The Influence of Gesture on Undergraduates' Responses to Questions About Infinite Divisibility

• In Event: 69.045 - On the Interaction Between Embodied and Symbolic Mathematics Knowledge: Implications for Instruction

Abstract

Gestures that speakers produce have the potential to highlight features of a topic that the speaker views as most important in any particular moment. That is, gestures may reveal aspects of the speaker’s mental model of the topic, and thus provide a particular schematization of the topic. Gestural schematization may offer pragmatic cues to the listener about how to interpret the topic. We experimentally investigate how different gestural schematizations influence undergraduates’ responses to questions about infinite divisibility.

Participants (N = 53) view video clips of an actor seated at a table with two printed fractions on the table in front of her. In the clips, the actor asks, “How many possible fractions are between this number and this number?” Participants then verbally respond to this question.

The gestures that the actor makes while speaking vary by condition. In the gaze-only condition, the actor simply looks at each number. In the “continuous sweep” condition, the actor gestures toward one number and slides her hand across the table to the other number. In the “discrete many-chops” condition, the actor gestures at the first number, gestures to three locations along the invisible number line between the two numbers, then gestures at the second number. In the “discrete one-chop” condition the actor gestures at the first number, gestures once at the midpoint of the invisible number line, then gestures at the second number.

The gesture in the one-chop condition is intended to highlight a single point along the number line. We hypothesize that people who view this schematization of the number line will be the least likely to give the only correct answer, which is that there are an infinite number of fractions between any two numbers. In addition, we hypothesize that people in this condition might make a particular error: giving “one” as their answer. Preliminary results lend some support for these hypotheses. Indeed, average performance in this condition was lowest, and participants in this condition were most likely to answer “one”.

The continuous gesture in the sweep condition is intended to highlight the continuous and infinitely divisible nature of the number line. We hypothesize that people who view this schematization of the number line will be the most likely to give the correct answer. However, preliminary results do not support this hypothesis.

In the many-chops condition, the gesture is intended to highlight many discrete points along the number line. We hypothesize that people who view this schematization will be less likely than those in the sweep condition to answer correctly. Preliminary results do not support this hypothesis.

Overall, preliminary results are mixed, but suggest that viewing different schematizations of a topic can lead students to make particular errors. Further, our preliminary results emphasize the importance of additional exploration into the role of gesture in educational settings.

Authors

• Andrea Marquardt Donovan, University of Wisconsin

• Sarah Brown, University of Wisconsin - Madison

• Martha W. Alibali, University of Wisconsin - Madison