In this article, a theoretically derived grid is presented combining Pólya's phases of the problem-solving process with the way in which teachers emphasize their students' strategic diversity in problem solving. It is used to categorize previous results from the literature. In an empirical part, the grid is also used to describe mathematics teachers' behaviors in lessons on the topic of problem solving. Additionally, these teachers' beliefs regarding mathematics and problem solving have been obtained with interviews. Comparisons of the teachers' behavior and their beliefs reveal the importance of beliefs in the context of teaching for problem solving.