Abstract Thinking in Space and Time: Using Gesture to Learn Math

ABSTRACT Mathematical concepts and words for objects are generally thought of as abstract and disembodied. In this theoretical paper, I review a line of research demonstrating that hand gestures are important for mathematical thinking. Gestures are spontaneously produced in conversations about mathematical concepts, these gestures can influence speakers' processing, and gestures are implicated in changing children's and adults' mathematical thinking. This work offers evidence that mathematical representations may not be as abstract and disembodied as they seem, but rather may be supported by embodied representations. This example suggests that the body, and its affordance for action in the world, is important for conceptual development. KEYWORDS: gesture, mathematics, learning, embodied cognition, cognitive development EMBODIED THINKING Conceptual development is typically described as a progression towards increasingly abstract and disembodied representations. Mathematics provides a salient example. Mathematical concepts are generally thought of as abstract and disembodied, which can be seen in their wide-ranging applicability to a variety of situations, and in their inability to be observed in the real world. For example, a single function can represent relationships from a variety of possible real world situations, which can cause learners to have difficulty appropriately mapping between real world situations and their symbolic mathematical representations (Coquin-Viennot & Moreau, 2007; Mattarella-Micke & S. L. Beilock, 2010). I have been exploring the role of hand gestures in the development and communication of mathematical thinking. Hand gestures are produced by speakers of all languages during communication. These gestures generally provide a perspective on cognitive processes that is complementary to what is revealed in spoken language. In one line of work, I have been exploring the question of what hand gestures can reveal about mathematical thinking. In this theoretical paper, I review this work with an eye towards exploring how an embodied perspective can inform our interpretation of these findings. I seek to answer the question of whether or not mathematical reasoning can also be described as situated and embodied rather than as abstract and amodal. If gestures reflect embodied thinking, and if gestures are important in mathematical thinking, this would suggest that mathematical thinking is also embodied. This line of research is influenced by a now substantial body of data showing that language, as well as other cases of putatively abstract reasoning, may be embodied to a much greater extent than previously appreciated. I will first briefly discuss some of the evidence for embodied cognition in general, focusing on language and motor processes as these are most relevant for thinking about gesture as an embodied representation. I will then discuss evidence that hand gestures are functionally involved in mathematical thinking in both children and adults. Finally, I will address some possible criticisms and data that are difficult to explain from this perspective. Before reviewing data on the role of the body in language and communication, it is useful to make clear what I mean by the terms. Situated cognition reflects the notion that the real-world environment where processing takes place affects ongoing processing, because cognition involves systems supporting perception and action in the world (Wilson, 2002). Embodied cognition has been used to reflect a variety of claims about cognition (Wilson, 2002). Many claims about embodied cognition fit under the definition of situated cognition proposed here. For example, the notions that cognition can be offloaded onto the environment, and that the environment is part of the cognitive system (Wilson, 2002) are claims about cognition that do not directly reference the body in any manner but do reference the particular time and place where cognition is happening as being important for cognition. …