From cultural movement to structural equivalence: Modeling graph isomorphism through serampang dua belas dance

Rahmi Ramadhani; Nuraini Sri Bina; Suci Dahlya Narpila; Muhammad Rizky Mazaly; Rusmini Rusmini

doi:10.29408/jel.v12i2.34059

Authors

Rahmi Ramadhani Universitas Potensi Utama https://orcid.org/0000-0002-8049-7234
Nuraini Sri Bina Universitas Potensi Utama https://orcid.org/0000-0002-5019-2034
Suci Dahlya Narpila Universitas Islam Negeri Sumatera Utara https://orcid.org/0000-0002-5273-2663
Muhammad Rizky Mazaly Universitas Potensi Utama https://orcid.org/0000-0002-9401-2883
Rusmini Rusmini Universitas Potensi Utama https://orcid.org/0000-0002-5301-1438

DOI:

https://doi.org/10.29408/jel.v12i2.34059

Keywords:

directed graph modeling, embodied learning, ethnomathematics, graph isomorphism, structural equivalence

Abstract

This study addresses a limitation in ethnomathematics research, which often stops at identifying visual patterns, by examining how ethnomathematical modeling of traditional dance can illuminate graph isomorphism. Focusing on the Serampang Dua Belas dance of North Sumatra, the study employs a qualitative ethnographic approach, with data collected through performance observations, video documentation, interviews with cultural experts in Serdang Bedagai Regency, and a review of choreographic literature. Movement sequences were analyzed through data reduction, categorization of transition patterns, and reconstruction of spatial–temporal relations, then modeled as directed graphs using GeoGebra. Dancers’ positions were represented as vertices and transitions as directed edges, enabling formal analysis through adjacency matrices and bijective mappings to verify isomorphism. The findings reveal that although the variations differ visually, several segments exhibit structural equivalence across linear, cyclic, and loop-containing graphs. This study advances ethnomathematics toward formal structural verification grounded in graph theory and highlights its potential to support relational understanding in discrete mathematics learning.

Author Biographies

Rahmi Ramadhani, Universitas Potensi Utama

This study addresses a limitation in ethnomathematics research, which often stops at identifying visual patterns, by examining how ethnomathematical modeling of traditional dance can illuminate graph isomorphism. Focusing on the Serampang Dua Belas dance of North Sumatra, the study employs a qualitative ethnographic approach, with data collected through performance observations, video documentation, interviews with cultural experts in Serdang Bedagai Regency, and a review of choreographic literature. Movement sequences were analyzed through data reduction, categorization of transition patterns, and reconstruction of spatial–temporal relations, then modeled as directed graphs using GeoGebra. Dancers’ positions were represented as vertices and transitions as directed edges, enabling formal analysis through adjacency matrices and bijective mappings to verify isomorphism. The findings reveal that although the variations differ visually, several segments exhibit structural equivalence across linear, cyclic, and loop-containing graphs. This study advances ethnomathematics toward formal structural verification grounded in graph theory and highlights its potential to support relational understanding in discrete mathematics learning.

Nuraini Sri Bina, Universitas Potensi Utama

This study addresses a limitation in ethnomathematics research, which often stops at identifying visual patterns, by examining how ethnomathematical modeling of traditional dance can illuminate graph isomorphism. Focusing on the Serampang Dua Belas dance of North Sumatra, the study employs a qualitative ethnographic approach, with data collected through performance observations, video documentation, interviews with cultural experts in Serdang Bedagai Regency, and a review of choreographic literature. Movement sequences were analyzed through data reduction, categorization of transition patterns, and reconstruction of spatial–temporal relations, then modeled as directed graphs using GeoGebra. Dancers’ positions were represented as vertices and transitions as directed edges, enabling formal analysis through adjacency matrices and bijective mappings to verify isomorphism. The findings reveal that although the variations differ visually, several segments exhibit structural equivalence across linear, cyclic, and loop-containing graphs. This study advances ethnomathematics toward formal structural verification grounded in graph theory and highlights its potential to support relational understanding in discrete mathematics learning.

Suci Dahlya Narpila, Universitas Islam Negeri Sumatera Utara

This study addresses a limitation in ethnomathematics research, which often stops at identifying visual patterns, by examining how ethnomathematical modeling of traditional dance can illuminate graph isomorphism. Focusing on the Serampang Dua Belas dance of North Sumatra, the study employs a qualitative ethnographic approach, with data collected through performance observations, video documentation, interviews with cultural experts in Serdang Bedagai Regency, and a review of choreographic literature. Movement sequences were analyzed through data reduction, categorization of transition patterns, and reconstruction of spatial–temporal relations, then modeled as directed graphs using GeoGebra. Dancers’ positions were represented as vertices and transitions as directed edges, enabling formal analysis through adjacency matrices and bijective mappings to verify isomorphism. The findings reveal that although the variations differ visually, several segments exhibit structural equivalence across linear, cyclic, and loop-containing graphs. This study advances ethnomathematics toward formal structural verification grounded in graph theory and highlights its potential to support relational understanding in discrete mathematics learning.

Muhammad Rizky Mazaly, Universitas Potensi Utama

This study addresses a limitation in ethnomathematics research, which often stops at identifying visual patterns, by examining how ethnomathematical modeling of traditional dance can illuminate graph isomorphism. Focusing on the Serampang Dua Belas dance of North Sumatra, the study employs a qualitative ethnographic approach, with data collected through performance observations, video documentation, interviews with cultural experts in Serdang Bedagai Regency, and a review of choreographic literature. Movement sequences were analyzed through data reduction, categorization of transition patterns, and reconstruction of spatial–temporal relations, then modeled as directed graphs using GeoGebra. Dancers’ positions were represented as vertices and transitions as directed edges, enabling formal analysis through adjacency matrices and bijective mappings to verify isomorphism. The findings reveal that although the variations differ visually, several segments exhibit structural equivalence across linear, cyclic, and loop-containing graphs. This study advances ethnomathematics toward formal structural verification grounded in graph theory and highlights its potential to support relational understanding in discrete mathematics learning.

Rusmini Rusmini, Universitas Potensi Utama

This study addresses a limitation in ethnomathematics research, which often stops at identifying visual patterns, by examining how ethnomathematical modeling of traditional dance can illuminate graph isomorphism. Focusing on the Serampang Dua Belas dance of North Sumatra, the study employs a qualitative ethnographic approach, with data collected through performance observations, video documentation, interviews with cultural experts in Serdang Bedagai Regency, and a review of choreographic literature. Movement sequences were analyzed through data reduction, categorization of transition patterns, and reconstruction of spatial–temporal relations, then modeled as directed graphs using GeoGebra. Dancers’ positions were represented as vertices and transitions as directed edges, enabling formal analysis through adjacency matrices and bijective mappings to verify isomorphism. The findings reveal that although the variations differ visually, several segments exhibit structural equivalence across linear, cyclic, and loop-containing graphs. This study advances ethnomathematics toward formal structural verification grounded in graph theory and highlights its potential to support relational understanding in discrete mathematics learning.

References

Abrahamson, D., Nathan, M. J., Williams-Pierce, C., Walkington, C., Ottmar, E. R., Soto, H., & Alibali, M. W. (2020). The future of embodied design for mathematics teaching and learning. Frontiers in Education, 5. https://doi.org/10.3389/feduc.2020.00147

Bernales, M., & Powell, A. B. (2018). Decolonizing ethnomathematics. Ensino Em Re-Vista, 25(3), 565–587. https://doi.org/10.14393/ER-v25n3a2018-3

Bito, G. S., & Fredy, F. (2020). Ethnomathematics: Musical instrument in ja’i dances for culturally responsive teaching in elementary schools. PrimaryEdu: Journal of Primary Education, 4(2), 183–194. https://doi.org/10.22460/pej.v4i2.1853

Boonstra, K., Kool, M., Shvarts, A., & Drijvers, P. (2023). Theories and practical perspectives on fostering embodied abstraction in primary school geometry education. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1162681

Budinski, N., Joksimović, J., Vučićević, D., & Lavicza, Z. (2022). Case study of a mathematical dance performance “point has no parts.” European Journal of STEM Education, 7(1), 08. https://doi.org/10.20897/ejsteme/12617

Chatain, J., Gashaj, V., Muttappillil, B., Sumner, R. W., & Kapur, M. (2024). Designing for embodied sense-making of mathematics: Perspectives on directed and spontaneous bodily actions. Designing Interactive Systems Conference, 3318–3335. https://doi.org/10.1145/3643834.3661571

Demaine, E. D., Demaine, M. L., Taslakian, P., & Toussaint, G. T. (2007). Sand drawings and gaussian graphs. Journal of Mathematics and the Arts, 1(2), 125–132. https://doi.org/10.1080/17513470701413451

Dominikus, W. S., Madu, A., Blegur, I. K. S., & Jemamun, M. U. (2024). Ethnomathematics in caci dance of manggarai community and its integration in mathematics learning. Journal of Law and Sustainable Development, 12(2), e3035. https://doi.org/10.55908/sdgs.v12i2.3035

Endilina, E., Mariana, N., Rahaju, E. B., & Purwoko, B. (2025). Ethnomathematics in traditional Indonesian dance. Journal of Innovation and Research in Primary Education, 4(4), 2992–3001. https://doi.org/10.56916/jirpe.v4i4.1871

Faiziyah, N., Khoirunnisa, M., Azizah, N. N., Nurrois, M., Prayitno, H. J., Desvian, Rustamaji, & Warsito. (2021). Ethnomathematics: Mathematics in batik Solo. Journal of Physics: Conference Series, 1720, 12013. https://doi.org/10.1088/1742-6596/1720/1/012013

Fouze, A. Q., & Amit, M. (2019). Ethnomathematics and geometrical shapes in bedouin women’s traditional dress. Creative Education, 10(07), 1539–1560. https://doi.org/10.4236/ce.2019.107112

Fouze, A. Q., & Amit, M. (2021). Teaching feometry by integrating ethnomathematics of bedouin values. Creative Education, 12(02), 402–421. https://doi.org/10.4236/ce.2021.122029

Gazanofa, F. S., & Wahidin, W. (2023). Eksplorasi etnomatematika pada gerak tari piring [An exploration of ethnomathematics in the piring dance]. Jurnal Cendekia: Jurnal Pendidikan Matematika, 7(3), 3162–3173. https://doi.org/10.31004/cendekia.v7i3.2679

González, A., Gallego-Sánchez, I., Gavilán-Izquierdo, J. M., & Puertas, M. L. (2021). Characterizing levels of reasoning in graph theory. Eurasia Journal of Mathematics, Science and Technology Education, 17(8), em1990. https://doi.org/10.29333/ejmste/11020

Harding, J. L. (2022). Ethnomathematics affirmed through cognitive mathematics and academic achievement: Quality mathematics teaching and learning benefits. In Handbook of Cognitive Mathematics (pp. 221–249). Springer International Publishing. https://doi.org/10.1007/978-3-031-03945-4_5

Hausberger, T. (2017). The (homo)morphism concept: Didactic transposition, meta-discourse and thematisation. International Journal of Research in Undergraduate Mathematics Education, 3(3), 417–443. https://doi.org/10.1007/s40753-017-0052-7

Hicks, M. D. (2024). “I’ll just try to mimic that”: an exploration of students’ analogical structure creation in abstract algebra. Educational Studies in Mathematics, 117(2), 303–327. https://doi.org/10.1007/s10649-024-10345-1

Irawan, A., Lestari, M., Rahayu, W., & Wulan, R. (2019). Ethnomathematics batik design Bali island. Journal of Physics: Conference Series, 1338, 12045. https://doi.org/10.1088/1742-6596/1338/1/012045

Khairullah, Prahmana, R. C. I., & Peni, N. R. N. (2025). Wura Bongi Monca dance as a promising context for fostering problem-solving skills in learning set theory. Jurnal Elemen, 11(4), 828–844. https://doi.org/10.29408/jel.v11i4.30579

Khasanah, B. A., Prahmana, R. C. I., Adiputra, S., & Arnal-Palacián, M. (2025). The beauty of mathematics in Indonesian culture: An impactful and meaningful context in number patterns learning. JRAMathEdu (Journal of Research and Advances in Mathematics Education). https://doi.org/10.23917/jramathedu.v10i2.10441

Khatin-Zadeh, O., Farsani, D., & Yazdani-Fazlabadi, B. (2022). Transforming dis-embodied mathematical representations into embodied representations, and vice versa: a two-way mechanism for understanding mathematics. Cogent Education, 9(1). https://doi.org/10.1080/2331186X.2022.2154041

Kholid, M. N., & Husodo, H. D. (2025). Ethnomathematics: Arithmetic and discrete mathematics concepts in batik sidomukti Solo. Mathematics Education Journal, 19(3), 489–508. https://doi.org/10.22342/mej.v19i3.pp489-508

Kurniawan, W., & Hidayati, T. (2020). Ethnomathematics in borobudur temple and its relevance in mathematics education. Jurnal Pendidikan Progresif, 10(1), 91–104. https://doi.org/10.23960/jpp.v10.i1.202011

Leandro, C. R., Monteiro, E., & Melo, F. (2018). Interdisciplinary working practices: can creative dance improve math? Research in Dance Education, 19(1), 74–90. https://doi.org/10.1080/14647893.2017.1354838

Levin, M., & Walkoe, J. (2022). Seeds of algebraic thinking: A knowledge in pieces perspective on the development of algebraic thinking. ZDM – Mathematics Education, 54(6), 1303–1314. https://doi.org/10.1007/s11858-022-01374-2

Lorente, A. G. (2024). On graph representation of bee’s dances. Universal Journal of Applied Mathematics, 12(3), 78–83. https://doi.org/10.13189/ujam.2024.120302

Mannone, M., & Turchet, L. (2019). Shall we (math and) dance? In Lecture Notes in Computer Science (Vol. 11502, pp. 84–97). Springer. https://doi.org/10.1007/978-3-030-21392-3_7

Ma’rifah, N., Widada, W., Aida, A., Yulfitri, Y., & Effendi, J. (2019). The students’ mathematics understanding through ethnomathematics based on kejei dance. Journal of Physics: Conference Series, 1318, 12079. https://doi.org/10.1088/1742-6596/1318/1/012079

Nasrum, A., Salido, A., & Chairuddin, C. (2025). Unveiling emerging trends and potential research themes in future ethnomathematics studies: A global bibliometric analysis (from inception to 2024). International Journal of Learning, Teaching and Educational Research, 24(2), 206–226. https://doi.org/10.26803/ijlter.24.2.11

Nicol, C. (2018). Connecting mathematics, community, culture and place: Promise, possibilities, and problems. In G. Kaiser, Forgaszm H., M. Graven, A. Kuzniak, E. Simmt, & B. Xu (Eds.), ICME-13 Monographs (pp. 423–440). Springer. https://doi.org/10.1007/978-3-319-72170-5_24

Orey, D., & Rosa, M. (2021). Ethnomodelling as a glocalization process of mathematical practices through cultural dynamism. The Mathematics Enthusiast, 18(3). https://scholarworks.umt.edu/tme/vol18/iss3/5

Owusu-Darko, I., Sabtiwu, R., Doe, F., Owusu-Mintah, B., & Ofosu, E. K. (2023). An ethnomathematics: Demonstrating its pedagogical action on the teaching and learning of mensuration and geometry. Journal of Mathematics and Science Teacher, 3(2), em042. https://doi.org/10.29333/mathsciteacher/13281

Özcan, Ö., & Bahadır, E. (2023). Opinions of mathematics teachers and pre-service teachers about the relationship between mathematics and culture. European Journal of Education Studies, 10(10). https://doi.org/10.46827/ejes.v10i10.5053

Radiusman, R., Wardani, K. S. K., Apsari, R. A., Nurmawanti, I., & Gunawan, G. (2021). Ethnomathematics in balinese traditional dance: A study of angles in hand gestures. Journal of Physics: Conference Series, 1779, 12074. https://doi.org/10.1088/1742-6596/1779/1/012074

Risdiyanti, I., & Prahmana, R. C. I. (2021). Designing learning trajectory of set through the Indonesian shadow puppets and Mahabharata stories. Infinity Journal, 331–348. https://doi.org/10.22460/infinity.v10i2.p331-348

Rosa, M., & Orey, D. C. (2020). Discussing culturally relevant education and its connection to cultural aspects of mathematics through ethnomathematics. Revista Eletrônica de Educação Matemática, 15(1), 1–20. https://doi.org/10.5007/1981-1322.2020.e67502

Sari, P., & Rosramadhana, R. (2018). Eksistensi tari serampang dua belas pada suku Melayu di kampung Juani Kelurahan Simpang Tiga Pekan, Kabupaten Serdang Bedagai [The existence of the Serampang Dua Belas Dance among the Malay People in Juani Village, Simpang Tiga Pekan Subdistrict, Serdang Bedagai Regency]. Buddayah: Jurnal Pendidikan Antropologi, 1(1), 66. https://doi.org/10.24114/bdh.v1i1.8558

Shahidayanti, T., Prahmana, R. C. I., & Fran, F. A. (2024). Integrating Ethno-Realistic Mathematics Education in developing three-dimensional instructional module. Journal of Honai Math, 7(3), 379–400. https://doi.org/10.30862/jhm.v7i3.698

Stern, E., & Bachman, R. (2021). Pattern play: The case for dance in college mathematics and beyond. Journal of Dance Education, 21(3), 158–167. https://doi.org/10.1080/15290824.2021.1939357

Supiyati, S., Hanum, F., & Jailani. (2019). Ethnomathematics in sasaknese architecture. Journal on Mathematics Education, 10(1), 47–58. https://doi.org/10.22342/jme.10.1.5383.47-58

Thomas, M., & Peebles, C. (2016). A Graph-theoretic approach to the analysis of contra dances. Proceedings of Bridges 2016: Mathematics, Music, Art, Architecture, Education, Culture, 285–292.

Tiwari, S., Obradovic, D., Rathour, L., Narayan Mishra, L., & Mishra, V. N. (2021). Visualization in mathematics teaching. Journal of Advances in Mathematics, 20, 431–439. https://doi.org/10.24297/jam.v20i.9136

Tran, L. M., & Castro Schepers, O. (2023). Making mathematics meaningful for culturally and linguistically diverse students with a mathematics learning disability: a focus on culturally responsive practices. Frontiers in Education, 8. https://doi.org/10.3389/feduc.2023.1276423

Valentini, M., & Guarnacci, S. (2021). Embodied cognition, effective learning and physical activity as a shared feature: Systematic review. Journal of Human Sport and Exercise - 2021 - Autumn Conferences of Sports Science, 539–552. https://doi.org/10.14198/jhse.2021.16.Proc2.38

Veith, J. M., Girnat, B., Krause, M., Straulino, M., Becker, E., Becher, R., & Bitzenbauer, P. (2025). Consistent responses on concept items reflect confidence, and vice versa. International Journal of Science and Mathematics Education, 23(8), 3903–3928. https://doi.org/10.1007/s10763-025-10605-3

Vidal Alangui, W. (2020). Beyond songs and dances: Ethnomathematics and the challenge of culture. Revista Latinoamericana de Etnomatemática Perspectivas Socioculturales de La Educación Matemática, 13(3), 88–107. https://doi.org/10.22267/relatem.20133.63

Vieyra, R. E., Megowan Romanowicz, C., Johnson-Glenberg, M. C., O’Brien, D., & Vieyra Cortés, C. (2024). Making motion meaningful: Mapping body movements onto graphs. The Science Teacher, 91(6), 57–64. https://doi.org/10.1080/00368555.2024.2404956

Zenkl, D., & Vondrová, N. (2023). Combinatorial strategies based on isomorphism. HAL (Le Centre Pour La Communication Scientifique Directe).

From cultural movement to structural equivalence: Modeling graph isomorphism through serampang dua belas dance

Authors

DOI:

Keywords:

Abstract

Author Biographies

Rahmi Ramadhani, Universitas Potensi Utama

Nuraini Sri Bina, Universitas Potensi Utama

Suci Dahlya Narpila, Universitas Islam Negeri Sumatera Utara

Muhammad Rizky Mazaly, Universitas Potensi Utama

Rusmini Rusmini, Universitas Potensi Utama

References

Downloads

Published

How to Cite

Issue

Section

License

Similar Articles

addmenu

akreditasi

templateNew

info

publisher

visitor

Jurnal Elemen