Exploring the Contribution of Gestures to Mathematical Argumentation Processes from a Semiotic Perspective

Abstract

A multimodal perspective on mathematics thinking processes is addressed through the semiotic bundle lens and considering a wide notion of sign drawing from Vygotsky's works. Within this frame, the paper focuses on the role of gestures in their interaction with the other signs (speech, in particular) and investigates the support they can provide to mathematical argumentation processes. A case study in primary school in the context of strategic interaction games provides data to show that gestures can support students in developing argumentations that depart from empirical stances and shift to a hypothetical plane in which generality is addressed. In this regard, by combining synchronic and diachronic analysis of the semiotic bundle, specific features of gestures are pointed out and discussed: the semiotic contraction, the condensing character of gestures, and the use of gesture space in a metaphorical sense.Keywords Argumentation Á Gestures Á Multimodality Á Semiotic contraction Semiotic bundle IntroductionAt the turn of the millennium, in 2000, the provocative essay Where Mathematics Comes From by George Lakoff and Rafael Núñez pointed out the crucial role of perceptual and bodily aspects on the formation of abstract concepts, including mathematical concepts (Lakoff and Núñez 2000). The new stance emphasized sensory and motor functions, as well as their importance for successful interaction with the environment. Criticizing the platonic idealism and the Cartesian mindbody dualism, Lakoff and Núñez advocated that all kinds of ideas, including the most sophisticated mathematical ideas, are founded on our bodily experiences and develop through cognitive metaphorical mechanisms. More recently, embodied stances seem to receive a certain confirmation by neuroscientific results on "mirror neurons" and "multimodal neurons," which are neurons firing when subjects performs actions, when they observe somebody else doing the same action, and when they imagine it (Gallese and Lakoff 2005). On the basis of these results, Gallese and Lakoff (2005) provide a new theoretical account on how the brain works, according to which "action and perception are integrated at the level of the sensory-motor system and not via higher association areas" (p. 459).In particular, such an integration would appear to be crucial not only for motor control, but also for planning actions, an activity typical of what is generally understood as "thinking."The terms multimodal and multimodality come therefore to indicate a feature of human cognition opposed to "modularity." On the other hand, in the communication field the term multimodal is used with reference to multiple modalities that we have to communicate and express meanings to our interlocutors: words, sounds, images, and so on (Kress 2004). These communicative affordances have been acquiring increasing attention due the diffusion of new technological affordances, which are constantly developing new possibilities of interaction with them through our body.In this paper, in line with Radf...

Gestures and the Spoken Language: A Crucial Semiotic and Symbiotic Relationship in Multilingual Mathematics Classes

“…In the teaching of mathematics, teachers routinely and regularly produce gestures along with their speech which, I argue have the potential to influence pupils' learning. Research has shown that the combination of teachers' speech and gesture often provides greater insight into learners' mathematical knowledge and understanding than either words or gestures alone (McNeill, 1992;Sabena, 2018). This access to knowledge and understanding that gestures may enable, is necessary in multilingual classes, where the LOLT is neither the teacher's nor the learners' first.…”

“…McNeill (1992) posited that, "gestures are an integral part of language as much as are words, phrases and sentences" (p. 2). My focus on teachers' gestures is informed by the large body of research showing that gestures contribute to communication in a wide range of settings (Kendon, 2004;Sabena, 2018). The use of visualization processes such as gestures in teaching mathematics is an important component to help learners to build their own adequate internal representations of mathematical ideas.…”

“…Several studies have pointed towards the importance of gestures' ability to communicate the visual appearance of mathematical objects, such as shapes and slopes on line graphs (Sabena, 2018;Yoon, Thomas, & Dreyfus, 2011). Gestures are hence crucial for communicating and constructing mathematical understanding (Yoon et al, 2011) especially in situations where learners are not proficient in the LOLT.…”

Insegnare matematica con il teatro: apprendimento embodied ed emozioni

“…A partire poi da ricerche riguardanti il cervello e il funzionamento neuronale (Gallese & Lakoff, 2005) e gli aspetti semiotici della comunicazione (Kress, 2000) si è affermato in didattica della matematica il concetto di "multimodalità" inteso come «[...] la coesistenza e l'importanza di diverse modalità o risorse nei processi di apprendimento-insegnamento [...]» come parole, gesti, simboli, posizioni del corpo, toni della voce (Sabena et al, 2019, p. 19). In particolare, numerosi studi si sono soffermati sul ruolo dei gesti, mostrando il ruolo preminente di questi ultimi e dell'esperienza senso-motoria nella costruzione e condivisione di significati, nel dispiegarsi dell'argomentazione e della discussione matematica e nello sviluppo di nuove conoscenze (Arzarello et al, 2009;Arzarello et al, 2005;Radford, 2014;Sabena, 2018). Un altro filone di ricerca si è invece concentrato sul ruolo del corpo nella sua interezza e del movimento nell'emergere dei concetti matematici e nel favorire la loro comprensione: ne sono un esempio gli studi di Susan Gerofsky (2011Gerofsky ( , 2016Gerofsky ( , 2018, che, con il progetto Graph & Gestures, ha messo in luce la maggiore capacità intuitiva degli studenti che utilizzano movimenti a largo spettro, coinvolgendo…”

Abstraction and embodiment: exploring the process of grasping a general

“…In the more radical approaches, mathematics is not considered a body of transcendental ideas, but as part of concrete human activity, dependent on bodily and sensuous experience. As a consequence of the increased focus on embodiment, the role of gestures in and for thinking has also gained attention in educational research and has been found important in the formation of mathematical concepts, for example, in teaching-learning about spatial concepts (Elia & Evangelou, 2014), numerical relations (Sabena, 2018), and algebraic structures (Radford, 2009). Despite the increasing focus on the role of the body in mathematics thinking and learning, and the acceptance that young children use artefacts and gestures while solving mathematical tasks, the literature is still sparse on the more precise role of the body in young children's mathematical thinking.…”