Promoting prospective elementary teachers' knowledge about the role of assumptions in mathematical activity

Although the notion of assumptions is important in the discipline of mathematics and permeates ( often tacitly) mathematical activity in school classrooms, instruction in the elementary school pays little attention to it. This situation is unlikely to change unless elementary teachers have a good understanding of the role of assumptions in mathematical activity and an appreciation of the pedagogical implications of that role. In this paper, we investigate how teacher education can promote this dual goal by illustrating a promising, task-based approach to supporting prospective elementary teachers to develop pedagogically functional mathematical knowledge about the role of assumptions in mathematical activity. We developed the approach in a 4-year design experiment we conducted in a mathematics course for prospective elementary teachers in the United States.