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Tangible Math

Project Description

The following text is excerpted from the Tangible Math Project description. Download the full text and references with the links at the right.

Our understandings of what it is to be human—basic aspects of social life, thinking, learning, and productive activity—have historically been enmeshed with the development and use of new technologies. For example, over the history of scientific psychology (Genter & Grudin, 1985; Leary 1994) we have understood cognition by analogy to hydraulic systems, clockwork mechanisms, symbolic computation, dynamically configured networks (Thelen & Smith, 1994), or distributions across cultural and technical media (Hutchins, 1995). Our understandings of cognition and learning have also been shaped by the technologies researchers use to capture and analyze data (Danziger, 1990). The “linguistic turn” in the social sciences was largely made possible by audio recordings of human speech and conversation. Similarly, the recent growth of interest in multi-modal aspects of communication have been enabled by high quality video recording of human activity (e.g., Levine & Scollon, 2004), and claims for multi-modal mental simulation as the basis of cognitive processing have been advanced by new developments in brain imaging (e.g., Barsalou, in press; Gallese & Lakoff, 2005). In a parallel but (as yet) largely unexplored development, advances in location-aware technologies and spatial analysis are making it possible to study human activity and learning in natural settings and at larger spatial and temporal scales (Christensen, 2003; Miller, 2007). For example, wearable GPS devices can be used to capture personal space-time paths, and a growing suite of GIS software tools can be used to analyze path structures in relation to other spatially anchored data (e.g., the accessibility of cultural resources that provide children with learning opportunities).

Three of these recent developments—human communication as multi-modal interaction, human thinking as multi-modal simulation of sensory-motor activity, and embodied experience as following/producing pathways through social and cultural space—challenge a traditional view of human cognition and learning as information processing, in which the mind is a computational device designed to process a-modal symbolic structures that are separated from bodily experience in the world. But these new perspectives can also be difficult to reconcile or integrate, since they have arisen in research communities that are historically separate, or even embroiled in controversy over the nature of human cognition and learning. Finding a productive way forward is particularly important for new research in mathematics and science education, which is subject to recurring demands for the reform of traditional instruction (e.g., moving away from a didactic pedagogy of symbolic manipulation), yet has found little guidance from basic research on human cognition and learning in how to do this.

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