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Problem Solving in Mathematics, Grades 3-6

Powerful Strategies to Deepen Understanding

By: Alfred S. Posamentier, Stephen Krulik

Help students succeed as problem solvers in and out of the classroom!

Based on the premise that teachers must directly teach problem-solving skills as part of mathematics instruction, this book presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. With the sample problems and detailed solutions provided, teachers can:

Apply the strategies to problems at different grade levels
Incorporate these strategies into a mathematics program
Understand how each strategy can be applied to real-life situations
Make each strategy an integral part of students' thinking processes

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Product Details

Grade Level: 3-6
ISBN: 9781412960670
Published By: Corwin
Year: 2009
Page Count: 152
Publication date: March 18, 2009

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Review copies may be requested by individuals planning to purchase 10 or more copies for a team or considering a book for adoption in a higher ed course. To request a review copy, contact sales@corwin.com.

Description

"Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level."
—Janice L. Richardson, Associate Professor and Education Coordinator, Department of Mathematics
Elon University

Help students succeed as problem solvers in and out of the classroom!

Problem solving skills are critical to students' success in mathematics, but the techniques can't be caught; they must be taught. Based on the premise that educators must take a deliberate approach to the teaching of problem solving skills, this book helps teachers engage students in the process.

Problem Solving in Mathematics, Grades 3–6 stresses the importance of problem solving in mathematics and presents nine strategies that students can use to solve problems, such as working backwards, finding a pattern, making a drawing, or solving a simpler equivalent problem. Each chapter demonstrates how teachers can:

Apply the strategies to problems at different grade levels
Incorporate these strategies into a mathematics program
Understand how each strategy can be applied to real-life situations
Make each strategy an integral part of students' thinking processes

With helpful teaching notes, sample problems for students that fit into any mathematics curriculum, and step-by-step solutions to sample problems, this book is perfect for teachers who want their students to succeed in mathematics!

Key features

Demonstrates how to apply the strategies to problems at different grade levels
Analyzes and discusses how to use the strategies to solve various problems
Shows how each of these strategies occurs in and ought to be consciously used in real-life situations
Offers guidance for incorporating these strategies into the mathematics program
Helps make each strategy a part of the teacher's thinking processes

Author(s)

Alfred S. Posamentier

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

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.

Table of Contents

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

Reviews

“A wonderful collection of problems that were thoroughly researched and presented.”

Timothy J. McNamara, National K-12 Consultant/Professional Developer
Author, Teaching Essential Mathematics, Grades K-8

“Helps fill a gap in the field of mathematics education—a specific explication with appropriate examples of the variety of problem solving approaches.”

Pearl Solomon, Author
The Math We Need to Know and Do in Grades PreK–5

“Demonstrates problem solving strategies with solutions and teaching notes and allows the teacher to create a collection of problems to fit a particular grade level.”

Janice L. Richardson, Associate Professor and Education Coordinator, Department of Mathematics
Elon University

Other Titles in: Mathematics | Teaching Methods & Learning Styles | Elementary Teaching Methods

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