However, despite massive efforts, funding, and resources for teacher education in universities and schools, we know very little about what teachers know, and especially, how teachers interpret and respond to student invented strategies (CBMS, 2001; Wilson, Floden, & Ferrini-Mundy, 2001). As part of a larger effort to characterize mathematics knowledge for teaching, this study examined, through a teaching-scenario task, the nature of thirty-five preservice elementary teachers’ reasoning and responses to students’ correct and incorrect invented strategies for whole number multiplication. Implications for teacher education and professional development were discussed in accordance with the findings of the study.

The purpose of this presentation was not to add to the collection of studies documenting prospective teacher weakness, but rather to inform the design of teacher education in this area. Exploration of preservice teachers’ interpretations of and responses to student ideas, in particular, student invented strategies in connection with the traditional method helped enrich a dialogue among reformers, teacher educators, and professional developers in what ways they could help preservice teachers learn to teach math in ways that promote student understanding.

Throughout the session, the audience was invited to participate in three ways: (1) the analysis of examples of preservice teachers’ responses, (2) the sharing and discussing their analysis, and (3) questions to presenters. With this interaction, we gained insights from other mathematics teacher educators that can extend our research.