THE EMERGENCE OF PROPORTIONAL REASONING FROM EMBODIED INTERACTION WITH A TABLET APPLICATION: AN EYE-TRACKING STUDY

S. Shayan1, D. Abrahamson2, A. Bakker1, C. Duijzer1, M. van der Schaaf1

1Utrecht University (NETHERLANDS)
2University of California, Berkeley (UNITED STATES)
Embodied cognition, or the idea that we “think” with and through our bodies is a promising approach in educational technology. According to this theory human cognition is deeply rooted in the body’s interactions with the physical environment; when the appropriate sensorimotor systems are engaged, the converging inputs of perceptual experience together with physical interaction work together to create stronger and more stable knowledge representations. (Barsalou 2008, Clark 2001, Wilson 2002).

There is compelling evidence from various research domains supporting the view that embodiment is a powerful underpinning of cognition. These include findings from mathematics (Lakoff & Nunez 2000, Johnson 2007, Nunez 2008), role of gesture in learning mathematics (Goldin-Meadow, 2009; Hostetter & Alibali, 2008), cognitive psychology (Barsalou, 2008; Glenberg, 2010), and linguistics (Lakoff & Johnson, 1980).

The most appealing implications of this theory for education research is that if we instruct people using body movements and activating appropriate sensorimotor codes, then students might learn better.Challenge of understanding is bigger when students are younger, or the problem they face is more difficult. Specially in domains like mathematics in which learning based on bodily experience allows the learner to develop a “feel” for the concept being described; a sense that is more comprehensible than an abstract concept.

The subject matter of ratio and proportion is one such example. It is an essential component of early curriculum yet the failing point of many students. Our project focuses on possibilities for embodied learning of proportion. In close collaboration with the Embodied Design Research Laboratory in Berkeley and based on the project MIT-P (mathematical imagery trainer for proportion, Abrahamson & Lindgren in press), our goal is to understand the relationship between bodily action, perception and reasoning in learning proportions. Targeting vocational education, we focus on some of the mathematical skills (e.g., scaling and zooming) underlying many vocational tasks related to visualization (e.g., reading 2D maps of buildings, electricity wiring). We have an iPad app designed based on the MIT-P in which students have to move two bars with two fingers and turn the color of the bars green. Based on the visual feedback (red or green) provided they learn that green is only achieved if they move their fingers with a speed relative to a pre-set proportion. We record Their looking pattern, through an eye-tracker, keep a log of their hand movement and initiate conversations to probe their reasoning on how they solve the problem. Our preliminary data shows that after a period of exploration students utilize an attentional anchor to master the coordination of the motor-action in turning the bars green. Once the students have developed a feel for a proportional motor control, there is a moment of discovery in which they find the rule. Next when they see the grids and numbers next to the bars they are able to aim for pairs of heights (ex. 2:4, 3:6, 4:8) of the same proportion and keep the bars green. In Further analysis we investigate the correlation between their hand-movement and their gaze data during the play and hope to answer fundamental questions on the underlying mechanism of their learning behavior. An understanding of the dynamics of this task results in designing better such tools in similar technological environments.