Main Article Content
Abstract
Mathematics exists as rooted in human ideas, ways, and techniques to respond to their environments. Along with its development, mathematics has been taught through formal education or schooling in the flat- not flexible ways and far from students' social and cultural lives. Indonesia is rich with culture, including the Special Region of Yogyakarta (DIY). It is called a city of culture. Educators are not yet aware of this richness in the learning process to integrate it as the starting point. It is hard to find in mathematics textbooks in Indonesia, which put cultural context as starting points. Therefore, this study aims to explore Yogyakarta's culture in terms of contexts used in mathematics learning. It is an ethnography study. Furthermore, the data was collected through literature artifacts, field observation, and interviews with resource persons who understand the seasons, system, and calculation of birth and death days. It is to clarify the researcher's understanding of the literature. This study showed that Yogyakarta's people use mathematical modeling to determine the seasons' system and funerary dates. These models have the potential to be used as a starting point in learning mathematics.
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References
- Abdullah, A. S. (2017). Ethnomathematics in perspective of Sundanese culture. Journal on Mathematics Education, 8(1), 1-16. https://doi.org/10.22342/jme.8.1.3877.1-16
- Alangui, W. V. (2010). Stone walls and water flows: Interrogating cultural practice and mathematics. Doctoral Dissertation. Auckland: University of Auckland. http://hdl.handle.net/2292/5732
- Arisetyawan, A., Suryadi, D., Herman, T., & Rahmat, C. (2014). Study of ethnomathematics: A lesson from the Baduy culture. International Journal of Education and Research, 2(10), 681-688. http://www.ijern.com/journal/2014/October-2014/54.pdf
- Ascher, M., & D'Ambrosio, U. (1994). Ethnomathematics: A dialogue. For the Learning of Mathematics, 14(2), 36-43. https://www.jstor.org/stable/40248114
- Bassanezi, R. C. (2002). Ensino-aprendizagem com modelagem matemática [Teaching and learning with mathematical modeling]. São Paulo: Editora Contexto.
- D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44-48. https://www.jstor.org/stable/40247876
- D'Ambrosio, U. (1999). Literacy, matheracy, and technocracy: A trivium for today. Mathematical Thinking and Learning, 1(2), 131-153. https://doi.org/10.1207/s15327833mtl0102_3
- D'Ambrosio, U. (2007). Ethnomathematics: Perspectives. North American Study Group on Ethnomathematics News, 2(1), 2-3. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.417.9195&rep=rep1&type=pdf
- D'Ambrosio, U., & D'Ambrosio, B. S. (2013). The role of ethnomathematics in curricular leadership in mathematics education. Journal of Mathematics Education at Teachers College, 4(1), 19-25. https://doi.org/10.7916/jmetc.v4i1.767
- D’Ambrosio, U. (2016). An overview of the history of Ethnomathematics. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.), Current and Future Perspectives of Ethnomathematics as A Program (pp. 5-10). Cham: Springer. https://doi.org/10.1007/978-3-319-30120-4_2
- Freudenthal, H. (2006). Revisiting mathematics education: China lectures (Vol. 9). Cham: Springer Science & Business Media.
- Gasiman. (2017). Pranatamangsa dalam Pertanian Masyarakat Yogyakarta [Pranatamangsa in Yogyakarta Agricultural Society]. Personal Communication.
- Irawan, A., Lestari, M., Rahayu, W., & Wulan, R. (2019). Ethnomathematics batik design Bali island. Journal of Physics: Conference Series, 1338(1), 012045. https://doi.org/10.1088/1742-6596/1338/1/012045
- Joseph, G. G. (2010). The crest of the peacock: Non-European roots of mathematics. New Jersey: Princeton University Press.
- Kaomea, J. (2019). Hawaiian math for a sustainable future: Envisioning a conceptual framework for rigorous and culturally relevant 21st-century elementary mathematics education. In C. Nicol, J. A. Q. Q. Xiiem, F. Glanfield, & A. J. S. Dawson (Eds.), Living Culturally Responsive Mathematics Education with/in Indigenous Communities (pp. 189-201). Leiden: Brill Sense. https://doi.org/10.1163/9789004415768_010
- Koentjaraningrat. (2015). Pengantar llmu Antropologi [Introduction to Anthropology]. Yogyakarta: Rineka Cipta.
- Kridalaksana, H. (2001). Wiwara: Pengantar bahasa dan kebudayaan Jawa [Wiwara: Introduction to Javanese language and culture]. Jakarta: Gramedia Pustaka Utama.
- Kusuma, D. A., Dewanto, S. P., Ruchjana, B. N., & Abdullah, A. S. (2017). The role of ethnomathematics in West Java (A preliminary analysis of case study in Cipatujah). Journal of Physics: Conference Series, 893(1), 012020. https://doi.org/10.1088/1742-6596/893/1/012020
- Lestari, M., Irawan, A., Rahayu, W., & Parwati, N. W. (2018). Ethnomathematics elements in Batik Bali using backpropagation method. Journal of Physics: Conference Series, 1022(1), 012012. https://doi.org/10.1088/1742-6596/1022/1/012012
- Lestariningsih, Putri, R. I. I., & Darmawijoyo. (2012). The legend of Kemaro Island for supporting students in learning average. Journal on Mathematics Education, 3(2), 165-174. https://doi.org/10.22342/jme.3.2.1932.165-174
- Muhtadi, D., Sukirwan, Warsito, & Prahmana, R.C.I. (2017). Sundanese ethnomathematics: Mathematical activities in estimating, measuring, and making patterns. Journal on Mathematics Education, 8(2), 185-198. https:// doi.org/10.22342/jme.8.2.4055.185-198
- Nasrullah & Zulkardi. (2011). Building counting by traditional game a mathematics program for young children. Journal on Mathematics Education, 2(1), 41-54. https://doi.org/10.22342/jme.2.1.781.41-54
- Nurhasanah, F., Kusumah, Y. S., & Sabandar, J. (2017). Concept of triangle: Examples of mathematical abstraction in two different contexts. International Journal on Emerging Mathematics Education, 1(1), 53-70. http://dx.doi.org/10.12928/ijeme.v1i1.5782
- Pariyem. (2017). Neptu, hari kelahiran dan pasaran dalam kebudayaan masyarakat Yogyakarta [Neptu, birth day, and pasaran in Yogyakarta community culture]. Personal Communication.
- Partosuwiryo, S. (2013). Kajian pranatamangsa sebagai pedoman penangkapan ikan di Samudra Hindia Selatan Jawa [Study of pranatamangsa as a guide to fishing in the Java Indian Ocean]. Jurnal Perikanan Universitas Gadjah Mada, 15(1), 20-25. https://doi.org/10.22146/jfs.9097
- Pramudita, K., & Rosnawati, R. (2019). Exploration of Javanese culture ethnomathematics based on geometry perspective. Journal of Physics: Conference Series, 1200(1), 012002. https://doi.org/10.1088/1742-6596/1200/1/012002
- Risdiyanti, I., & Prahmana, R. C. I. (2018). Ethnomathematics: Exploration in Javanese culture. Journal of Physics: Conference Series, 943(1), 012032. https://doi.org/10.1088/1742-6596/943/1/012032
- Risdiyanti, I., & Prahmana, R. C. I. (2020). The learning trajectory of number pattern learning using "Barathayudha" war stories and uno stacko. Journal on Mathematics Education, 11(1), 157-166. https://doi.org/10.22342/jme.11.1.10225.157-166
- Risdiyanti, I., Prahmana, R. C. I., & Shahrill, M. (2019). The learning trajectory of social arithmetic using an Indonesian traditional game. Elementary Education Online, 18(4), 2094-2108. https://doi.org/10.17051/ ilkonline.2019. 639439
- Riyadi, S. (2017). Pranatamangsa dalam penangkapan ikan oleh nelayan Pantai Selatan Yogyakarta dan dalam pertanian [Pranatamangsa in fishing by fishermen in the South Coast of Yogyakarta and in agriculture]. Personal Communication.
- Robiyanto & Puryandani, S. (2015). The Javanese lunar calendar's effect on Indonesian stock returns. Gadjah Mada International Journal of Business, 17(2), 125-137. https://doi.org/10.22146/gamaijb.6906
- Rosa, M., & Orey, D. C. (2013). Ethnomodeling as a research theoretical framework on ethnomathematics and mathematical modeling. Journal of Urban Mathematics Education, 6(2), 62-80. https://files.eric.ed.gov/fulltext/EJ1085784.pdf
- Rosa, M., & Orey, D. C. (2016). State of the art in Ethnomathematics. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.). Current and Future Perspectives of Ethnomathematics as A Program (pp. 11-37). Cham: Springer. https://doi.org/10.1007/978-3-319-30120-4_3
- Rosa, M., & Orey, D. C. (2017). Ethnomodelling as the mathematization of cultural practices. In G. Stillman, W. Blum, & G. Kaiser. (Eds.), Mathematical Modelling and Applications (pp. 153-162). Cham: Springer. https://doi.org/10.1007/978-3-319-62968-1_13
- Shirley, L., & Palhares, P. (2016). Ethnomathematics and its diverse pedagogical approaches. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.). Current and Future Perspectives of Ethnomathematics as A Program (pp. 13-17). Cham: Springer. https://link.springer.com/content/pdf/10.1007%2F978-3-319-30120-4.pdf
- Spradley, J. P., & McCurdy, D. W. (1989). Anthropology: The cultural perspective. Reissued Long Grove, IL: Waveland Press.
- Stacey, K. (2011). The PISA view of mathematical literacy in Indonesia. Journal on Mathematics Education, 2(2), 95-126. https://doi.org/10.22342/ jme.2.2.746.95-126
- Sugianto, A., Abdullah, W., & Widodo, S. T. (2019). Reyog Ponorogo art exploration as mathematics learning resources: An ethnomathematics study. Journal of Physics: Conference Series, 1188(1), 012095. https://doi.org/10.1088/1742-6596/1188/1/012095
- Suminah. (2017). Peringatan hari kematian dalam kebudayaan masyarakat Yogyakarta [Commemoration of death day in the culture of Yogyakarta society]. Personal Communication.
- Utami, N. W., Sayuti, S. A., & Jailani. (2019). Math and mate in Javanese primbon: Ethnomathematics study. Journal on Mathematics Education, 10(3), 341-356. https://doi.org/10.22342/jme.10.3.7611.341-356
- Utami, N. W., Sayuti, S. A., & Jailani. (2020). An ethnomathematics study of the days on the Javanese Calendar for learning mathematics in elementary school. Elementary Education Online, 19(3), 1295-1305. https://doi.org/10.17051/ilkonline.2020.728063
- Wijaya, A., Doorman, L. M., & Keijzer, R. (2011). Emergent Modelling: From Traditional Indonesian Games to a Standard Unit of Measurement. Journal of Science and Mathematics Education in Southeast Asia, 34(2), 149-173.
- Zevenbergen, R. (2001). Changing contexts in tertiary mathematics: Implications for diversity and equity. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.). The Teaching and Learning of Mathematics at University Level (pp. 13-26). Dordrecht: Springer. https://doi.org/10.1007/0-306-47231-7_2
References
Abdullah, A. S. (2017). Ethnomathematics in perspective of Sundanese culture. Journal on Mathematics Education, 8(1), 1-16. https://doi.org/10.22342/jme.8.1.3877.1-16
Alangui, W. V. (2010). Stone walls and water flows: Interrogating cultural practice and mathematics. Doctoral Dissertation. Auckland: University of Auckland. http://hdl.handle.net/2292/5732
Arisetyawan, A., Suryadi, D., Herman, T., & Rahmat, C. (2014). Study of ethnomathematics: A lesson from the Baduy culture. International Journal of Education and Research, 2(10), 681-688. http://www.ijern.com/journal/2014/October-2014/54.pdf
Ascher, M., & D'Ambrosio, U. (1994). Ethnomathematics: A dialogue. For the Learning of Mathematics, 14(2), 36-43. https://www.jstor.org/stable/40248114
Bassanezi, R. C. (2002). Ensino-aprendizagem com modelagem matemática [Teaching and learning with mathematical modeling]. São Paulo: Editora Contexto.
D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the Learning of Mathematics, 5(1), 44-48. https://www.jstor.org/stable/40247876
D'Ambrosio, U. (1999). Literacy, matheracy, and technocracy: A trivium for today. Mathematical Thinking and Learning, 1(2), 131-153. https://doi.org/10.1207/s15327833mtl0102_3
D'Ambrosio, U. (2007). Ethnomathematics: Perspectives. North American Study Group on Ethnomathematics News, 2(1), 2-3. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.417.9195&rep=rep1&type=pdf
D'Ambrosio, U., & D'Ambrosio, B. S. (2013). The role of ethnomathematics in curricular leadership in mathematics education. Journal of Mathematics Education at Teachers College, 4(1), 19-25. https://doi.org/10.7916/jmetc.v4i1.767
D’Ambrosio, U. (2016). An overview of the history of Ethnomathematics. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.), Current and Future Perspectives of Ethnomathematics as A Program (pp. 5-10). Cham: Springer. https://doi.org/10.1007/978-3-319-30120-4_2
Freudenthal, H. (2006). Revisiting mathematics education: China lectures (Vol. 9). Cham: Springer Science & Business Media.
Gasiman. (2017). Pranatamangsa dalam Pertanian Masyarakat Yogyakarta [Pranatamangsa in Yogyakarta Agricultural Society]. Personal Communication.
Irawan, A., Lestari, M., Rahayu, W., & Wulan, R. (2019). Ethnomathematics batik design Bali island. Journal of Physics: Conference Series, 1338(1), 012045. https://doi.org/10.1088/1742-6596/1338/1/012045
Joseph, G. G. (2010). The crest of the peacock: Non-European roots of mathematics. New Jersey: Princeton University Press.
Kaomea, J. (2019). Hawaiian math for a sustainable future: Envisioning a conceptual framework for rigorous and culturally relevant 21st-century elementary mathematics education. In C. Nicol, J. A. Q. Q. Xiiem, F. Glanfield, & A. J. S. Dawson (Eds.), Living Culturally Responsive Mathematics Education with/in Indigenous Communities (pp. 189-201). Leiden: Brill Sense. https://doi.org/10.1163/9789004415768_010
Koentjaraningrat. (2015). Pengantar llmu Antropologi [Introduction to Anthropology]. Yogyakarta: Rineka Cipta.
Kridalaksana, H. (2001). Wiwara: Pengantar bahasa dan kebudayaan Jawa [Wiwara: Introduction to Javanese language and culture]. Jakarta: Gramedia Pustaka Utama.
Kusuma, D. A., Dewanto, S. P., Ruchjana, B. N., & Abdullah, A. S. (2017). The role of ethnomathematics in West Java (A preliminary analysis of case study in Cipatujah). Journal of Physics: Conference Series, 893(1), 012020. https://doi.org/10.1088/1742-6596/893/1/012020
Lestari, M., Irawan, A., Rahayu, W., & Parwati, N. W. (2018). Ethnomathematics elements in Batik Bali using backpropagation method. Journal of Physics: Conference Series, 1022(1), 012012. https://doi.org/10.1088/1742-6596/1022/1/012012
Lestariningsih, Putri, R. I. I., & Darmawijoyo. (2012). The legend of Kemaro Island for supporting students in learning average. Journal on Mathematics Education, 3(2), 165-174. https://doi.org/10.22342/jme.3.2.1932.165-174
Muhtadi, D., Sukirwan, Warsito, & Prahmana, R.C.I. (2017). Sundanese ethnomathematics: Mathematical activities in estimating, measuring, and making patterns. Journal on Mathematics Education, 8(2), 185-198. https:// doi.org/10.22342/jme.8.2.4055.185-198
Nasrullah & Zulkardi. (2011). Building counting by traditional game a mathematics program for young children. Journal on Mathematics Education, 2(1), 41-54. https://doi.org/10.22342/jme.2.1.781.41-54
Nurhasanah, F., Kusumah, Y. S., & Sabandar, J. (2017). Concept of triangle: Examples of mathematical abstraction in two different contexts. International Journal on Emerging Mathematics Education, 1(1), 53-70. http://dx.doi.org/10.12928/ijeme.v1i1.5782
Pariyem. (2017). Neptu, hari kelahiran dan pasaran dalam kebudayaan masyarakat Yogyakarta [Neptu, birth day, and pasaran in Yogyakarta community culture]. Personal Communication.
Partosuwiryo, S. (2013). Kajian pranatamangsa sebagai pedoman penangkapan ikan di Samudra Hindia Selatan Jawa [Study of pranatamangsa as a guide to fishing in the Java Indian Ocean]. Jurnal Perikanan Universitas Gadjah Mada, 15(1), 20-25. https://doi.org/10.22146/jfs.9097
Pramudita, K., & Rosnawati, R. (2019). Exploration of Javanese culture ethnomathematics based on geometry perspective. Journal of Physics: Conference Series, 1200(1), 012002. https://doi.org/10.1088/1742-6596/1200/1/012002
Risdiyanti, I., & Prahmana, R. C. I. (2018). Ethnomathematics: Exploration in Javanese culture. Journal of Physics: Conference Series, 943(1), 012032. https://doi.org/10.1088/1742-6596/943/1/012032
Risdiyanti, I., & Prahmana, R. C. I. (2020). The learning trajectory of number pattern learning using "Barathayudha" war stories and uno stacko. Journal on Mathematics Education, 11(1), 157-166. https://doi.org/10.22342/jme.11.1.10225.157-166
Risdiyanti, I., Prahmana, R. C. I., & Shahrill, M. (2019). The learning trajectory of social arithmetic using an Indonesian traditional game. Elementary Education Online, 18(4), 2094-2108. https://doi.org/10.17051/ ilkonline.2019. 639439
Riyadi, S. (2017). Pranatamangsa dalam penangkapan ikan oleh nelayan Pantai Selatan Yogyakarta dan dalam pertanian [Pranatamangsa in fishing by fishermen in the South Coast of Yogyakarta and in agriculture]. Personal Communication.
Robiyanto & Puryandani, S. (2015). The Javanese lunar calendar's effect on Indonesian stock returns. Gadjah Mada International Journal of Business, 17(2), 125-137. https://doi.org/10.22146/gamaijb.6906
Rosa, M., & Orey, D. C. (2013). Ethnomodeling as a research theoretical framework on ethnomathematics and mathematical modeling. Journal of Urban Mathematics Education, 6(2), 62-80. https://files.eric.ed.gov/fulltext/EJ1085784.pdf
Rosa, M., & Orey, D. C. (2016). State of the art in Ethnomathematics. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.). Current and Future Perspectives of Ethnomathematics as A Program (pp. 11-37). Cham: Springer. https://doi.org/10.1007/978-3-319-30120-4_3
Rosa, M., & Orey, D. C. (2017). Ethnomodelling as the mathematization of cultural practices. In G. Stillman, W. Blum, & G. Kaiser. (Eds.), Mathematical Modelling and Applications (pp. 153-162). Cham: Springer. https://doi.org/10.1007/978-3-319-62968-1_13
Shirley, L., & Palhares, P. (2016). Ethnomathematics and its diverse pedagogical approaches. In M. Rosa, U. D’Ambrosio, D. C. Orey, L. Shirley, W. V. Alangui, P. Palhares, & M. E. Gavarrete (Eds.). Current and Future Perspectives of Ethnomathematics as A Program (pp. 13-17). Cham: Springer. https://link.springer.com/content/pdf/10.1007%2F978-3-319-30120-4.pdf
Spradley, J. P., & McCurdy, D. W. (1989). Anthropology: The cultural perspective. Reissued Long Grove, IL: Waveland Press.
Stacey, K. (2011). The PISA view of mathematical literacy in Indonesia. Journal on Mathematics Education, 2(2), 95-126. https://doi.org/10.22342/ jme.2.2.746.95-126
Sugianto, A., Abdullah, W., & Widodo, S. T. (2019). Reyog Ponorogo art exploration as mathematics learning resources: An ethnomathematics study. Journal of Physics: Conference Series, 1188(1), 012095. https://doi.org/10.1088/1742-6596/1188/1/012095
Suminah. (2017). Peringatan hari kematian dalam kebudayaan masyarakat Yogyakarta [Commemoration of death day in the culture of Yogyakarta society]. Personal Communication.
Utami, N. W., Sayuti, S. A., & Jailani. (2019). Math and mate in Javanese primbon: Ethnomathematics study. Journal on Mathematics Education, 10(3), 341-356. https://doi.org/10.22342/jme.10.3.7611.341-356
Utami, N. W., Sayuti, S. A., & Jailani. (2020). An ethnomathematics study of the days on the Javanese Calendar for learning mathematics in elementary school. Elementary Education Online, 19(3), 1295-1305. https://doi.org/10.17051/ilkonline.2020.728063
Wijaya, A., Doorman, L. M., & Keijzer, R. (2011). Emergent Modelling: From Traditional Indonesian Games to a Standard Unit of Measurement. Journal of Science and Mathematics Education in Southeast Asia, 34(2), 149-173.
Zevenbergen, R. (2001). Changing contexts in tertiary mathematics: Implications for diversity and equity. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.). The Teaching and Learning of Mathematics at University Level (pp. 13-26). Dordrecht: Springer. https://doi.org/10.1007/0-306-47231-7_2