Cognitive functions of gestures in mathematical working processes

Abstract

Although gestures and their role in teaching and learning mathematics gain increasingly interest in mathematics education research, most research focuses on the social aspects of gesture use, like their role in knowledge construction in social interaction, the representational side of students' gestures, or teachers' instructional gestures. Little is known about the cognitive functions gestures might fulfil in mathematical learning. To understand better how gestures can contribute to cognitive processes when learning math, we adapt a framework from psychology which distinguishes the four cognitive functions of activating, manipulating, packaging and exploring. To explore the potential of this model for understanding the role of gestures in cognitive processes in mathematical contexts better, we analyze two existing data sets in which university students think aloud while working by themselves in the content area of trigonometry, once with worked examples and once with a task on a special class of trigonometric functions. In our analyses, certain cognitive functions appear as related to certain typical mathematical situations which will be illustrated by means of specific cases concerning the validation of hypotheses, situations of functional thinking and when using specific representations.