In our research on gestures in mathematical understanding, we start by assuming that gestures, along with other body aspects (e.g., gazes), are an important component of emotional and cognitive manifestations and an inseparable component of speech discourse, as research in psychological and related domains have shown (e.g. Goldin-Meadow, 2003; McNeill, 1992, 2005). From our own observation in the classrooms and from recent literature, we have become increasingly convinced that gestures play important roles in the mathematics classroom when: students solve problems (Radford, 2010), students and teachers interact (Arzarello, Paola, Robutti, & Sabena, 2009), students explain a mathematical concept (Edwards, 2009), or the teacher lectures (Pozzer-Ardenghi & Roth, 2008). In all such cases gestures are considered not as isolated variables but rather as part of the multi-semiotic arsenal at the students’ disposal to bridge the gap between everyday experience and formal mathematics. Keeping these premises as our starting points, in this chapter we focus on the gesture-speech relationship and study their contribution in structuring a mathematical argumentation. Our goal is to show how gestures can contribute not only to the semantic content of mathematical ideas but also to the logical structure that organizes them in mathematical arguments. We will base our analysis on the results and methodologies from three domains, which are presented in the next section: • Gesture studies, mainly referring to McNeill’s frame on the gesture-language relationship and the notion of catchment; • the analytic-linguistic frame given by Chomsky; and • the prosodic element of intonation of a phrase. We then substantiate our claim through an episode from a case study related to a 5th grade problem solving activity, involving 10-year-old Italian students. The episode will be analyzed in detail, by integrating typical methodologies of gesture studies with the analytic-linguistic and the prosodic ones. A final discussion will reflect on the implications of this research.
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