‘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.
विषयसूची
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
लेखक के बारे में
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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