Previously, we have studied the Communication Standard. In this session, we will examine Problem Solving.

Problem solving is at the heart of mathematics. Formulating problems, finding ways to work on them, learning from both errors and solutions, and making connections between and among problems is a key task for the mathematics teacher and student. It is also a deeply rewarding and stimulating human activity. Inherent in the idea of problem solving is learning how to skillfully apply techniques and strategies to familiar problems; but it is equally important to learn how to extend a problem-solving disposition to new problems and new subjects. Problems are both a means to engage what we have already learned, but also to extend that learning, both in the mathematics classroom and outside of it.

"A major goal of high school mathematics is to equip students with knowledge and tools that enable them to formulate, approach, and solve problems beyond those that they have studied. High school students should have significant opportunities to formulate and refine problems because problems that occur in real settings do not often arrive neatly packaged." (NCTM, 2000, p. 335)

This session shows how to help students do the following:

• Make sense of new mathematical concepts by developing understanding through problem-solving settings
• Develop and work with a range of problem-solving strategies and see the connections among them
• Learn to review and reflect on their work, both on their own and when communicating with students and teachers

Instructional programs . . . should enable all students to do the following:

• 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