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

Front Cover
Corwin Press, Mar 20, 2008 - Education - 280 pages

"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.

 

Selected pages

Contents

Chapter 1 Introduction to ProblemSolving Strategies
1
Chapter 2 Working Backwards
17
The Working Backwards Strategy in Everyday Life ProblemSolving Situations
18
Applying the Working Backwards Strategy to Solve Mathematics Problems
19
Problems using the Working Backwards Strategy
21
Chapter 3 Finding a Pattern
39
The Finding a Pattern Strategy in Everyday Life ProblemSolving Situations
40
Applying the Finding a Pattern Strategy to Solve Mathematics Problems
42
Chapter 7 Making a Drawing Visual Representation
141
Applying the Making a Drawing Visual Representation Strategy to Solve Mathematics Problems
142
Problems using the Making a Drawing Visual Representation Strategy
143
Chapter 8 Intelligent Guessing and Testing Including Approximation
167
The Intelligent Guessing and Testing Including Approximation Strategy in Everyday Life ProblemSolving Situations
168
Problems using the Intelligent Guessing and Testing Including Approximation Strategy
170
Chapter 9 Accounting for all Possibilities
189
Applying the Accounting for all Possibilities Strategy to Solve Mathematics Problems
190

Problems using the Finding a Pattern Strategy
43
Chapter 4 Adopting a Different Point of View
69
The Adopting a Different Point of View Strategy in Everyday Life ProblemSolving Situations
70
Applying the Adopting a Different Point of View Strategy to Solve Mathematics Problems
71
Problems using the Adopting a Different Point of View Strategy
72
Chapter 5 Solving a Simpler Analogous Problem
97
Applying the Solving a Simpler Analogous Problem Strategy to Solve Mathematics Problems
98
Problems using the Solving a Simpler Analogous Problem Strategy
100
Chapter 6 Considering Extreme Cases
117
The Considering Extreme Cases Strategy in Everyday Life ProblemSolving Situations
118
Problems using the Considering Extreme Cases Strategy
121
Problems Using the Accounting for all Possibilities Strategy
191
Chapter 10 Organizing Data
203
Applying the Organizing Data Strategy to Solve Mathematics Problems
204
Problems using the Organizing Data Strategy
206
Chapter 11 Logical Reasoning
225
Applying the Logical Reasoning Strategy to Solve Mathematics Problems
226
Afterword
243
Sources for Problems
249
Readings on Problem Solving
257
Copyright

Other editions - View all

Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12 ...
Alfred S. Posamentier,Stephen Krulik
Limited preview - 2008
Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12 ...
Alfred S. Posamentier,Stephen Krulik
Limited preview - 2008
Problem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12 ...
Alfred S. Posamentier,Stephen Krulik
Snippet view - 2008
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Common terms and phrases

ÁÁÁ adopting a different algebraic angle bisector approach area of triangle arithmetic mean backwards strategy begin calculator circle column considering extreme correct answer count diagonals different point digit sum Diophantine equation drawing eggs equal equation examine this problem Figure finding a pattern fraction given guessing and testing icosagon integers intelligent guessing Krulik line segments logical reasoning strategy look Mathematics Teacher method multiple NCTM obtain odd number organize the data organizing data original problem pairs palindromes parallelogram Parsifal pattern strategy pentagram perfect squares player point of view poison ivy possible prime number probability problem-solving strategies puppy represents the number right triangle Sam Loyd scores sequence sides simpler analogous problem Solution The traditional SOLVE MATHEMATICS PROBLEMS solve this problem solving a simpler STRATEGY IN EVERYDAY STRATEGY TO SOLVE subtracting testing strategy total number train variables visual representation yields York

About the author (2008)

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 EdD in mathematics education from Columbia University’s Teachers College.

Bibliographic information

TitleProblem-Solving Strategies for Efficient and Elegant Solutions, Grades 6-12: A Resource for the Mathematics Teacher
AuthorsAlfred S. Posamentier, Stephen Krulik
Edition2
PublisherCorwin Press, 2008
ISBN1452295573, 9781452295572
Length280 pages
Subjects ›  ›  › 

Education / Schools / Levels / Secondary
Education / Teaching / General
Education / Teaching / Subjects / Mathematics
Juvenile Nonfiction / Mathematics / General
  
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