Mathematics MOVES Me: Digital Solutions for Coordinating Enactive and Symbolic Perspectives—The Case of Basic Arithmetic With Positive and Negative Integers

Abstract

We present an innovative educational design for basic arithmetic that responds to students’ documented difficulties with adding and subtracting single-digit positive and negative numbers. The design utilizes MOVES, a technological architecture that combines floor- and wall-projected interactive interfaces. Students enact arithmetic operations, e.g., “3 - (-2)” by walking along a projected body-scale number line, while their actions are captured and analyzed to provide in-the-moment feedback on elements of their solution procedure. Next, a screen-based avatar is introduced who mimics their whole-body movements. Finally, analogous problems are presented on a tablet that utilizes tangible interaction, where students walk the avatar, now as an action-figure, along a standard-sized number line. Our theoretical framework, design conjecture, product evaluation, and data analysis all pertain to fostering conceptual understanding through coordinating full-body egocentric experiences on a body-scale number line with the allocentric experience of “puppeting” the avatar along the desk-scale number line. Based on pilot trials, we speculate on the nature and type of supports students require to coordinate these perspectives and discuss implications for future iterations of the design.