THE INTERPLAY AMONG GESTURES, DISCOURSE AND DIAGRAMS IN STUDENTS’ GEOMETRICAL REASONING

This study identifies forms of interactions with diagrams that are involved in conjecturing; more specifically, how students display their thinking publicly through using multimodal representations. We describe how students interact with diagrams in both gestural and verbal forms, and examine how such multimodal interactions with diagrams reveal their reasoning about diagrams. We hypothesize that when limited information is given in a diagram, students make use of gestural and verbal expressions to compensate for those limitations as they engage in making conjectures. As a byproduct, the study also proposes a set of graphical representations of gestures that have been identified as important for geometrical reasoning. These can be employed to codify the gestural interactions and to depict the practices of teaching and learning in geometry classrooms.The research reported in this study was done with the support of a National Science Foundation CAREER grant, REC 0133619 to the second author. All opinions are those of the authors and do not necessarily represent the views of the Foundation.http://deepblue.lib.umich.edu/bitstream/2027.42/78015/1/CC&PH-Gesture-share.pd