Problem solving has been defined as a four-part process: understanding the problem, devising a plan, executing the plan, and reviewing the process. If you only apply a rule that you've learned from someone else, you are missing out on the learning that is possible in the first two parts of that process.

So, how do we help students become better problem solvers? One approach is to provide rich mathematical problems that will be of interest to students. Students need to develop a wide variety of strategies to get their arms around a problem and begin their work. However, problem solving shouldn't be limited to just the application of strategies; whenever possible, it should also include exploring the underlying mathematical concepts. These two elements can strengthen each other: As good problems provide opportunities for students to gain knowledge and develop understanding, they may also build students' skills in using strategies.

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