Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12: A Resource for the Mathematics Teacher / Edition 2

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Overview

This updated edition presents ten strategies for solving a wide range of mathematics problems, plus new sample problems.

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Editorial Reviews

Howard W. Smith
“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.”
Daniel Jaye
"This terrific resource helps bothnew 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."
MAA Reviews
"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."
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Product Details

  • ISBN-13: 9781412959704
  • Publisher: SAGE Publications
  • Publication date: 3/20/2008
  • Edition description: Second Edition
  • Edition number: 2
  • Pages: 280
  • Product dimensions: 6.90 (w) x 9.90 (h) x 0.70 (d)

Meet the Author

Alfred S. Posamentier is professor of mathematics education and dean of the School of Education at the City College of the City University of New York. He has authored and co-authored several resource books in mathematics education for Corwin Press.

Stephen Krulik is professor of mathematics education at Temple University in Philadelphia, where he is responsible for the undergraduate and graduate preparation of mathematics teachers for Grades K-12, as well as in the inservice training of mathematics teachers at the graduate level. He teaches a wide variety of courses, among them the History of Mathematics, Methods of Teaching Mathematics, and the Teaching of Problem Solving. Before coming to Temple University, he taught mathematics in the New York City public schools for 15 years, where he created and implemented several courses designed to prepare students for the SAT examination. Nationally, Krulik has served as a member of the committee responsible for preparing the Professional Standards for Teaching Mathematics of the National Council of Teacher of Mathematics (NCTM). He was also the editor of the NCTM’s 1980 yearbook Problem Solving in School Mathematics. He is the author or co-author of more than 20 books for teachers of mathematics, including Assessing Reasoning and Problem Solving: A Sourcebook for Elementary School Teachers. He has served as a consultant to and has conducted many workshops for school district throughout the United States and Canada, as well as delivering major presentations in Austria, Hungary, Australia, and international professional meetings, where his major focus is on preparing all students to reason and problem-solve in their mathematics classroom, as well as in their lives. Krulik received his BA degree in mathematics from Brooklyn College of the City University of New York, and his MA and Ed D in mathematics education from Columbia University’s Teachers College.

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Table of Contents

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

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