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

###### Alfred S. Posamentier and Stephen Krulik
Publisher:
Corwin Press
Publication Date:
2008
Number of Pages:
260
Format:
Paperback
Edition:
2
Price:
36.95
ISBN:
9781412959704
Category:
General
[Reviewed by
Jane Ries Cushman
, on
07/4/2008
]

Having just taught a problem-solving course to future mathematics teachers, I am very impressed by this book. Each chapter covers a different strategy (working backwards, finding a pattern, adopting a different point of view, solving a simpler analogous problem, considering extreme cases, making a drawing, intelligent guessing and checking, accounting for all possibilities, organizing data, and logical reasoning) and includes problems that could be solved using that strategy. I write, “could be solved,” since there are multiple ways to solve most problems in this book. The authors even discuss the non-elegant solutions in order to compare that solution with the efficient and elegant solution using the strategy of the chapter.

There are, on average, 20 problems and solutions in the ten chapters (there are eleven chapters but chapter one is an introduction). The problems are accessible to high school teachers and their students and cover many topics in high school mathematics.

This would be a great resource for any secondary mathematics teacher and a wonderful resource for the mathematics teacher educator.

Jane Ries Cushman currently works at Buffalo State College in Buffalo, NY as an assistant professor. She received her doctorate at The University of Texas at Austin in August 2006. She is editor of the Association of Mathematics Teachers of New York State Newsletter and she is the chair of the Association of Mathematics Teacher Educators Affiliate’s Connection Committee. Her research interests include Inquiry-Based Learning, Problem-Solving and Functions-Based Approach to Algebra.

 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