What Preservice Teachers Say and Do When Deciphering Students’ Multiple Solution Strategies

In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students’ standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did—what we refer to as “subpractices”—as they engaged in the broad practice of deciphering multiple strategies. Inductive analysis revealed the presence of 10 subpractices. The subpractice of comparing and contrasting nonstandard methods was associated with success in deciphering students’ strategies, whereas two other subpractices—identifying number decompositions and relating nonstandard methods to the standard algorithm—were at times associated with success but at other times with a lack thereof. This study adds to a growing body of work seeking to support preservice teachers in learning the complex practices of reform-oriented mathematics teaching by decomposing these practices into their component parts.