The Nature of Prospective Mathematics Teachers’ Designed Manipulatives and their Potential as Anchors for Conceptual and Pedagogical Knowledge

Abstract

While traditionally teachers have been positioned as implementers of curricular materials designed by others, this work positions them as designers of their own curricular resources, thereby inviting opportunities for their exploration at the intersection of content, pedagogy, and design. As researchers accepting greater responsibility for preparing teachers to maintain a commitment to their pedagogical vision in practice, this work seeks to cultivate the imagination of humanistic forms of mathematics teaching and learning by supporting these explorations. Toward that end, this paper reports on research that examines connections between the pedagogical/conceptual knowledge that prospective teachers embed in the designs of original manipulatives and how those designs mediate the pedagogical moves they make in teaching situations. The promise of this work is in connections that may offer a viable means to support bolder connections between teacher preparation and practice. We share findings from the analysis of prospective teachers’ design activity that conveys (1) the diversity of design decisions, rationales, and mediating resources that it entailed, and (2) how the designed manipulative act as anchors for their conceptual/pedagogical moves. The implications of these findings for teacher preparation and professional learning are considered.