On the role of gestures for the descriptive analysis of "Grundvorstellungen"

a case of linear functions

Christina M. Krause

Alexander Salle

pp. 293-313

in: Norma Presmeg, Luis Radford, Wolff-Michael Roth, Gert Kadunz (eds), Signs of signification, Berlin, Springer, 2018

Abstract

In a German tradition, the concept of "Grundvorstellungen" (GV) concerns mental models that carry the meaning of mathematical concepts or procedures. While research on these GVs is mostly based on the analysis of verbal utterances or written products, we turn towards an embodied approach and investigate the question of how gestures can take part in revealing the activation of students' GVs, focusing on the specific case of linear functions. In the presented empirical study, we found that gestures are used not only to specify deictic terms, but that they can also reveal a link between a mathematical idea and its non-mathematical grounding as it becomes explicit in speech. How gestures might contribute not only to the descriptive analysis of GVs, but also to the mathematical learning process, is discussed against the background of re-analyzing selected results within two different semiotic approaches.