Help students succeed as problem solvers in mathematics and in real-life situations! Based on the premise that problem solving is a key mathematics skill and an essential life skill, this book is designed to help teachers at all grade levels engage students in active problem solving. This resource presents ten easy-to-use strategies that offer elegant alternate approaches for resolving many types of mathematics problems. The authors demonstrate how you can: apply the strategies to problems at different grade levels; incorporate the strategies into your mathematics program; use the strategies in real-life situations; and, make each strategy a part of your thinking processes.
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.
Acknowledgments About the Authors Preface 1. An Introduction to Problem Solving 2. Organizing Data Applying the Organizing Data Strategy Teaching Notes Problems for Students 3. Intelligent Guessing and Testing Applying the Intelligent Guessing and Testing Strategy Teaching Notes Problems for Students 4. Solving a Simpler Equivalent Problem Applying the Solving a Simpler Equivalent Problem Strategy Teaching Notes Problems for Students 5. Acting It Out or Simulation Applying the Acting It Out or Simulation Strategy Teaching Notes Problems for Students 6. Working Backwards Applying the Working Backwards Strategy Teaching Notes Problems for Students 7. Finding a Pattern Applying the Finding a Pattern Strategy Teaching Notes Problems for Students 8. Logical Reasoning Applying the Logical Reasoning Strategy Teaching Notes Problems for Students 9. Making a Drawing Applying the Making a Drawing Strategy Teaching Notes Problems for Students 10. Adopting a Different Point of View Applying the Adopting a Different Point of View Strategy Teaching Notes Problems for Students Readings on Problem Solving
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