Promoting elements of mathematical knowledge for teaching related to the notion of assumptions

Abstract

ABSTRACT Although the notion of assumptions is important in mathematical activity as early as the elementary school, there is limited research on how to help elementary teachers develop mathematical knowledge for teaching related to assumptions. In this paper, we discuss the theoretical foundation and implementation of an intervention that aimed to promote three key elements of this knowledge among prospective elementary teachers. We developed the intervention in a 4-year design experiment that we conducted in an undergraduate mathematics course for prospective elementary teachers. The intervention’s design utilized the notion of productive ambiguity in the context of a deliberately ambiguous task where the role of assumptions surfaced and was reflected upon in purposefully organized ways. We focus on the implementation of the intervention in the last of 5 research cycles of our design experiment to exemplify our theoretical framework and to discuss the promise of the intervention to promote the three targeted elements of knowledge. The approach to promoting mathematical knowledge for teaching that we discuss in the paper offers a paradigmatic case of how teacher educators can use productive ambiguity to design learning opportunities for prospective teachers to intertwine mathematical learning with pedagogical awareness thus developing pedagogically functional mathematical knowledge.