Mathematical Manipulatives as Designed Artifacts: The Cognitive, Affective, and Technological Dimensions

Abstract

Mathematical manipulatives-tangible objects with a pedagogical purpose-have become popular tools in mathematics education. But typically, the notion of a "manipulative" carries with it a number of additional assumptions: that these objects are designed for elementary (as opposed to advanced) mathematics instruction; that they have little in the way of emotional meaning for their users; and that they are relatively simple, "low-tech" objects. In this paper we challenge these assumptions. Drawing on our experiences in two related projects in educational computing, we suggest that manipulatives may be designed for advanced mathematical topics; that they may offer creative (and thus affectively important) opportunities for students; and that they may be designed in ways that accompany or incorporate computational media.