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Abstract

Indonesia has many cultures that can be used as a starting point in learning mathematics. Yet, many teachers still use conventional methods to provide explicit mathematical content without connecting with students' culture and daily activities. One of the learning approaches that can solve these problems is Realistic Mathematics Education (RME). This approach uses context as one of its characteristics containing students' culture and their daily activities. On the other hand, Wayang (Indonesian shadow puppets) and Mahabharata stories have the characteristics that can be a context in the learning of set. This research aims to design the Hypothetical Learning Trajectory (HLT) of the set using the RME approach through Wayang and Mahabharata stories, which are familiar with students' culture in Yogyakarta. This HLT will then be tested on students in further research until it becomes the Local Instructional Theory (LIT) on set. Students can study about set by grouping Wayang in Mahabharata stories based on their characters. The research result is the HLT of set through the context of wayang and Mahabharata stories containing learning goals, learning activities, and the conjecture of every activity. This HLT can be a promising solution to overcome students' difficulties in understanding the concept of sets and values in the cultural context to improve the students' character.

Keywords

Ethnomathematics Realistic Mathematics Education Design Research Indonesian Shadow Puppets Mahabharata Stories Set

Article Details

References

  1. Alangui, W. V. (2010). Stone walls and water flows: Interrogating cultural practice and mathematics. Doctoral Dissertation. Auckland: University of Auckland.

  2. [Article]     [Google Scholar]


  3. Amidi, A., & Zahid, M. Z. (2017). Membangun Kemampuan Berpikir Kreatif Matematis Dengan Model Pembelajaran Berbasis Masalah Berbantuan E-Learning. In PRISMA, Prosiding Seminar Nasional Matematika (pp. 586-594). Universitas Negeri Semarang.

  4. [Article]     [Google Scholar]


  5. As’ari, A. R., Tohir, M., Valentino, E., Imron, Z., & Taufiq, I. (2017). Buku guru matematika kelas VII SMP/MTs kurikulum 2013. Jakarta: Pusat Kurikulum dan Perbukuan, Balitbang, Kemendikbud.

  6. [Article]


  7. D'Ambrosio, U. (1985). Ethnomathematics and its place in the history and pedagogy of mathematics. For the learning of Mathematics, 5(1), 44-48.

  8. [Article]     [Google Scholar]


  9. D'Ambrosio, U. (2007). Ethnomathematics: perspectives. North American Study Group on Ethnomathematics News, 2(1), 2-3.

  10. [Article]     [Google Scholar]


  11. 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 (Ed.). Current and Future Perspectives of Ethnomathematics as A Program (pp. 5-10). Cham: Springer. doi:10.1007/978-3-319-30120-4_2

  12. [Article]     [Google Scholar]


  13. Dwidarti, U., Mampouw, H. L., & Setyadi, D. (2019). Analisis kesulitan siswa dalam menyelesaikan soal cerita pada materi himpunan. Jurnal Cendekia: Jurnal Pendidikan Matematika, 3(2), 315-322. doi:10.31004/cendekia.v3i2.110

  14. [Article]     [Google Scholar]


  15. Ernest, P., Skovsmose, O., Van Bendegem, J. P., Bicudo, M., Miarka, R., Kvasz, L., & Moeller, R. (2016). The philosophy of mathematics education. Cham: Springer Nature. doi:10.1007/978-3-319-40569-8

  16. [Article]     [Google Scholar]


  17. Freudenthal, H. (2006). Revisiting mathematics education: China lectures (Vol. 9). Cham: Springer Science & Business Media. doi:10.1007/0-306-47202-3

  18. [Article]     [Google Scholar]


  19. Gravemeijer, K. P. E. (1994). Developing realistic mathematics education. Utrecht: Faculty of Sciences, Freudenthal Institute.

  20. [Article]     [Google Scholar]


  21. Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Jvd. Akker, K. Gravemeijer, S. Mckenney, & N. Nieveen (Ed.). Educational Design Research (pp. 17-51). London: Routledge Taylor and Francis Group. doi:10.4324/9780203088364

  22. [Article]     [Google Scholar]


  23. Hadi, S. (2017). Pendidikan matematika realistik (Teori, pengembangan dan implementasinya). Jakarta: PT Raja Grafindo Persada.

  24. [Article]     [Google Scholar]


  25. Hendriana, H., Rohaeti, E. E., & Sumarmo, U. (2017). Hard skill dan soft skills matematik siswa. Bandung: Refika Aditama.

  26. [Google Scholar]


  27. Jaelani, A., Putri, R. I. I., & Hartono, Y. (2013). Students’ strategies of measuring time using traditional Gasing game in third grade of primary school. Journal on Mathematics Education, 4(1), 29-40. doi:10.22342/jme.4.1.560.29-40

  28. [Article]     [Google Scholar]


  29. Joseph, G. G. (2010). The crest of the peacock: Non-European roots of mathematics. New Jersey: Princeton University Press. doi:10.1515/9781400836369

  30. [Article]     [Google Scholar]


  31. Joyner, J., & Reys, B. (2000). Principles and standards for school mathematics: What's in it for you?. Teaching children mathematics, 7(1), 26-29. doi:10.5951/TCM.7.1.0026

  32. [Article]     [Google Scholar]


  33. Kasim, S. (2018). Wayang dalam kajian ontologo, epistimologi dan aksiologi sebagai landasan filsafat ilmu. Jurnal Sangkareang Mataram, 4(1), 47-50.

  34. [Article]     [Google Scholar]


  35. Komariyah, S., & Laili, A. F. N. (2018). Pengaruh kemampuan berpikir kritis terhadap hasil belajar matematika. JP3M (Jurnal Penelitian Pendidikan dan Pengajaran Matematika), 4(2), 53-58.

  36. [Article]     [Google Scholar]


  37. Lim, Y. S. (2017). Wayang kulit and its influence on modern entertainment. In The Asian Conference on Media, Communication & Film 2017 Official Conference Proceedings (pp. 111–124). The International Academic Forum.

  38. [Article]     [Google Scholar]


  39. Maryati, M., & Prahmana, R. C. I. (2020). Designing learning rotation using the context of bamboo woven motif. Prima: Jurnal Pendidikan Matematika, 4(2), 100-108. doi:10.31000/prima.v4i2.2600

  40. [Article]     [Google Scholar]


  41. Meirisa, A., Rifandi, R., & Masniladevi, M. (2018). Pengaruh pendekatan pendidikan matematika realistik indonesia (PMRI) terhadap keterampilan berpikir kritis siswa SD. Jurnal Gantang, 3(2), 127-134. doi:10.31629/jg.v3i2.508

  42. [Article]     [Google Scholar]


  43. Muhtadi, D., Sukirwan, S., Warsito, W., & Prahmana, R. C. I. (2017). Sundanese Ethnomathematics: mathematical activities in estimating, measuring, and making patterns. Journal on Mathematics Education, 8(2), 185-198. doi:10.22342/jme.8.2.4055.185-198

  44. [Article]     [Google Scholar]


  45. Nasrullah, N., & Zulkardi, Z. (2011). Building counting by traditional game: A mathematics program for young children. Journal on Mathematics Education, 2(1), 41-54. doi:10.22342/jme.2.1.781.41-54

  46. [Article]     [Google Scholar]


  47. Novrika, D., Putri, R. I. I., & Hartono, Y. (2016). Desain pembelajaran materi refleksi menggunakan motif kain Batik untuk siswa kelas VII. In Prosiding Seminar Nasional Matematika dan Pendidikan Matematika. Universitas Negeri Sebelas Maret.

  48. [Article]     [Google Scholar]


  49. Nursyahidah, F., Saputro, B. A., Albab, I. U., & Aisyah, F. (2020). Pengembangan learning trajectory based instruction materi kerucut menggunakan konteks megono gunungan. Mosharafa: Jurnal Pendidikan Matematika, 9(1), 47-58.

  50. [Article]     [Google Scholar]


  51. Nurtasari, A. R., Jamiah, Y., & Suratman, D. (2017). Miskonsepsi Siswa pada Materi Himpunan di Kelas VII SMP Santa Monika Kubu Raya. Jurnal Pendidikan dan Pembelajaran Khatulistiwa, 6(2), 1-10.

  52. [Article]     [Google Scholar]


  53. Plomp, T. (2013). Educational Design Research: An Introduction. In T. Plomp & N. Nieveen (Ed.). Educational Design Research (pp. 10-51). Enschede: Netherlands Institute for Curriculum Development (SLO).

  54. [Article]     [Google Scholar]


  55. Prahmana, R. C. I. (2017). Design Research (Teori dan Implementasinya: Suatu Pengantar). Depok : Rajawali Pers.

  56. [Article]     [Google Scholar]


  57. Prahmana, R. C. I., Sagita, L., Hidayat, W., & Utami, N. W. (2020). Two decades of realistic mathematics education research in Indonesia: A survey. Infinity Journal, 9(2), 223-246. doi:10.22460/infinity.v9i2.p223-246

  58. [Article]     [Google Scholar]


  59. Prahmana, R. C. I., Yunianto, W., Rosa, M., & Orey, D. C. (2021). Ethnomathematics: Pranatamangsa system and the birth-death ceremonial in Yogyakarta. Journal on Mathematics Education, 12(1), 93-112. doi:10.22342/jme.12.1.11745.93-112

  60. [Article]     [Google Scholar]


  61. Prahmana, R. C. I., Zulkardi, Z., & Hartono, Y. (2012). Learning multiplication using Indonesian traditional game in third grade. Journal on Mathematics Education, 3(2), 115-132. doi:10.22342/jme.3.2.1931.115-132

  62. [Article]     [Google Scholar]


  63. Putra, R. Y., Wijayanto, Z., & Widodo, S. A. (2020). Etnomatematika: Masjid Soko Tunggal dalam pembelajaran geometri 2D. Jurnal Riset Pendidikan dan Inovasi Pembelajaran Matematika (JRPIPM), 4(1), 10-22. doi:10.26740/jrpipm.v4n1.p10-22

  64. [Article]     [Google Scholar]


  65. Rahmawati, Y. (2020). Pendekatan matematika realistik bernuansa Etnomatematika: Rumah gadang minangkabau pada materi teorema pythagoras. Jurnal Azimut, 3(SMAR), 22-29.

  66. [Article]     [Google Scholar]


  67. Ratnasari, S., & Setiawan, W. (2019). Analisis kesulitan belajar siswa pada materi himpunan. Journal on Education, 1(2), 473-479.

  68. [Article]     [Google Scholar]


  69. Risdiyanti, I., & Prahmana, R. C. I. (2017). Ethnomathematics: Exploration in javanese culture. Journal of Physics: Conference Series, 943(1), 012032. doi:10.1088/1742-6596/943/1/012032

  70. [Article]     [Google Scholar]


  71. Risdiyanti, I., & Prahmana, R. C. I. (2020a). Ethnomathematics (Teori dan Implementasinya: Suatu Pengantar). Yogyakarta: UAD Press.

  72. [Article]     [Google Scholar]


  73. Risdiyanti, I., & Prahmana, R. C. I. (2020b). The learning trajectory of number pattern learning using Barathayudha war stories and Uno Stacko. Journal on Mathematics Education, 11(1), 157-166. doi:10.22342/jme.11.1.10225.157-166

  74. [Article]     [Google Scholar]


  75. 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. doi:10.17051/ilkonline.2019.639439

  76. [Article]     [Google Scholar]


  77. 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 (Ed.). Current and Future Perspectives of Ethnomathematics as A Program (pp. 11-37). Cham: Springer. doi:10.1007/978-3-319-30120-4_3

  78. [Article]     [Google Scholar]


  79. Sabunga, B., Budimansyah, D., Sauri, S., & Sanusi, A. (2014). Wayang Golek education values: Their potential to strengthen nationalism. International Journal of Education and Management Studies, 4(4), 287-292.

  80. [Article]     [Google Scholar]


  81. Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM, 40(6), 927-939. doi:10.1007/s11858-008-0125-9

  82. [Article]     [Google Scholar]


  83. Soedjadi, R. (2007). Inti dasar-dasar pendidikan matematika realistik Indonesia. Jurnal pendidikan matematika, 1(2), 1-10. doi:10.22342/jpm.1.2.807.

  84. [Article]     [Google Scholar]


  85. Utami, N. W., Sayuti, S. A., & Jailani, J. (2019). Math and Mate in Javanese Primbon: Ethnomathematics study. Journal on Mathematics Education, 10(3), 341-356. doi:10.22342/jme.10.3.7611.341-356

  86. [Article]     [Google Scholar]


  87. Wijaya, A. (2008). Design research in mathematics education: Indonesian traditional games as means to support second graders’ learning of linear measurement. Thesis. Utrecht: Utrecht University.

  88. [Article]     [Google Scholar]


  89. Zulkardi, Putri R. I. I., & Wijaya A. (2020). Two decades of realistic mathematics education in Indonesia. In van den Heuvel-Panhuizen M. (Ed.). International Reflections on the Netherlands Didactics of Mathematics (pp. 325-340). ICME-13 Monographs. Cham: Springer. doi:10.1007/978-3-030-20223-1_18

  90. [Article]     [Google Scholar]