Unpacking mathematical content through problem solving.

Abstract

Current calls for reform of preservice teacher education include suggested changes in the mathematics content courses required for elementary education programs. One suggestion is the inclusion of more complex problem solving activities. The context of this study was a homogeneous group of preservice teachers in a two-course sequence of college mathematics content courses. I investigated the use of complex problem solving as a vehicle for these preservice teachers to unpack previously learned mathematics, reconstruct their understandings, and connect mathematical concepts for deeper understanding. With the support of a mathematical classroom community, collaboration, and reflection, students reported gaining deeper understandings of the mathematics, a change in their beliefs about the nature of mathematics and themselves as mathematicians, and a significant decrease in negative emotional baggage.

As I considered what preservice teachers bring with them to the college mathematics content classroom, and how using problem solving to unpack mathematical content could deepen mathematical knowing, I found that frustration played a large role in the process. Choosing tasks that perturb student thinking and bring them to a level of frustration that provokes facilitative anxiety seemed to best encourage students to engage in mathematical collaboration, communication, and reflection during the problem solving process. Students reported frustration as the most common experience when starting and working on problems. However, in their reflective essays at the end of the semester, students had coupled their feelings of frustration with their feelings of accomplishment, satisfaction, and higher levels of mathematical confidence.