Poster #38 - The Influence of Gesture on Middle Schoolers’ Responses to Questions About Infinite Divisibility

• In Event: 2-110 - Poster Session 07
  In Poster Session: PS 07 Section - Cognitive Processes

Integrative Statement

By highlighting features of a topic that a speaker views as important, gestures may reveal aspects of a speaker’s mental model of a topic, thus providing a particular schematization of that topic (Kita, Alibali & Chu, 2016). Gestural schematization, in turn, may offer cues to the listener about how to interpret the message. This research investigated how gestures influence middle schoolers’ responses to questions about infinite divisibility. We were interested both in children’s overall accuracy as well as the prevalence of errors that suggest a whole number bias (WNB), which refers to children’s (and adults’) tendency to focus on either the numerator or denominator of a fraction rather than on the magnitude of the fraction itself (Ni & Zhou, 2005).

Middle-school students (N = 121) were randomly assigned to one of four conditions in which they viewed video clips that showed an actor seated behind a table. She asked, “How many possible fractions are between this number and this number?” while she referenced two printed fractions in front of her. Participants verbally responded to the questions. Participants also completed a worksheet containing multiple-choice questions about infinite divisibility.

The way the actor gestured to the fractions varied by condition. In the “sweep” condition, she gestured toward one fraction and then the other with a continuous motion. This gesture was intended to highlight the continuous and infinitely divisible nature of the number line. In the “many-chops” condition, the actor gestured at the first fraction, gestured to three locations along the invisible number line, then finally gestured at the second fraction. This gesture was intended to highlight many discrete points along the number line. In the “one-chop condition” the actor gestured at the first fraction, the midpoint of the invisible number line, and the second fraction. This gesture was intended to highlight a single point along the number line. In the gaze-only condition, the actor simply looked at each fraction while her hands were folded in her lap.

We predicted that those in the sweep condition would perform best. We also predicted that students with more math experience would be less susceptible to WNB errors. Preliminary results indicate that middle-school students struggle with the concept of infinite divisibility. Only 27% of children answered all verbal questions correctly, and 49% answered all worksheet questions correctly. Although no differences between the conditions emerged, math level predicted performance on video questions about infinite divisibility B = 0.30, t(111) = 3.00, p = .003. Math level also predicted performance on the worksheet questions B = 0.48, t(111) = 3.35, p = 0.001. In addition, more students with low math experience (75%) made WNB errors than students with high math experience (52%), X2(3) = 6.05, p = .01.

Although our preliminary results do not show condition differences in performance, associations between math level and WNB errors are emerging. The lack of condition differences may be explained by the brevity of the manipulation. Ongoing research will continue to investigate the role of gestural schematization on student performance.

Authors

• Sarah A Brown, Boston University
  Non-Presenting Author

• Andrea Marquardt Donovan, University of Wisconsin-Madison
  Presenting Author

• Martha W Alibali, University of Wisconsin-Madison
  Non-Presenting Author