It is not the hand that writes, but the thought: Gestures of prospective mathematics teachers

In this text, four examples of gestures produced and arising from an investigation with mathematics undergraduate students are presented. Gesticulations were used to convey the concepts of point, line, and plane in conversations about the spatial geometry of position. [Objective] Thus, we aim to share an analysis of the gestures produced by prospective mathematics teachers to indicate the primitive entities of geometry. [Methodology] The data come from a research study involving students aged between 19 and 23 years as participants at a public university in the state of São Paulo, Brazil. This research is qualitative. The analysis of the gestures, as well as their possible meanings, was conducted through an attentive and detailed examination of the video recordings of the two meetings held for each of the six pairs of undergraduates, facilitated by teaching experiments. [Results] As a result, we noticed that the same geometric notion was communicated through identical gestures at different times. It was also found, in line with the assumed theoretical framework, that gestures are an integral part of the discourse. Finally, we verified the presence of three gestures produced sequentially, one after the other, to indicate notions of point, line, and plane. [Conclusions] These considerations are relevant and show the power of gestures in the sense that they can provide clues to how students are expressing and/or learning concepts of greater complexity.