Learning Trajectory on Probability Using the Context of the Bekulo Tradition

Novianti Mandasari, Zulkardi Zulkardi, Ratu Ilma Indra Putri, Ely Susanti, Budi Mulyono

Abstract


In everyday life, individuals are required to be cautious in making decisions and analyzing the possibilities of various alternatives. Probability theory emerges as one of the important branches of mathematics that provides an understanding of uncertainty and ways to measure the likelihood of an event. However, field observations reveal that many students still encounter difficulties in understanding probability, particularly in the subtopic of combinations. These difficulties are generally caused by abstract learning processes, limited contextual activities, and the lack of connection between mathematics and real-life experiences or local culture close to students’ lives. This study aims to design probability learning based on Indonesian Realistic Mathematics Education (IRME) by utilizing the Bekulo tradition in Rejang Lebong Regency as a relevant local cultural context. The method employed is design research with a validation study type, involving ninth-grade students of SMP IT Salsabillah Rejang Lebong as research subjects. Data were collected through observation, documentation, and interviews. In this study, the researchers developed a Hypothetical Learning Trajectory (HLT) adapted to the Bekulo tradition context. The results show that integrating IRME with cultural contexts can effectively support the development of students’ understanding of the concept of combinations in a more meaningful way. These findings affirm that culturally rooted learning designs not only enrich students’ learning experiences but also foster their appreciation of local wisdom while making mathematics more relevant to everyday life.

Keywords


Learning Trajectory; Probability; Bekulo Tradition

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References


Aisy, F. R., Fitriyani, D. E., Ningrum, R. R., & Zuliana, E. (2024). P Pembelajaran Matematika Realistik Terkait Peluang Berkonteks Permainan Ular Tangga. JURNAL MathEdu (Mathematic Education Journal), 7(1), 20–27. https://doi.org/https://doi.org/10.37081/mathedu.v7i1.5712

Aminah, S., Wijaya, T. T., & Yuspriyati, D. (2018). Analisis kemampuan komunikasi matematis siswa kelas viii pada materi himpunan. Jurnal Cendekia: Jurnal Pendidikan Matematika, 2(1), 15–22.

Anggraini, M., Fauzan, A., & Musdi, E. (2022). Pengembangan Desain Pembelajaran Topik Peluang Berbasis Realistic Mathematics Education. Edukatif: Jurnal Ilmu Pendidikan, 4(1), 70–78. https://doi.org/https://doi.org/10.31004/edukatif.v4i1.1612

Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools.

Batanero, C., Chernoff, E. J., Engel, J., Lee, H. S., & Sánchez, E. (2016). Research on teaching and learning probability. Springer Nature. https://doi.org/DOI 10.1007/978-3-319-31625-3

Bishop, A. (1991). Mathematical enculturation: A cultural perspective on mathematics education (Vol. 6). Springer Science & Business Media.

Cai, S., Liu, E., Shen, Y., Liu, C., Li, S., & Shen, Y. (2023). Probability learning in mathematics using augmented reality: impact on students’ learning gains and attitudes. In Cross Reality (XR) and Immersive Learning Environments (ILEs) in Education (pp. 22–35). Routledge. https://doi.org/https://doi.org/10.4324/9781003457121

Cárcamo Bahamonde, A. D., Fortuny Aymemí, J. M., & Gómez i Urgellés, J. V. (2017). Mathematical modelling and the learning trajectory: tools to support the teaching of linear algebra. International Journal of Mathematical Education in Science and Technology, 48(3), 338–352. https://doi.org/https://doi.org/10.1080/0020739X.2016.1241436

Domu, I., & Mangelep, N. O. (2023). Developing mathematical literacy problems based on the local wisdom of the Tempang community on the topic of space and shape. AIP Conference Proceedings, 2621(1), 70014. https://doi.org/https://doi.org/10.1063/5.0142362

Fauzan, A., Harisman, Y., & Sya’bani, F. (2022). Local Instructional Theory of Probability Topics Based on Realistic Mathematics Education for Eighth-Grade Students. Journal on Mathematics Education, 13(4), 703–722. https://doi.org/http://doi.org/10.22342/jme.v13i4.pp703-722

Fida, R. N. (2025). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Permutasi dan Kombinasi Berdasarkan Kemampuan Matematika di MAN 1 Pasuruan. PenaEmas, 3(1), 506–517. https://doi.org/http://doi.org/10.22342/jme.v13i4.pp703-722

Gravemeijer, K. (2004). Local Instruction Theories as Means of Support for Teachers in Reform Mathematics Education. Mathematical Thinking and Learning, 6(2), 105–128. https://doi.org/10.1207/s15327833mtl0602_3

Gravemeijer, K. (2013). Revisiting ‘Mathematics education revisited.’ Freudental, 100(24), 106–113.

Gravemeijer, K., & Cobb, P. (2006). Design research from a learning design perspective. In Educational Design Research (pp. 17–51). Routledge. https://doi.org/10.4324/9780203088364-12

Gravemeijer, K., & Terwel, J. (2000). Hans Freudenthal: a mathematician on didactics and curriculum theory. Journal of Curriculum Studies, 32(6), 777–796. https://doi.org/https://doi.org/10.1080/00220270050167170

Hasbi, M., Lukito, A., & Sulaiman, R. (2019). Mathematical connection middle-school students 8th in realistic mathematics education. Journal of Physics: Conference Series, 1417(1), 12047. https://doi.org/DOI10.1088/1742-6596/1417/1/012047

Huang, R., Zhang, Q., Chang, Y., & Kimmins, D. (2019). Developing students’ ability to solve word problems through learning trajectory-based and variation task-informed instruction. ZDM, 51(1), 169–181.

Johar, R., Zubainur, C. M., & Hayati, R. (2020). A Study of Teachers’ Understanding about the Characteristics of Realistic Mathematics Education through Video. Journal of Education and Learning (EduLearn), 14(3). https://doi.org/DOI: 10.11591/edulearn.v14i3.8458

Jones, G. A., Langrall, C. W., & Mooney, E. S. (2007). Research in probability: Responding to classroom realities. Second Handbook of Research on Mathematics Teaching and Learning, 2, 909–955.

Kairuddin, K., Samosir, M. I., Sitorus, G. E., Sihotang, H. M. W., & Tanjung, J. Y. (2024). Penerapan Media Pembelajaran menggunakan Papan Peluang, Dadu, dan Multimedia Pembelajaran Interaktif dengan Pendekatan RME di SMA Swasta PAB 8 Saentis Percut. Mandalika Mathematics and Educations Journal, 6(2), 585–594. https://doi.org/DOI: 10.29303/jm.v6i2.7821

Khikmah, S. T. K., & Muttaqin, M. I. (2024). Pentingnya berilmu, bekerja keras, kreativitas, dan produktivitas serta metode pembelajarannya untuk sd/mi. Jurnal Ilmiah Multidisiplin Terpadu, 8(11).

Libka, J., & Adam, S. (2006). Mathematics in cultural contexts: salmon fishing investigation into probability. https://saruna.mnu.edu.mv/server/api/core/bitstreams/d19d2d29-064b-4633-819a-48c7bd038e3f/content

Matitaputty, C., Mataheru, W., & Talib, T. (2022). Analisis Kesalahan Mahasiswa Dalam Menyelesaikan Masalah Permutasi Dan Kombinasi. Jurnal Magister Pendidikan Matematika (JUMADIKA), 4(2), 43–49. https://doi.org/https://doi.org/10.30598

Mumu, J., & Tanujaya, B. (2019). Measure reasoning skill of mathematics students. International Journal of Higher Education, 8(6), 85–91. https://doi.org/10.5430/ijhe.v8n6p85

Niss, M., & Blum, W. (2020). The learning and teaching of mathematical modelling. Routledge. https://doi.org/https://doi.org/10.4324/9781315189314

Oehrtman, M., Swinyard, C., & Martin, J. (2014). Problems and solutions in students’ reinvention of a definition for sequence convergence. The Journal of Mathematical Behavior, 33, 131–148. https://doi.org/https://doi.org/10.1016/j.jmathb.2013.11.006

Pramartha, I. (2024). Pengembangan E-Modul Berbasis Realistic Mathematics Education untuk Meningkatkan Pemahaman Konsep dan Kemampuan Berpikir Kritis Mahasiswa ITB Stikom Bali pada Materi Fungsi. Universitas Pendidikan Ganesha. https://doi.org/https://repo.undiksha.ac.id/18589/

Putri, R. I. I. (2012). Pendisainan hypotetical learning trajectory (HLT) cerita Malin Kundang pada pembelajaran matematika. Prosiding Seminar Nasional Jurusan Pendidikan Matematika, 10. https://repository.unsri.ac.id/6791/1/MAKALAH_SEMNAS_UNY_RATUILMA_2012.pdf

Putri, S. M., Kartika, A. S., & Zuliana, E. (2024). Lintasan Belajar Siswa Kelas 6 Materi Data dan Peluang dengan Pendekatan PMRI Berkonteks Uang. Jurnal Ilmiah Profesi Guru (JIPG), 5(2), 157–165. https://doi.org/10.30738/jipg.vol5.no2.a16894

Rifa’i, A., & Anni, C. T. (2012). Psikologi pendidikan. Semarang: Pusat Pengembangan MKU/MKDK-LP3 Unnes.

Rochim, A. (2022). Analisis kesalahan siswa dalam menyelesaikan soal permutasi dan kombinasi berdasarkan kemampuan matematika di SMKN 1 Purwoasri. EDUCATOR: Jurnal Inovasi Tenaga Pendidik Dan Kependidikan, 2(3), 265–276. https://doi.org/https://doi.org/10.51878/educator.v2i3.1637

Rosa, M., Orey, D. C., Shirley, L., Palhares, P., Rosa, M., Orey, D. C., Rosa, M., Gavarrete, M. E., Alangui, W. V, & Rosa, M. (2016). State of the art in Ethnomathematics. In Current and future perspectives of ethnomathematics as a program (pp. 11–37). Springer. file:///Users/apple/Downloads/978-3-319-30120-4_3.pdf

Sari, D. L., Fitriani, D. A., Khaeriyah, D. Z., Hartono, H., & Nursyahidah, F. (2022). Hypothetical learning trajectory pada materi peluang: konteks mainan tradisional ular naga. Mosharafa: Jurnal Pendidikan Matematika, 11(2), 203–214. https://doi.org/https://doi.org/10.31980/mosharafa.v11i2.699

Sembiring, R. K. (2010). Pendidikan matematika realistik Indonesia (PMRI): Perkembangan dan tantangannya. Indonesian Mathematical Society Journal on Mathematics Education, 1(1), 11–16. https://download.garuda.kemdikbud.go.id/article.php?article=152182&val=5844&title=PENDIDIKAN MATEMATIKA REALISTIK INDONESIA PMRI PERKEMBANGAN DAN TANTANGANNYA

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/DOI: https://doi.org/10.30862/jhm.v7i3.698

Susanto, J., Laurens, T., & Tamalene, H. (2024). Pengembangan hypothetical learning trajectory pada materi luas persegi dan persegi panjang melalui pendidikan matematika realistik indonesia (pmri) di siswa kelas iv mis al-hilaal wanakarta. Jurnal Pendidikan Matematika Unpatti, 5(2), 79–87. https://doi.org/https://doi.org/10.30598/jpmunpatti.v5.i2.p79-87

Triliana, T., & Asih, E. C. M. (2019). Analysis of students’ errors in solving probability based on Newman’s error analysis. Journal of Physics: Conference Series, 1211(1), 12061. https://doi.org/10.1088/1742-6596/1211/1/012061

Ul-Haq, W. R. (2023). Pengaruh Model Realistic Mathematics Education Berbasis Etnomatematika Permainan Tradisional Terhadap Pemahaman Konsep Geometri Siswa. Jakarta: FITK UIN Syarif Hidayatullah Jakarta.

Van den Akker, J., Gravemeijer, K., & McKenney, S. (2006). Introducing educational design research. In Educational design research (pp. 15–19). Routledge.

Van den Heuvel-Panhuizen, M., & Drijvers, P. (2020). Realistic mathematics education. Encyclopedia of Mathematics Education, 713–717.

Widyastuti, N. S., & Pujiastuti, P. (2014). Pengaruh pendidikan matematika realistik indonesia (PMRI) terhadap pemahaman konsep dan berpikir logis siswa. Jurnal Prima Edukasia, 2(2), 183–193. https://doi.org/https://doi.org/10.21831/jpe.v2i2.2718

Ziliwu, F., Febri, F., Hidayatullah, M. A. N., & Subekti, R. (2024). Desain Pembelajaran pada Teori Dasar Peluang Menggunakan Permainan UNO: Usaha Meningkatkan Pemahaman Konsep Peluang. MUKADIMAH: Jurnal Pendidikan, Sejarah, Dan Ilmu-Ilmu Sosial, 8(1), 287–297. https://doi.org/https://doi.org/10.30743/mkd.v8i1.9203

Zubainur, C. M., Johar, R., Hayati, R., & Ikhsan, M. (2020). Teachers’ understanding about the characteristics of realistic mathematics education. Journal of Education and Learning (EduLearn), 14(3), 456–462. https://doi.org/10.11591/edulearn.v14i3.8458

Zulkardi, Z. (2002). Developing a learning environment on realistic mathematics education for Indonesian student teachers. University of Twente, Enschede.

Zulkardi, Z. (2013). Designing Joyful and Meaningful New School Mathematics Using Indonesian Realistic Mathematics Education. Southeast Asian Mathematics Education Journal, 3(1), 17–26. https://doi.org/10.46517/seamej.v3i1.22

Zulkardi, Z., Putri, R. I. I., & Wijaya, A. (2020). Two decades of realistic mathematics education in Indonesia. International Reflections on the Netherlands Didactics of Mathematics: Visions on and Experiences with Realistic Mathematics Education, 325–340. https://doi.org/https://doi.org/10.1007/978-3-030-20223-1




DOI: https://doi.org/10.53400/mimbar-sd.v12i4.95283

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