Problem solving is a fundamental means of developing mathematical knowledge at any level. For this reason, it is one of the most important, if not the most important, aspect of doing mathematics. Before we begin to examine the elements of problem solving and examples of student work involving solving problems, it is important for us to share an understanding of what is meant by "problem solving."

According to NCTM, "Problem solving means engaging in a task for which the solution method is not known in advance. In order to find a solution, students must draw on their knowledge, and through this process, they will often develop new mathematical understandings. Solving problems is not only a goal of learning mathematics, but also a major means of doing so." (NCTM, 2000, p. 52)

Problem solving gives students a context to help them make sense out of the mathematics they are learning. Problems can be used to introduce new concepts and extend previously learned knowledge.

In this session, we will illustrate and reflect on different aspects of problem solving in the early grades.

This session shows you how to help students do the following:

• Make sense of mathematical concepts by applying them to a variety of problem-solving settings
• Solve problems using a variety of strategies
• Learn to monitor and reflect on their own ideas in solving problems by sharing their thinking with other students and the teacher

Instructional programs . . . should enable all students to-

• Build new mathematical knowledge through problem solving
• Solve problems that arise in mathematics and in other contexts
• Apply and adapt a variety of appropriate strategies to solve problems
• Monitor and reflect on the process of mathematical problem solving

Principles and Standards of School Mathematics (NCTM, 2000). For more information on this Process Standard, see the NCTM Web site

  Observe a math problem