Teaching mathematics and the problems of practice: understanding situations and teacher reasoning through teacher perspectives

In this study, 4 teachers were asked to identify classroom-teaching situations that they “wondered” about. Each teacher was using an inquiry-based, National Science Foundation funded curriculum (Investigations in Data Number and Space or Connected Mathematics) to teach fractions. Results showed that teachers’ problems of practice centered on interactions in which they struggled to understand students’ strategies, both invented and school based. Though difficult, the teachers strove to find ways to support student thinking and instructional intentions of inquiry-based mathematics practices rather than resorting to more didactic approaches. Teachers recognized and valued children’s construction and use of representations for fractions that were often in the form of area models, and teachers wanted to find ways to interpret these strategies from the children’s point of view. Teachers in this study often perceived themselves as “stuck” rather then empowered because they did not have the strategies for teaching needed to support these novel uses of models and often unexpected strategies.