Preservice mathematics teachers’ conceptions of mathematically rich and contextually realistic problems

This study investigated the middle school preservice mathematics teachers’ conceptualization of what it means for a problem to be mathematically rich and contextually realistic and how their conceptions evolved during a series of professional development activities. Fifteen middle school preservice mathematics teachers were involved in this design-based research. The professional development activities were designed based on L. Shulman and J. Shulman’s (Shulman and Shulman, Journal of Curriculum Studies 36:257–271, 2004) reflective and communal clusters with psychological roots in Schön’s notion of “reflective practitioners” and Vygotsky’s social development theory. These professional development activities were integrated into the methods and field experience courses of the teacher education program. The audio records of the whole group and small group discussions and all written products (i.e., problems, criteria list, and reflection memos) were analyzed to understand preservice teachers’ conceptions. This study revealed that the professional development activities helped preservice teachers produce the problems that would be interesting and encouraging for students to develop their own solution methods. Preservice teachers’ conceptions also evolved in a collective and reflective community. In this respect, this study presented a way to design professional development for teachers that nurtures their understanding of the components supporting mathematical richness and contextual meaningfulness of a problem. Hence, this study provided implications for teacher education practices and future research on mathematics teacher preparation.