Embodied Learning of Integer Operations Using a Multitouch Design: Touchy Pinchy Integers

Abstract

We report the design and pilot testing of a digital application to help middle school children learn integers, Touchy-Pinchy Integers (TPI). The design rationale for this touchscreen-based learning system was based on a neutralization model of integers. To design this embodied mathematics learning system, we associated commonly used touchscreen interaction gestures with mathematical meaning related to integers. Users could manipulate two collinear towers of stacked positive and negative blocks, which together represent an integer expression. The learner could add either type of block, by tapping on the appropriate part of the screen. They could also subtract a desired number of either type of block, by slicing across the blocks. They could also neutralize a pair of positive and negative blocks, by pinching in. The pinch-out actions generated a new pair of positive and negative blocks. A flipping gesture reversed the polarity of the integer expression, which corresponded to a multiplication by -1. Results from a pilot study with grade 7s students indicated that the application helped students resolve deep conceptual issues related to negative numbers, through embodied learning. We present some of our observations from the study and interpret these episodes using embodied learning theory.