Language, gestures and touchscreen dragging in school calculus: Bilinguals' linguistic and non-linguistic communication

This research study concerns patterns of high school bilingual learners’ communication when they interact with touchscreen-based dynamic geometry environments (DGEs) during calculus discussion and exploration. Specifically, three research questions are proposed for the study, addressing respectively: (1) the interplay between linguistic and non-linguistic communication, (2) the mathematical competence demonstrated in the activity and (3) the role of the technology for facilitating calculus thinking. Using aparticipationist lens and the theoretical framing of thinking-as-communicating, I provide qualitative video analyses of six pairs of high school bilingual calculus students’ communication by focussing on their word-use, gestures, and touchscreen-dragging actions with DGEs during their mathematical activities. The goal of this study is to identify bilingual learners’ competence during pair-work on mathematical activities with touchscreen-based DGEs.In Part I of the study, I compared two pairs of participants’ thinking in two different types of visual mediators: “static” as those found in textbook diagrams, and “dynamic” as exploited by the use of DGEs. The analysis provides evidence that the participants utilised different modes—utterances, gestures and touchscreen-dragging—of communication. In particular, touchscreen-dragging emerged as a form of gestures for communicating dynamic and temporal calculus relationships. In addition, the studentscommunicated about the fundamental calculus ideas differently when prompted by different types of visual mediators.In Part II of the study, I provide analyses of communication involving four pairs of participants while exploring the area-accumulating functions with touchscreen-based DGEs. Findings resonate with Part I: the students relied on gestures and touchscreen-dragging as non-linguistic features of the mathematical discourse to communicate dynamic aspects of calculus. Moreover, by adopting a non-deficit model and examining the interplay between word-use, gestures and touchscreen-dragging with DGEs, it waspossible to identify bilingual learners’ competence in mathematical communication. This study underscores the importance of considering bilingual learners’ non-linguistic forms of communication for understanding their mathematical thinking. It also presents implications for teaching dynamic aspects of functions and calculus, by arguing for amultimodal view of communication to capture the use of gestures and touchscreen-dragging in mathematical communication. Furthermore, it allowed me to identify new forms of communication mobilised in dynamic, touchscreen environments.