Transitional knowledge in the acquisition of concepts

These studies explore children's conceptual knowledge as it is expressed through their verbal and gestural explanations of concepts. We build on previous work that has shown that children who produce a large proportion of gestures that do not match their verbal explanations are in transition with respect to the concept they are explaining. This gesture/speech mismatch has been called "discordance." Previous work discovered this phenomenon with respect to 5- to 7-year-old children's explanations of conservation problems. Study 1 shows: (1) that older children (10 to 11 years old) exhibit gesture/speech discordance with respect to another concept, understanding the equivalence relationship in mathematical equations, and; (2) that children who produce many discordant responses in their explanations of mathematical equivalence are more likely to benefit from instruction in the concept than are children who produce few such responses. Studies 2 and 3 explore the properties and usefulness of discordance as an index of transitional knowledge in a child's acquisition of mathematical equivalence. Under any circumstance in which new concepts are acquired, there exists a mental bridge connecting the old knowledge state to the new. The studies reported here suggest that the combination of gesture and speech may be an easily observable and significantly interpretable reflection of knowledge states, both static and in flux.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27122/1/0000114.pd

Computational gesture research: Studying the functions of gesture in human-agent interaction

Kopp S. Computational gesture research: Studying the functions of gesture in human-agent interaction. In: Church RB, Alibali MW, Kelly SD, eds. Why Gesture?: How the hands function in speaking, thinking and communicating. Gesture Studies. Vol 7. Amsterdam: John Benjamins Publishing Company; In Press: 433

Teachers’ gestures and students’ learning: sometimes “hands off” is better

Abstract During mathematics instruction, teachers often make links between different representations of mathematical information, and they sometimes use gestures to refer to the representations that they link. In this research, we investigated the role of such gestures in students’ learning from lessons about links between linear equations and corresponding graphs. Eighty-two middle-school students completed a pretest, viewed a video lesson, and then completed a posttest comparable to the pretest. In all of the video lessons, the teacher explained the links between equations and graphs in speech. The lessons varied in whether the teacher referred to the equations in gesture and in whether she referred to the graphs in gesture, yielding four conditions: neither equations nor graphs, equations only, graphs only, and both equations and graphs. In all conditions, the gestures were redundant with speech, in the sense that the referents of the gestures were also mentioned in speech (e.g., pointing to “2” while saying “2”). Students showed substantial learning in all conditions. However, students learned less when the teacher referred to the equations in gesture than when she did not. This was not the case for gesture to graphs. These findings are discussed in terms of the processing implications of redundancy between gesture and speech, and the possibility of “trade-offs” in attention to the visual representations. The findings underscore the need for a more nuanced view of the role of teachers’ gestures in students’ comprehension and learning