Introduction

Problem solving is at the heart of today's goal of teaching and learning mathematics for understanding. It is the first of the five process standards addressed in the NCTM's Principals and Standards for School Mathematics (NCTM, 2000). More than just how to solve word problems, a problem-solving approach can be applied to mathematics found in either big multiday interdisciplinary projects or, more typically, to small problems that require deep thought.

In this publication, we focus on those problems—big and small—that encourage students to think, ask questions, try a variety of problem-solving approaches, and discuss their strategies and solutions. Built on the ideas found in the Standards, we feature in the Background section pedagogical examples and resources to expand teachers' understanding of mathematics and problem solving. Through the selected resources in the Activities sections, we recognize that there is a vast difference between numerical problems dressed up as episodes of everyday life and real mathematics used every day to facilitate understanding and decision making. The Standards document stresses that problem solving should not be taught in isolation, but rather used as an approach to develop concepts in all of the five mathematics learning strands. The problems and activities suggested here are based on the belief that "an item is an exercise (not a problem) if a learner knows exactly how to approach it." (Rubenstein, Beckmann, & Thompson, 2004, p. 18)

Reference

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: Author.

Rubenstein, R. N., Beckmann, C.E., & Thompson, D.R. (2004). Teaching and Learning Middle School Mathematics. Emeryville, CA: Key College Publishing.

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by Judy Spicer

Judy Spicer is the mathematics education resource specialist for digital library projects at Ohio State University. She has taught mathematics in grades 9-14. Email: spicer.21@osu.edu

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Copyright March 2005 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.