Making Space: A Comparison of Mathematical Work in School and Professional Design Practices

Abstract

Research accounts of mathematical and scientific competence play a central role in ongoing efforts to reorganize education. At the same time, new technologies change the character of work in settings where these competencies are learned and used. Two contemporary research programs—(1) cognitive science studies of expert versus novice skill and (2) interactional studies of scientific and technical practice—produce sharply diverging accounts of what competence is and how it develops. Cognitive science has been broadly accepted as a template for educational change, while relevant interactional perspectives have had little impact. We propose a synthetic approach that draws on both programs, illustrated with a comparative study of mathematical practices in design work. Starting with scenes in which groups of designers collaborate to make space for others, we restore material and social aspects of their work settings in an exploration of discipline-specific forms of competence. Our continuing project is to reassemble competence in terms of: (a) people's local representational practices, (b) their trajectories of participation within and across institutional settings, and (c) their capacity for managing social relations of accountability. Experts' schemata contain a great deal of procedural knowledge, with explicit conditions for applicability. Novices' schemata may be characterized as containing sufficiently elaborate declarative knowledge about the physical configurations of a potential problem, but lacking abstracted solution methods. (Chi, Feltovich, and Glaser, 1981:151). Rule 7. Before attributing any special quality to the mind or to the method of people, let us examine first the many ways through which inscriptions are gathered, combined, tied together and sent back. Only if there is something unexplained once the networks have been studied shall we start to speak of cognitive factors. (Latour, 1987:258).

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