Problem Solving in mathematics is often taught using a process that was outlined by the mathematician George Polya. Polya described the steps and strategies that he observed mathematicians using when they had to solve problems. Typically, students are told about these strategies, and then are asked to solve a series of problems by using them.

Rather than present these strategies to the students, I ask the students to behave like Polya did. Polya did not invent any of these strategies. He observed other people using them, and wrote them down. When we begin our study of problem solving, I break my class down into pairs of students, and give them problems to solve. Each pair observes another pair working on a problem, and writes down the strategies they observe being used. After several problem solutions have been observed, we compile the list of observed strategies. Invariably, our list looks like Polya's, so students still end up with a list of strategies to use when they are stuck on a problem. By arriving at that list through observation instead having it handed to them, I think that students have a better idea of what the strategies entail and how to apply them to actual problems. Rather than trying to memorize a list of steps, students analyze their own thinking and the problem solving strategies they use.