Laurie D. Edwards has written an article that was recently published in Educational Studies in Mathematics. The article is entitled Gestures and conceptual integration in mathematical talk. Here is the abstract:

Spontaneous gesture produced in conjunction with speech is considered as both a source of data about mathematical thinking, and as an integral modality in communication and cognition. The analysis draws on a corpus of more than 200 gestures collected during 3 h of interviews with prospective elementary school teachers on the topic of fractions. The analysis examines how gestures express meaning, utilizing the framework of cognitive linguistics to argue that gestures are both composed of, and provide inputs to, conceptual blends for mathematical ideas, and a standard typology drawn from gesture studies is extended to address the function of gestures within mathematics more appropriately.A key idea in the article is that mathematics is seen as "an embodied, socially constructed human product", and gestures therefore might provide a relevant contribution to the mathematical thinking and communication. Edwards provides a nice explanation for the role of research on gestures:

(...) gesture constitutes a particular modality of embodied cognition, and, along with oral speech, written inscriptions, drawings and graphing, it can serve as a window on how learners think and talk about mathematics.The article provides a good overview of the theoretical framework for this area of research, and the study itself is also interesting. The participants (all women) were twelve volunteers from a course for prospective elementary school teachers, and the course was taught by Edwards herself. The participants were interviewed in pair, and the interview sessions were videotaped. The gestures that were caught on videotape were classified by McNeill's scheme.

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