Abstract

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Symmetry: Culture and Science
Volume 35, Number 4, pages 503-517 (2024)
https://doi.org/10.26830/symmetry_2024_4_503

DANCING SYMMETRIES – UNVEILING PATTERNS IN COUPLE DANCES

Veronica Albanese^1*, Martín Eduardo Herrera-Janques²

¹ Departamento de Didáctica de la Matemática, Universidad de Granada, Calle Santander 1, Melilla, 52005, Spain.
Email: vealbanese@ugr.es
Web: https://didacticamatematica.ugr.es/informacion/directorio-personal/veronica-albanese
ORCID: 0000-0002-3176-2468

² Agrupación Melitango, Calle Santander 2, Melilla, 52005, Spain.
Email: martinhjanques@gmail.com
Web: https://melitango9.webnode.es

^* corresponding author

Abstract: From an ethnomathematical perspective, a dialogue of mutual interrogation is proposed to describe the relation between the mathematical concept of symmetry and displacement movements performed in some couple dances: chacarera, swing, salsa, and tango. A rotational symmetry arises in the analysis of the figure of the chacarera, while a specular symmetry is described in some step structures of swing and salsa. The case of tango makes it necessary to define a new pattern based on translated translations. Some connections between the type of symmetry and the type of link in the couple, the management of the space on the dance floor, and the origins of each dance are determined. This research provides insights for future educational proposals that weave an embodiment approach with a focus on dynamic geometry.

References:
Abrahamson, D., Nathan, M. J., Williams-Pierce, C., Walkington, C., Ottmar, E. R., Soto, H., and Alibali, M. W. (2020) The Future of Embodied Design for Mathematics Teaching and Learning. Frontiers in Education, 5(article 147), 1–29. https://doi.org/10.3389/feduc.2020.00147

Adam, A., Alangui, W. V., and Barton, B. (2010) Lights and Questions: Using Mutual Interrogation. For the Learning of Mathematics, 30(3), 10–16. https://doi.org/10.2307/41319532

Albanese, V. (2016) La danza del malambo y las matemáticas [Malambo dance and mathematics]. In C. Cabellero, J. A. Meneses, and M. A. Moreira (Eds.), VII Encuentro Internacional Sobre Aprendizaje Significativo V Encuentro Iberoamericano sobre Investigación en Enseñanza de las Ciencias (pp. 959–964). Universidad de Burgos.

Albanese, V., Adamuz-Povedano, N., and Bracho-López, R. (2017) The Evolution of Ethnomathematics: Two Theoretical Views and Two Approaches to Education. In M. Rosa, L. Shirley, M. E. Gavarrete, and W. V. Alangui (Eds.), Ethnomathematics and its Diverse Approaches for Mathematics Education (pp. 307–328). Springer. https://doi.org/10.1007/978-3-319-59220-6

Albanese, V., and Perales, F. J. (2014) Microproyectos Etnomatemáticos sobre Danzas Folclóricas: Aprender Matemática desde el Contexto con maestros en formación. Profesorado. Revista de Currículum y Formación de Profesorado, 18(3), 457–472.

Belcastro, S. M., and Schaffer, K. (2011) Dancing Mathematics and the Mathematics of Dance. Math Horizons, 18(3), 16–20. https://doi.org/10.4169/194762111x12954578042939

Berruti, A. D. (1921) El trenzador sudamericano: Método práctico para la enseñanza del arte trenzado en general. Tall. Gráf. Argentinos de L.J. Rossi.

Chan, K. K., and Leung, S. W. (2014) Dynamic geometry software improves mathematical achievement: Systematic review and meta-analysis. Journal of Educational Computing Research, 51(3), 311–325. https://doi.org/10.2190/EC.51.3.c

D’Ambrosio, U. (2006) Ethnomathematics: Link between traditions and modernity. Sense Publishers.

Di Paola, B., Sortino, C., and Ferreri, M. (2008) Il tango e la matematica: muoversi all’interno delle figure [Tango and mathematics: moving inside the figures]. Quaderni Di Ricerca in Didattica, 18, 153–162.

Drake-Boyt, E. (2011) Latin dance. Bloomsbury Publishing USA.

Knijnik, G. (2012) Differentially positioned language games: ethnomathematics from a philosophical perspective. Educational Studies in Mathematics, 80(1–2), 87–100.

Meaney, T., Trinick, T., and Allen, P. (2021) Ethnomathematics in Education: The Need for Cultural Symmetry. In M. Danesi (Ed.), Handbook of Cognitive Mathematics (p. 1-29). Springer. https://doi.org/10.1007/978-3-030-44982-7_4-1

Nasiakou, L., Lehto, S., Goranova, S., Osborne, K., and Fenyvesi, K. (2019). Exploring Rotational Symmetries and Triangles through Dance and Body Movement: Maths in Motion. Bridges 2019 Conference Proceedings, 621–628.

Núñez, R. E., Edwards, L. D., and Matos, J. F. (1999). Embodied cognition as grounding for situatedness and context in mathematics education. Educational Studies in Mathematics, 39, 45–65. https://doi.org/10.1023/a:1003759711966

Parra-Sánchez, A. (2017). Ethnomathematical Barters. In H. Straehler-Pohl, N. Bohlmaer, and A. Pais (Eds.), The Disorder of Mathematics Education (pp. 89–106). Springer, Cham.

Sardella, O. (2004). La geometría en las danzas folklóricas argentinas. Acta Latinoamericana de Matemática Educativa, 801–806.

Schaffer, K. (2014). Dancing Deformations. Bridges Conference Proceedings, 253–260. http://t.archive.bridgesmathart.org/2014/bridges2014-253.pdf

Schaffer, K. (2019). Three-Dimensional Symmetries in Dance and Other Movement Arts. Bridges Conference Proceedings, 247–254.

Schaffer, K., Stern, E., and Kim, S. (2001). Math Dance. MoveSpeakSpin.

Stevens, T., and Stevens, E. (2011). Swing dancing. Bloomsbury Publishing USA.