert A. Hauptman



March 2008 | 280 pages | Corwin

"The authors have provided a unique, 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

"Helps both new and veteran teachers better understand the nature of problem solving as a critical mathematics process. The authors present in very simple terms 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

Help students become skilled and confident problem solvers!

Demonstrating there is always more than one approach to solving a problem, well-known authors and educators Alfred S. Posamentier and Stephen Krulik present ten basic strategies that are effective for finding solutions to a wide range of mathematics problems. These tried-and-true methods—including working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, and making a visual representation—make problem solving easier, neater, and more understandable for students as well as teachers.
Providing numerous sample problems that illustrate how mathematics teachers and specialists can incorporate these techniques into their mathematics curriculum, this updated edition also includes:

  • A variety of new problems that show how to use the strategies
  • References to current NCTM standards
  • Solutions to the problems in each chapter
  • Extensive discussions of the empowering strategies used to solve sample problems

The second edition of Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6–12 helps teachers develop students' creative problem-solving skills for success in and out of school.


 
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
Key features
  • Presents 10 effective problem-solving strategies
  • Includes references to current mathematics standards
  • Provides a generous collection of problems showing how to use the strategies
  • Includes solutions to the problems and extensive discussions of the strategies used to solve them

Sample Materials & Chapters

Preface

Chapter 1


Preview this book

For instructors

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