Comparing Calculus Communication across Static and Dynamic Environments Using a Multimodal Approach

Abstract

In this article, a thinking-as-communicating approach is used to analyse calculus students’ thinking in two environments. The first is a ‘static’ environment in the sense of static visual representations, such as those found in textbook diagrams, while the second is a dynamic environment as exploited by the use of dynamic geometry environments (DGEs). The purpose of the article is to compare calculus students’ communication as it is facilitated by each of these two environments, and to explore the role of paper- and digital-mediated representations for positioning certain ways of thinking about calculus. The analysis provides evidence that the participants employed different modes of communication – utterances, gestures and touchscreen-dragging – and they communicated about fundamental calculus ideas differently when prompted by different types of representations. The study presents implications for teaching dynamic aspects of functions and calculus, and argues for a multimodal view of communication to capture the use of gestures and dragging for communicating dynamic and temporal mathematical relationships.