Music as Embodied Mathematics: A Study of a Mutually Informing Affinity |
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Authors: | Jeanne Bamberger and Andrea diSessa |
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Institution: | (1) Music and Theater Arts, Buildin t 4-246, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA 02139, USA;(2) University of California, Berkeley, California, USA |
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Abstract: | The argument examined in this paper is that music – when approached through making and responding to coherent musical structures,facilitated
by multiple, intuitively accessible representations – can become a learning context in which basic mathematical ideas can
be elicited and perceived as relevant and important. Students' inquiry into the bases for their perceptions of musical coherence
provides a path into the mathematics of ratio,proportion, fractions, and common multiples. Ina similar manner, we conjecture
that other topics in mathematics – patterns of change,transformations and invariants – might also expose, illuminate and account
for more general organizing structures in music. Drawing on experience with 11–12 year old students working in a software
music/math environment, we illustrate the role of multiple representations, multi-media, and the use of multiple sensory modalities
in eliciting and developing students' initially implicit knowledge of music and its inherent mathematics.
This revised version was published online in July 2006 with corrections to the Cover Date. |
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Keywords: | implicit knowledge mathematics in music multiple representations musical cognition |
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