Music-driven geometric and topologic intuition: a case study with the Klein bottle

Abstract

The comprehension of mathematical notions can profit from the personal background of a population of students, drawing upon their former knowledge in another field. In particular, the embodiment of mathematics provides us with a bridge to transfer competencies from music to intuitive understanding of non-trivial geometries and topologies. In this study, we analyse an experiment in which music composition students are introduced to the Klein bottle for the first time. Through the Ontological and Semiotic Approach (OSA), a conceptual framework in mathematics education, we evaluate the evolution from an initial intuition of the Klein bottle to a formal understanding of the object via musical renditions and verbal presentations to both neophyte and specialist audiences in mathematics.

Keywords:

• Embodiment
• gesture
• semiotic function
• dialogic–collaborative instructional processes
• STEAM
• geometry

2010 Mathematics Subject Classifications:

• 00A35
• 97M80

Disclosure statement

No potential conflict of interest was reported by the authors.

Supplemental online material

Supplemental online material for this article can be accessed at http://dx.doi.org/10.1080/17459737.2024.2344095http://dx.doi.org/10.1080/17459737.2024.2344095