Abstract
This paper reports from a case study which explores kindergarten children’s mathematical abstraction in a teaching–learning activity about reflection symmetry. From a dialectical perspective, abstraction is here conceived as a process, as a genuine part of human activity, where the learner establishes “a point of view from which the concrete can be seen as meaningfully related” (van Oers & Poland Mathematics Education Research Journal, 19(2), 10–22, 2007, p. 13–14). A cultural-historical semiotic perspective to embodiment is used to explore the characteristics of kindergarten children’s mathematical abstraction. In the selected segment, two 5-year-old boys explore the concept of reflection symmetry using a doll pram. In the activity, the two boys first point to concrete features of the sensory manifold, then one of the boys’ awareness gradually moves to the imagined and finally to grasping a general and establishing a new point of view. The findings illustrate the essential role of gestures, bodily actions, and rhythm, in conjunction with spoken words, in the two boys’ gradual process of grasping a general. The study advances our knowledge about the nature of mathematical abstraction and challenges the traditional view on abstraction as a sort of decontextualised higher order thinking. This study argues that abstraction is not a matter of going from the concrete to the abstract, rather it is an emergent and context-bound process, as a genuine part of children’s concrete embodied activities.
Highlights
The significance of the body in the development of human cognition has gained increasing focus in diverse fields of psychology and raised the prominence given to the role of the body in the formation of concepts, including mathematical concepts
The research question formulated to guide this study is: What characterises the process of grasping a general? The question is applied to a case where two boys, John and Elias,1 together with their kindergarten teacher (KT), explore the concept of reflection symmetry
The segment examined in this study is selected from a whole-group session where one kindergarten teacher (KT) and a group of six 5-year-old children engage in a mathematical pre-school activity2 about reflection symmetry
Summary
The significance of the body in the development of human cognition has gained increasing focus in diverse fields of psychology and raised the prominence given to the role of the body in the formation of concepts, including mathematical concepts. Except for, perhaps, the rather moderate perspective by Núñez et al (1999), the other, more radical, approaches to embodiment aim to erase the body–mind dualism that has been prominent in cognitive psychology in the past and the long-standing assumption that thinking is a purely mental activity, immaterial and independent of the body. As a consequence of the increased focus on embodiment, the role of gestures in and for thinking has 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). It is necessary to further scrutinise the roles played by gestures, artefacts, and other bodily means in children’s mathematical thinking and in the teaching–learning of mathematics
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