Mathematical Problem Solving pp 3-20 | Cite as

# “Looking Back” to Solve Differently: Familiarity, Fluency, and Flexibility

## Abstract

The present study focuses on a specific step of Pólya’s problem-solving process, namely, “looking back” to solve a problem differently. In particular, it examines the extent to which the practice of “looking back” to solve differently has been integrated into mathematics classroom instruction in the United States. The findings of the present study indicate, to a certain degree, that this practice is little known to high school students, even those from some very selective schools. Moreover, it demonstrates that a high level of mathematical preparation might not be a sufficient condition for a student’s inclination to search for (let alone consider the need for) more than one solution method. Pedagogical implications of emphasizing the importance of connections between different mathematical topics are discussed.

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