Learning Design for Translation Concepts Using Bola Kasti Games

Anadia Muli Mariela 1 Indonesia , Zulkardi 1 Indonesia , Ely Susanti 1 Indonesia , Meryansumayeka 1 Indonesia
1 Department of Mathematics Education, Faculty of Teacher Training and Education, Sriwijaya University
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Published 2026-03-26
Vol. 6 No. 1 (2026) PAGES 420 - 442
DOI 10.51574/kognitif.v6i1.4383
Views / Downloads 96 103

Students often struggle to grasp geometric transformation concepts, particularly translation. Although some students can recognize object movement visually, conceptual misconceptions persist in interpreting the meaning of displacement, along with difficulties in representing movement visually using Cartesian diagrams. This condition indicates the need for a more contextually and meaningfully grounded learning approach that connects mathematical concepts with activities familiar to students. In this study, the traditional game of bola kasti is employed as an effective learning medium, serving as a cultural activity that is relevant and closely related to students’ experiences. The traditional bola kasti game functions not merely as a contextual illustration but is systematically designed as a conceptual transition tool that bridges physical activities and formal coordinate representations in the concept of translation. This research aims to develop a learning trajectory using the PMRI approach, incorporating the context of the bola kasti game to support students in constructing a deep understanding of the concept of translation. The research employed a design research methodology with a validation study type, involving 32 ninth-grade students from SMP Negeri 52 Palembang. Data collection techniques included student activity sheets, classroom observations, and interviews, which were analyzed descriptively using a qualitative approach. The findings indicate that the Actual Learning Trajectory (ALT) aligns with the designed Hypothetical Learning Trajectory (HLT). Therefore, the developed HLT is considered successful and contributes to the development of a Local Instructional Theory (LIT) in enhancing students’ conceptual understanding progressively, as demonstrated by students’ ability to identify the direction and magnitude of translation and to represent translations using Cartesian diagrams through the PMRI approach with the context of the bola kasti game in translation learning.

Mariela, A. M., Zulkardi, Z., Susanti, E., & Meryansumayeka, M. (2026). Learning Design for Translation Concepts Using Bola Kasti Games. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 6(1), 420–442. https://doi.org/10.51574/kognitif.v6i1.4383
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  1. Doorman, M. (2019). Design and research for developing local instruction theories. Avances de Investigación En Educación Matemática, (15), 29–42. https://doi.org/10.35763/aiem.v0i15.266
  2. Faiza Izzati Mufti, & Tian Abdul Aziz. (2024). Desain Pembelajaran Matematika Topik Transformasi Geometri dengan Pendekatan Realistic Mathematics Education Berbasis Etnomatematika. Algoritma : Jurnal Matematika, Ilmu Pengetahuan Alam, Kebumian Dan Angkasa, 2(4), 115–129. https://doi.org/10.62383/algoritma.v2i4.102
  3. Fajria Septiani, P. Y. (2024). Pembelajaran Dengan Etnomatematika Dalam Meningkatkan Pemahaman Konsep Matematika Abstrak. Inovasi Pendidikan, 11(1). https://doi.org/10.31869/ip.v11i1.5649
  4. Fauziah, A., Putri, R. I. I., Zulkardi, Z., & Somakim. (2020). Pembelajaran PMRI Melalui Lesson Study (Cetakan I). Bening.
  5. Fitra, D. (2018). Penerapan Pendidikan Matematika Realistik Indonesia (PMRI) dalam Pembelajaran Matematika. JURNAL INOVASI EDUKASI, 1(1), 1–7. https://doi.org/10.35141/jie.v1i1.27
  6. Gravemeijer, K., & Cobb, P. (2006). Educational Design Research (J. Van den Akker, K. Gravemeijer, S. McKenney, & N. Nieveen, Eds.). Routledge. https://doi.org/10.4324/9780203088364
  7. Hamidah, I., Zulkardi, Z., Putri, R. I. I., Susanti, E., & Nusantara, D. S. (2024). Hypothetical Learning Trajectory Design In Reflection Learning Using The Context Of The Cirebon Red Mosque. Jurnal Pendidikan Matematika (JUPITEK), 7(1), 1–10. https://doi.org/10.30598/jupitekvol7iss1pp1-10
  8. Lestari, A. A. P., Nugroho, A. A., & Nursyahidah, F. (2021). Desain Pembelajaran Refleksi dan Translasi Berkonteks Klenteng Sam Poo Kong Semarang. Jurnal Elemen, 7(2), 381–393. https://doi.org/10.29408/jel.v7i2.3400
  9. Luvy Sylviana Zanthy, F. I. M. (2020). Analisis Kesulitan Siswa Dalam Menyelesaikan Soal Materi Transformasi Geometri. Gammath : Jurnal Ilmiah Program Studi Pendidikan Matematika, 5(1), 16–25. https://doi.org/10.32528/gammath.v5i1.3189
  10. Ni’matul Ula, V., & Hadi, S. (2023). Kemampuan Translasi Representasi Siswa pada Materi Aljabar Berdasarkan Tingkat Kemampuan Matematis Kelas VIII MTs PSM Tanen. Jurnal Penelitian Pendidikan Dan Pengajaran Matematika, 9(1), 69–80. https://doi.org/10.37058/jp3m.v7i1.5487
  11. Nizar Rangkuti, A., & Ibrahim Siregar, A. (2019). Lintasan Belajar Teorema Pythagoras dengan Pendekatan Pendidikan Matematika Realistik. In Jurnal Ilmu-ilmu Pendidikan dan Sains (Vol. 7). https://doi.org/10.24952/logaritma.v7i02.2112
  12. Novianti, I., Dimpudus, A., & Azainil. (2025). Transformasi Geometri dalam Pola Lantai Tari Dayak (Flying High). Jurnal Pemikiran Dan Penelitian Pendidikan Matematika (JP3M), 8(1), 120–134. https://doi.org/10.36765/jp3m.v8i1.770
  13. Nur, M. A. (2025). Meta Analisis Pengaruh Permainan Tradisional terhadap Hasil Belajar Matematika Siswa Sekolah Dasar di Indonesia. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 5(2), 494–505. https://doi.org/10.51574/kognitif.v5i2.2921
  14. Nurmaya, R. (2021). Pengembangan Bahan Ajar Berbasis Etnomatematika Pada Materi Transformasi Geometri. RANGE: Jurnal Pendidikan Matematika, 2(2), 123–129. https://doi.org/10.32938/jpm.v2i2.941
  15. Nursyahidah, F., Saputro, B. A., & Albab, I. U. (2020). Learning reflection through the context of Central Java historical building. Journal of Physics: Conference Series, 1567(2), 022095. https://doi.org/10.1088/1742-6596/1567/2/022095
  16. Plomp, Tj., & Nieveen, Nienke. (2013). Educational design research. Part A : an introduction. SLO.
  17. Putri, R. I. I., Dolk, M., & Zulkardi, Z. (2015). Professional Development Of Pmri Teachers For Introducing Social Norms. Journal on Mathematics Education, 6(1), 11–19. https://doi.org/10.22342/jme.6.1.1900.11-19
  18. Rosyada, A., Zulkardi, Z., Susanti, E., & Meryansumayeka, M. (2025). Learning Design in Translation Topic with Cinema Context for 9th Grade Students. SJME (Supremum Journal of Mathematics Education), 9(2), 215–231. https://doi.org/10.35706/sjme.v9i2.194
  19. Rusdi, Fauzan, A., Arnawa, I. M., & Lufri. (2020). Designing Mathematics Learning Models Based on Realistic Mathematics Education and Literacy. Journal of Physics: Conference Series, 1471(1), 012055. https://doi.org/10.1088/1742-6596/1471/1/012055
  20. Sam, F., Alam, S., & Patmaniar, P. (2025). Developing an Ethnomathematics-Based Transformational Geometry Textbook to Enhance Students’ Mathematical Literacy. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 5(4), 1653–1664. https://doi.org/10.51574/kognitif.v5i4.3860
  21. Samaran, M., Ratuanik, M., & Kewilaa, D. M. (2024). Analisis Kemampuan Representasi Matematis Peserta Didik Pada Materi Translasi Di Kelas Xi Sma Negeri 2 Kepulauan Tanimbar. In Sora Journal of Mathematics Education Mei. https://doi.org/10.30598/sora.5.1.65-76
  22. Sari, D. I., & Sari, N. (2019). Pengembangan Perangkat Pembelajaran Berbasis Realistic Mathematics Education Pada Materi Aritmatika Sosial. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 8(2), 310. https://doi.org/10.24127/ajpm.v8i2.1954
  23. Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM, 40(6), 927–939. https://doi.org/10.1007/s11858-008-0125-9
  24. Surgandini, A., Sampoerno, P. D., & Noornia, A. (2019). Pengembangan pembelajaran dengan pendekatan pmri berbantuan geogebra untuk membangun pemahaman konsep transformasi geometri. Prima: Jurnal Pendidikan Matematika, 3(2), 85. https://doi.org/10.31000/prima.v3i2.932
  25. Surya, S., Ikram, M., & Jumarniati, J. (2021). Kegagalan Dan Kesalahan Siswa Dalam Melakukan Translasi Antar Representasi Untuk Masalah Laju Perubahan. LINEAR: Journal of Mathematics Education, 57. https://doi.org/10.32332/linear.v2i2.3737
  26. Tamimi, H., Syawahid, M., & Nasrullah, A. (2025). Pengaruh Model Pembelajaran Realistic Mathematics Education (RME) terhadap Kemampuan Literasi Matematis Siswa pada Materi Statistika. Kognitif: Jurnal Riset HOTS Pendidikan Matematika, 5(3), 1066–1077. https://doi.org/10.51574/kognitif.v5i3.3540
  27. Van Zanten, M., & Van den Heuvel-Panhuizen, M. (2021). Mathematics Curriculum Reform and Its Implementation in Textbooks: Early Addition and Subtraction in Realistic Mathematics Education. Mathematics, 9(7), 752. https://doi.org/10.3390/math9070752
  28. Walid, A., Ilma Indra Putri, R., Susanti, E., Mulyono, B., & Sulthan Thaha Saifuddin Jambi, U. (2025). Designing a PMRI-Based Learning Trajectory for Algebraic Forms Using the Iftar Context. Jurnal Pendidikan Matematika, 15. https://doi.org/10.22437/edumatica.vl5i2.44218
  29. Wasilah Wasilah, Iltavia Iltavia, & Meli Amelia. (2023). Analisis Kesulitan Siswa Dalam Menyelesaikan Soal Materi Transformasi Di Kelas Xi Mipa Sman 1 Kecamatan Kapur IX. ALFIHRIS : Jurnal Inspirasi Pendidikan, 1(1), 177–189. https://doi.org/10.59246/alfihris.v1i1.130
  30. Zaini, A., & Marsigit, M. (2014). Perbandingan Keefektifan Pembelajaran Matematika Dengan Pendekatan Matematika Realistik Dan Konvensional Ditinjau Dari Kemampuan Penalaran Dan Komunikasi Matematik Siswa. Jurnal Riset Pendidikan Matematika, 1(2), 152. https://doi.org/10.21831/jrpm.v1i2.2672
  31. Zulkardi, & Putri, R. I. I. (2019). New School Mathematics Curricula, PISA and PMRI in Indonesia (pp. 39–49). https://doi.org/10.1007/978-981-13-6312-2_3

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Keywords
Learning Design Hypothetical Learning Trajectory (HLT) Translation PMRI