Students are often encouraged to work on problems "like mathematicians"--to be persistent, to investigate different approaches, and to evaluate solutions. This behavior, regarded as problem solving, is an essential component of mathematical practice. Some crucial aspects of problem solving include defining and interpreting problems, working with different solution methods, verifying solutions, and drawing conclusions. Students typically, however, are not encouraged to pose problems or carefully and critically analyze and reformulate the problems that they are given or that they find in textbooks. Problems present and contain situations. Word problems usually present scenarios that carry various implicit assumptions. When students recognize and grapple with assumptions, they become better problem solvers. Helping students become aware of the role that their assumptions play in mathematical problem solving is an essential attribute of critical thinking. It is recommended that students grapple with rich, well-structured problems that allow multiple paths for problem solving. (Contains 2 figures.)