I’ve been reading a brilliant Master’s thesis by Chloe Grace Fogarty-Bourget (https://www.researchgate.net/profile/Chloe_Fogarty-Bourget) on gesture and response elicitation in teaching mathematics. She’s part of a very exciting research project studying “Chalk Talk” as a genre. https://www.researchgate.net/project/Chalk-talk-International-Genre-of-Teaching-University-Mathematics
Theories of Legitimate Peripheral Participation (LPP) and situated learning (e.g., Lave, 1991; Lave & Wenger, 1991; Wenger, 1998) are based on the view that learning is a social process comprised of an individual being an active participant in the practices of social communities (Wenger, 1998).
The taxonomy of gestures proposed by McNeill (1992, McNeill & Levy, 1982) is now used as the base for most work concerned with the role gestures play in educational issues (e.g., Goldin-Meadow, Kim, & Singer, 1999; Gerofsky, 2010; Kelly, Barr, Church, & Lynch, 1999). In his work, McNeill (2005) suggests that there are four basic types of gestures. This quartet of gestures includes beats (up and down, back and forth ‘flicks’ of the hand which commonly correspond with rhythm of speech), deictic gestures (pointing), iconic gestures, and metaphoric gestures . The majority of research on the role of gestures in mathematics cognition places emphasis largely on the illustrating roles of iconic, metaphoric, and deictic gesturing and their role in understanding abstract concepts (e.g., Alibali & Nathan, 2012; Arzarello & Edwards, 2005; Roth, 2001; Roth & Lawless, 2002). This study, however, focuses on non-pictorial hand movements which Bavelas and colleagues have named ‘interactive gestures’, which generally consist of movements of the fingers and palms towards the addressee (Bavelas, Chovil, Coates, & Roe, 1995; Bavelas, Hagen, & Lane, 1989; Bavelas, Chovil, Lawrie, & Wade, 1992).