TAILIEUCHUNG - The Roles of the Aesthetic in Mathematical Inquiry
One topic of special interest is the influence of motor expertise on action observation. Greater activation in premotor cortex, pari- etal areas, which have a somatotopical organization, and superior temporal sulcus, involved in biological motion perception, has been observed when expert dancers view movements correspond- ing to their own style compared to the other style (Calvo-Merino, Glaser, Grèzes, Passingham, & Haggard, 2005; Cross, Hamilton, & Grafton, 2006; Orgs, Dombrowski, Heil, & Jansen-Osmann, 2008). Calvo-Merino, Ehrenberg, Leung, and Haggard (2010) showed that dance expertise enhances mainly configural, rather than featural, processing of dance movements | MATHEMATICAL THINKING AND LEARNING 6 3 261-284 Copyright 2004 Lawrence Erlbaum Associates Inc. The Roles of the Aesthetic in Mathematical Inquiry Nathalie Sinclair Department of Mathematics Michigan State University Mathematicians have long claimed that the aesthetic plays a fundamental role in the development and appreciation of mathematical knowledge. To date however it has been unclear how the aesthetic might contribute to the teaching and learning of school mathematics. This is due in part to the fact that mathematicians aesthetic claims have been inadequately analyzed making it difficult for mathematics educators to discern any potentialpedagogicalbenefits. This article provides apragmatic analysis oftheroles of the aesthetic in mathematical inquiry. It then probes some of the beliefs and values that underlie mathematical aesthetic responses and reveals the important interplay between the aesthetic cognitive and affective processes involved in mathematical inquiry. The affective domain has received increased attention over the past decade as mathematics education researchers have identified its central role in the learning of mathematics. Mathematicians however who are primarily concerned with the doing of mathematics have tended to emphasize the importance of another related noncognitive domain the aesthetic. They have long claimed that the aesthetic plays a fundamental role in the development and appreciation of mathematics . Hardy 1940 Poincaré 1908 1956 . Yet their claims have received little attention outside the élite world of the professional mathematician and even less explanation or justification. This state of affairs might be inconsequential to the practices of the professional mathematician but it severely constrains the ability of mathematics educators to analyze the possibilities of promoting aesthetic engagement in student Requests for reprints should be sent to Nathalie Sinclair Department of Mathematics Michigan State University
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