This research will provide a better understanding of the way in which gestures are taken up by students and how they are used in their own mathematical thinking. The study is original in that it focuses on the gestures by teachers that students imitate when they are not explicitly asked to attend to them or to copy them—a situation that is much more realistic than intentional gesture instruction.
Findings for this study will contribute to refining current theories in mathematics education about the role of gestures in mathematical communication. In particular, they will point to an expanded view of the embodiedness of mathematical ideas.
Hand gestures are present everywhere in our lives. They can be defined as the hand movements that occur with speech. The gestures we use amplify our speech, add additional and complementary information to the spoken word, and can even contradict it. Gestures can allow students to express ideas that they cannot yet express through words and are thus an important means of communication in the classroom.
The gestures used by teachers can enhance student learning in at least two ways. First, gestures convey additional, more intuitive meanings; and second, students can improve their understanding by imitating teacher gestures. The goals of this research are to discover the extent to which students copy/mimic/echo gestures when they are not explicitly instructed to do so and to investigate the nature of the gestures which students do imitate.
Data will be obtained through videotaping a lesson given by a teacher, focusing on four central and challenging ideas in the high school mathematics curriculum, and videotaping of students describing those concepts after the lesson.
Further, students will be asked to identify the concept of instruction related to a given gesture in order to determine the extent to which students attend to teacher gesturing.
Teachers and teacher educators can thus learn more about which gestures might draw students' attention, which concepts might benefit from carefully designed gestural communication, and how gestures shape students' understanding of these concepts.
Sinclair, N. and Gol Tabaghi, S. (2010). Drawing space: Mathematicians' kinetic conceptions of eigenvectors. Education Studies in Mathematics, 74(3), 223-240.
Sinclair, N. (2010). Knowing more than we can tell. In B. Sriraman & L. English (Eds.). Theories of Mathematics Education: Seeking New Frontiers, (pp. 591-608). Berlin: Springer-Verlag.
Allan, D. & Sinclair, N. (2012). Students' mimicry of intentional teacher gestures. Proceedings of PME-NA.