Chapter 3: Mathematical Problem Solving

Everyone can and should become proficient in mathematics. Furthermore, to become proficient in mathematics means to build several different—but intertwined—strands of mathematical proficiency (or kinds of mathematical knowledge) that can be used to solve mathematics problems. What does a person need to know to be proficient in mathematics? To answer this question, this chapter examines research on the cognitive processes involved in mathematical problem solving. I begin with an introduction that includes definitions of key terms and a summary of four cognitive processes in mathematical problem solving—translating, integrating, planning, and executing. Then, for each cognitive process, I provide examples and explore exemplary research. Finally, the chapter ends with a conclusion in which I suggest some future directions for research on the cognitive psychology of mathematical problem solving.