Applying spatial ethnomathematics to maintain the cultural values of Balinese and Thai traditional houses
DOI: https://doi.org/10.3846/jau.2026.25451Abstract
This study investigates how the cultural values embedded in Balinese and Thai traditional houses can be analytically extracted and maintained within contemporary residential design through the lens of spatial ethnomathematics. Drawing on D’Ambrosio’s ethnomathematics and Bishop’s pan-cultural activities of locating and designing, the research treats vernacular dwellings as operational diagrams of cultural cosmology, foregrounding proportion, modularity, orientation, and spatial hierarchy rather than ornament alone. The analysis is operationalized through the IMO(E) framework – Inner (cosmology), Middle (social practice), Outer (geometric form), and (E)xperimental (transformation) – extending Leong and Clark’s three-tier model of culture-based design. A practice-based qualitative methodology combines literature review, observation, typological-morphological reading, and design experimentation across two cases: the Balinese karang governed by Tri Hita Karana, Sanga Mandala, and Tri Angga; and the Thai ruean structured by hwang modularity, chan mediation, and stilt-based vertical cosmology. Findings demonstrate that spatial ethnomathematics, coupled with IMO(E), provides a methodological bridge that sustains cultural values not by replicating form but by maintaining the spatial-cosmological logic that form materialises. Applied to a contemporary two-storey residential proposal, the protocol shows how abstraction, substitution, and recombination carry Inner cosmology and Middle practice into Outer geometry while remaining responsive to present-day inhabitation.
Keywords:
spatial ethnomathematics, IMO(E) framework, Balinese traditional house, Thai traditional house, cultural values, vernacular architecture, culture-based designHow to Cite
Share
License
Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
Adam, S. (2004). Ethnomathematical ideas in the curriculum. Mathematics Education Research Journal, 16, 49–68. https://doi.org/10.1007/BF03217395
Adnyana, I. B. M. A. Y., Kardinal, N. G. D. A., & Sudharsana, I. M. G. (2021). Komparasi Permukiman Desa Adat Tenganan Pegringsingan dengan Desa Adat Tenganan Dauh Tukad di Karangasem Bali [Comparison of the settlements of Tenganan Pegringsingan tarditional village in Karangasem Bali]. Pranatacara Bhumandala, 2(1), 49–64. https://doi.org/10.32795/pranatacara_bhumandala.v2i1.1724
Albanese, V., & Perales, F. J. (2014). Pensar matemáticamente: una visión etnomatemática de la práctica artesanal soguera [Thinking mathematically: An ethnomathematical vision of the artisanal practice of Soguera]. Revista Latinoamericana de Investigación en Matemática Educativa, 17(3), 261–288. https://doi.org/10.12802/relime.13.1731
Antoniades, H. N., Neville-Golden, J., Galanopoulos, T., Kradin, R. L., Valente, A. J., & Graves, D. T. (1992). Expression of monocyte chemoattractant protein 1 mRNA in human idiopathic pulmonary fibrosis. Proceedings of the National Academy of Sciences, 89(12), 5371–5375. https://doi.org/10.1073/pnas.89.12.5371
Ardiana, P. A., Sujana, I. K., Natalia, S. A. P. D., & Yanthi, K. D. L. (2026). Tri Hita Karana: Balinese local wisdom and its role in the triumph over corruption. Journal of Accounting & Organizational Change, 22(1), 127–148. https://doi.org/10.1108/JAOC-11-2023-0182
Arunoprayote, S. (2022). A study of the physical characteristics of Chinese cemetery landscapes in Inner Bangkok. Sarasatr: Journal of Architecture and Design, 5(2), 233–247.
Aryani, N. P., & Tanuwidjaja, G. (2013). Sustainable architectural design in a traditional Balinese housing in accordance to the concept of Tri Mandala. Journal of Architecture&ENVIRONMENT, 12(2), 113–124. https://doi.org/10.12962/j2355262x.v12i2.a561
Ascher, M. (1991). Ethnomathematics: A multicultural view of mathematical ideas (1st ed.). Routledge. https://doi.org/10.1201/9780203756522
Birdwell-Pheasant, D., & Lawrence-Züniga, D. (1999). House life: space, place and family in Europe (1st ed.). Routledge. https://doi.org/10.4324/9781003103240
Bishop, A. (1991). Mathematical enculturation: A cultural perspective on mathematics education (Vol. 6). Springer. https://doi.org/10.1007/978-94-009-2657-8_6
Chiranthanut, C. (2020). Inherent wisdoms and the roles of sacred spaces in spatial organization of vernacular houses. The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, 44, 19–23. https://doi.org/10.5194/isprs-archives-XLIV-M-1-2020-19-2020
Chuapram, S., King, R., & Panin, O. (2012). Transformation of local living: Buddhist Thai communities and vernacular houses around Songkhla Lake basin. Procedia-Social and Behavioral Sciences, 50, 42–54. https://doi.org/10.1016/j.sbspro.2012.08.014
D’Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the learning of Mathematics, 5(1), 44–48.
D’Ambrosio, U. (2006). Ethnomathematics: Link between traditions and modernity. Brill. https://doi.org/10.1163/9789460911415
Dwijendra, N. K. A. (2008). Arsitektur rumah tradisional Bali: berdasarkan asta kosala-kosali. Kerjasama Bali Media Adhikarsa [dengan] [Traditional Balinese house architecture. A collaboration with Bali media adhikarsa [with]]. Udayana University Press.
Eglash, R. (1999). African fractals: Modern computing and indigenous design. Rutgers University Press.
Ferschin, P., Di Angelo, M., & Paskaleva, G. (2013 October 28–November 1). Parametric Balinese rumah: Procedural modeling of traditional Balinese architecture. In 2013 Digital Heritage International Congress (DigitalHeritage), (pp. 199–206). Marseille, France. IEEE. https://doi.org/10.1109/DigitalHeritage.2013.6744755
Frampton, K., Frampton, K., Frampton, K., & Frampton, K. (1980). Modern architecture: A critical history (Vol. 4). Thames and Hudson.
Gherardi, S. (2000). Practice-based theorizing on learning and knowing in organizations. Organization, 7(2), 211–223. https://doi.org/10.1177/135050840072001
Glassie, H., & Truesdell, B. (2008). A life in the field: Henry Glassie and the study of material culture. The Public Historian, 30(4), 59–87. https://doi.org/10.1525/tph.2008.30.4.59
Gelebet, I. N., & Puja, I. G. N. A. (2002). Arsitektur tradisional daerah Bali [Traditional Architecture of Bali]. Bagian Proyek Pengkajian dan Pemanfaatan Sejarah dan Tradisi Bali.
Halim, E. A. (2016). Studi Perilaku Adaptasi Manusia terhadap Lingkungan Sosial dalam Penambahan Fungsi Ruang Komersial Hunian Tradisional Bali di Ubud [A study of human adaptation behavior to the social environment in the addition of the function of commercial space of traditional Balinese housing in Ubud]. Serat Rupa: Journal of Design, 1(2), 389–405. https://doi.org/10.28932/srjd.v1i2.460
Halim, E. A., & Joneurairatana, E. (2024). Transforming of the Sumba pattern into light, shadow, and shade for contemporary lamp design [Doctoral dissertation, Silpakorn University].
Halim, E. A., Joneurairatana, E., Vongphantuset, J., & Jamuni, P. (2023). “Mamuli” pattern in East Sumba woven fabric as inspiration for “Kandunnu” standing lamp using the IMOE method. ISVS Ejournal, 7(3), 1–13.
He, M., & Qi, J. (2019). Study on the theory of Rafael Moneo architectural typology. IOP Conference Series: Materials Science and Engineering, 592, Article 012105. https://doi.org/10.1088/1757-899X/592/1/012105
Joneurairatana, E. (2021). Art and design research [Doctoral dissertation, Silpakorn University].
Kumurur, V. A., & Damayanti, S. (2009). Pola perumahan dan pemukiman Desa Tenganan Bali [Housing and Settlement Patterns in Tenganan Village, Bali]. Jurnal Sabua, 1(1), 1–7.
Leong, B. D., & Clark, H. (2003). Culture-based knowledge towards new design thinking and practice: A dialogue. Design Issues, 19(3), 48–58. https://doi.org/10.1162/074793603768290838
Massarwe, K., Verner, I., Bshouty, D., & Verner, I. (2010). An ethnomathematics exercise in analyzing and constructing ornaments in a geometry class. Journal of Mathematics and Culture, 5(1), 1–20.
Mildawani, I., Asmiwyati, I. G. A. A. R., Apriyanti, R., Prabawasari, V. W., & Akhirson, A. (2024). The application of Tri Hita Karana principles in landscape architecture and urban planning: A case study of Kedonganan Traditional Village, Bali. Evolutionary Studies in Imaginative Culture, 8(2), 869–878. https://doi.org/10.70082/esiculture.vi.741
Ministry of Tourism, Republic of Indonesia. (2026). Traditional houses in Bali. https://www.indonesia.travel/gb/en/travel-ideas/culture/traditional-houses-in-bali
Nivat, D., & Prince, H. (1955). The reconstruction of Rama I of the Chakri dynasty. Journal of the Siam Society, 43(1), 262–265.
Nurmala, C. W., Asrofi, M. H., Maqsuna, A. R., Madikha, A., Paramitha, S. A., Fatoni, F., & Virgiawan, D. B. (2025). Implementation of zoning theory based on the concept of Tri Hita Karana, Tri Mandala and Sanga Mandala of Mas Village, Ubud, Bali in Maintaining cultural values. Sustainability (STPP) Theory, Practice and Policy, 5(1), 59–73. https://doi.org/10.30631/sdgs.v5i1.3176
Oliver, P. (2006). Built to meet needs: Cultural issues in vernacular architecture (1st ed.). Routledge. https://doi.org/10.4324/9780080476308
Parwata, I. W. (2011). Rumah Tinggal Tradisional Bali dari Aspek Budaya dan Antropometri [Balinese traditional residence from cultural and anthropometric aspects]. Mudra Jurnal Seni Budaya, 26(1), 95–106. https://doi.org/10.31091/mudra.v26i1.1593
Peters, J. H. (2013). Tri Hita Karana. Kepustakaan Populer Gramedia.
Pintong, S. (2017). Revitalizing the fundamental elements of Thai House [Doctoral thesis, Silpakorn University]. http://ithesis-ir.su.ac.th/dspace/handle/123456789/684
Pradnyasari, N. K. I. (2017). The ‘Tri Mandala’ concept in the outdoor spatial layout of Badung Traditional Market, Denpasar City [Doctoral thesis, Universitas Brawijaya].
Prahmana, R. C. I. (2022). Ethno-realistic mathematics education: The promising learning approach in the city of culture. SN Social Sciences, 2(12), 257. https://doi.org/10.1007/s43545-022-00571-w
Prasertsuk, S. (2015). Architectural composition for utilities and spatial connection in modern Thai architecture. Journal of Architectural/Planning Research and Studies (JARS), 2, Article 257.
Rapoport, R., & Rapoport, R. N. (1969). The dual career family: A variant pattern and social change. Human Relations, 22(1), 3–30. https://doi.org/10.1177/001872676902200101
Riyanto, E. D., & Bhattacarya, W. (2022). Tri Mandala: Kearifan Lokal Bali dalam Pembagian Zonasi dan Ruang pada Bangunan Pura di Kabupaten Sidoarjo [Tri Mandala: Balinese local wisdom in the distribution of zoning and space in temple buildings in Sidoarjo Regency]. Sphatika: Jurnal Teologi, 13(1), 108–119. https://doi.org/10.25078/sphatika.v13i1.1272
Roth, D., & Sedana, G. (2015). Reframing Tri Hita Karana: From ‘Balinese culture’ to politics. The Asia Pacific Journal of Anthropology, 16(2), 157–175. https://doi.org/10.1080/14442213.2014.994674
Samadhi, T. N. (2004). Making cosmo-religious landscapes: The design of a Balinese town’s civic center (Bali, Indonesia). Habitat International, 28(1), 103–122. https://doi.org/10.1016/S0197-3975(03)00032-8
Sathāpitānon, N., & Mertens, B. (2012). Architecture of Thailand: A guide to tradition and contemporary forms. Editions Didier Millet.
Solihin, S., & Sumawidari, I. A. K. (2021). Tri hita karana implementation in accommodation management (the case of traditional balinese homestays in Ubud). International Journal of Glocal Tourism, 2(3), 146–159. https://doi.org/10.58982/injogt.v2i3.70
Sulistyawati, I., Nugoho, N., Suryokusumo, S., & Hadi, Y. S. (2008). Maximum stiffness and flexural strength of glulam and solid acacia wood beams. Jurnal Teknik Sipil ITB, 15(3), 113–122. https://doi.org/10.5614/jts.2008.15.3.3
Suryada, I., & Bagus, G. A. (2012). The concepts of Tri Mandala and Sanga Mandala in traditional Balinese architectural layout. Jurnal SUlapa, 4(1), 23–32.
Taş, E., & Özcan, U. (2023). Sustainable architecture applications based on culture and religion In Bali traditional architecture. International Journal of Social And Humanities Sciences, 7(3), 11–36.
Tengkaoprasert, R. (2018). The concept of energy conservation in architectural design and the creation of modern Thai architectural identity. Athens Journal of Architecture, 4(2), 171–190. https://doi.org/10.30958/aja.4-2-2
Throsby, D. (1999). Cultural capital. Journal of Cultural Economics, 23(1), 3–12. https://doi.org/10.1023/A:1007543313370
Wastika, D. N. (2005). Application of the Tri Hita Karana concept in housing planning in Bali. Jurnal Permukiman Natah, 3(2), 62–105.
Wolfrum, S., & Janson, A. (2019). The city as architecture. Birkhäuser. https://doi.org/10.1515/9783035618051
View article in other formats
CrossMark check
Published
Issue
Section
Copyright
Copyright (c) 2026 The Author(s). Published by Vilnius Gediminas Technical University.
License
This work is licensed under a Creative Commons Attribution 4.0 International License.