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.
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Bamberger, J., diSessa, A. Music as Embodied Mathematics: A Study of a Mutually Informing Affinity. International Journal of Computers for Mathematical Learning 8, 123–160 (2003). https://doi.org/10.1023/B:IJCO.0000003872.84260.96
- implicit knowledge
- mathematics in music
- multiple representations
- musical cognition