One way students learn mathematics is through active involvement in solving a variety of rich mathematical problems. Traditionally, both examples in which students practiced skills ("story problems") and computational drills were considered "problems." For example, a textbook might present a multiplication exercise in two ways: with numbers, as in "Find 4 x 56," or with words, as in problems "How many legs are on 56 elephants?"

The process of problem solving encompasses mathematics far beyond completing examples presented with words. In fact, a problem is actually a task for which a means to a solution is not known in advance. The "problem" in the lesson on multiplication was actually an "exercise" for practicing the skill, rather than an actual problem. The students did not have to think about the situation in order to answer it -- they could do so by applying the procedure taught in the lesson.

So, how do we help students become better problem solvers? First, the teacher needs to provide rich mathematical problems that will be of interest to students. Good problems will provide opportunities for students to build on their knowledge to develop understanding of the mathematical concepts. Students need to develop a wide variety of approaches or strategies to get their arms around the problem and begin their work.

In the next part of this session, we take a closer look at some problem-solving strategies that middle school students should be familiar with.

  Different ways to organize data