Introduction: beyond words

Abstract

In Plato's famous dialogue Phaedo, Simmias is asked to determine who, amongst all sorts of men, is able to attain true knowledge. Is it not he, Socrates asks, who pursues the truth by applying his pure and unadulterated thought to the pure and unadulterated object, cutting himself off as much as possible from his eyes and ears and virtually all the rest of his body, as an impediment which by its presence prevents the soul from attaining to truth and clear thinking? (Plato, 1961, 65e-66a, p. 48) He then continues: "we are in fact convinced that if we are ever to have pure knowledge of anything, we must get rid of the body and contemplate things by themselves with the soul by itself" (Plato, 1961, 66b-67b, p. 49). In tune with Plato's ideas, Descartes maintained that the objects of the external world are known "by the intellect alone," for things "are not perceived because they are seen and touched, but only because they are rightly comprehended by the mind" (Descartes, 1651, II.16).The belief in a dualism that separates the mind from the body has had a strong influence on both mathematics and mathematics education for some time. The purpose of this Special Issue is not only to bring the body fully into our attempts to understand mathematical thinking but also to explore the range of specific ways that embodiment is enacted in mathematical situations. We will examine the construction of mathematical meaning from the perspective of multimodality, that is, taking into account the range of cognitive, physical, and perceptual resources that people utilize when working with mathematical ideas. These resources or modalities include both oral and written symbolic communication Educ Stud Math (2009) 70:91-95

The role of gestures in making connections between space and shape aspects and their verbal representations in the early years: findings from a case study

“…It involves the use of speech, symbols, drawings, gestures, and actions with cultural artifacts such as signs and objects. This multimodal approach of examining mathematical thinking has been adopted by a number of researchers in the past few years (e.g., Arzarello et al 2009;Radford et al 2009) and is in agreement with the theory of embodied cognition which considers bodily experiences as the basis of mathematical understanding and thinking (Nunez et al 1999). According to this latter theoretical position, the body serves as a source and a reference point for building up mathematical concepts (Kim et al 2010).…”

“…The present study took place within the theoretical frameworks of Duval's (2006) semiotic approach and the multimodal approach Radford et al 2009) to learning mathematics. Furthermore, the study built on research on gestures (McNeill 1992).…”

The coherence of enactivism and mathematics education research: A case study

“…No reference is made to the work of Varela, except indirectly through references to publications of Edwards and Núñez. A third thread focusses on the use of gestures in mathematics education. This thread can be represented by a special issue of the journal Educational Studies in Mathematics, (Radford, Edwards & Arzarello 2009) in which embodied mathematics is used in combination with semiotics to research the role of gestures in mathematical thinking and communication. In this work Varela's ideas play a limited role, acting mainly as a reference for the concept of embodied cognition.…”

The relationality in/of teacher–student communication

“…The semiotic turn we observe in the study of classroom communication-conceptualized as the active creation and use of signs from which mathematical significations 3 emerge (e.g., Radford 2011)-takes first steps in that direction. Challenging the theoretical separation of language and mathematics in use (Ongstad 2006), an awareness of how teachers and students live in a world of "signs" highlights the wide variety of semiotic resources used in the production of dynamical, embodied, enacted mathematical ideas or ways of being-in-the-know (Radford et al 2009). …”