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A learning trajectory as a sequence of mathematical activities that could facilitate the growth of students’ understanding of learning goals. This research aimed to produce an instructional sequence to learn the concepts of translation and reflection and to investigate how students develop their understanding informally using a South Sumatra dance context. The research employed the design research method, which consisted of three stages: preliminary design, design experiment (pilot experiment and teaching experiment), and retrospective analysis. This research involved six students who have the high, medium, low capability at the first cycle and 32 students ninth graders at the second cycle at Junior High School 1 Palembang. Data from observations, tests, interviews, and documentation were analyzed descriptively. The tests used were aimed to determine the improvement made by the students; while the classroom observations, interviews, and documentations were used to develop the local instructional theory. This study produced a learning trajectory with three activities include: the students watched a dance video to describe the dancer’s’ positions in relation to floor tiles; the students were asked to determine the starting points of the dancers in Cartesian coordinates to learn concepts; and the students developed a formal concept based on their own knowledge.


Design Research Local Instructional Theory Realistic Mathematics Education South Sumatra Dance Translation and Reflection

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Rawani, D., Putri, R. I. I., Zulkardi, & Susanti, E. (2023). RME-based local instructional theory for translation and reflection using of South Sumatra dance context. Journal on Mathematics Education, 14(3), 545–562.


  1. Akker, J. V., Gravemeijer, K. (2020). Introducing educational design research. In Educational Design Research.
  2. Albanese, V., & Perales, F. J. (2015). Enculturation with Ethnomathematical Microprojects: From Culture to Mathematics. Journal of Mathematics & Culture.
  3. Armiati, A., & Sari, R. P. (2022). Local Instructional Theory of Derivative Topics Based on Realistic Mathematics Education for Grade Xi Senior High School Students. Jurnal Pendidikan Matematika (JUPITEK), 5(2), 71–82.
  4. Bossé, M. J., Adu-Gyamfi, K., & Chandler, K. (2014). Students ’ Differentiated Translation Processes. International Journal for Mathematics Teaching and Learning.
  5. Brenda Pugh, M. (2006). Teaching Dance as Art in Education. In Human Kinetics. Human Kinetics.
  6. Cobb, P., Stephan, M., McClain, K., & Gravemeijer, K. (2010). Participating in Classroom Mathematical Practices. In A Journey in Mathematics Education Research.
  7. D’Ambrosio, U. (2016). An Overview of the History of Ethnomathematics.
  8. de Beer, H., Gravemeijer, K., & van Eijck, M. (2017). A proposed local instruction theory for teaching instantaneous speed in grade five. Mathematics Enthusiast.
  9. de Villiers, M. (2017). An explanatory, transformation geometry proof of a classic treasure-hunt problem and its generalization. In International Journal of Mathematical Education in Science and Technology.
  10. Ekowati, D. W., Kusumaningtyas, D. I., & Sulistyani, N. (2017). Ethnomathematica dalam Pembelajaran Matematika (Pembelajaran bilangan dengan Media Batik Madura, Tari Khas Trenggal dan tari Khas Madura). Jurnal Pemikiran Dan Pengembangan Sekolah Dasar (JP2SD).
  11. Ellis, A. B., Ozgur, Z., Kulow, T., Dogan, M. F., & Amidon, J. (2016). An Exponential Growth Learning Trajectory: Students’ Emerging Understanding of Exponential Growth Through Covariation. Mathematical Thinking and Learning.
  12. Fauzan, A., Yerizon, Y., & Yulianti, D. (2020). The RME-based local instructional theory for teaching LCM and GCF in primary school. Journal of Physics: Conference Series, 1554(1).
  13. Febrian, F., & Astuti, P. (2018). The RME principles on geometry learning with focus of transformation reasoning through exploration on Malay woven motif. Journal of Turkish Science Education.
  14. Fife, J. H., James, K., & Bauer, M. (2019). A Learning Progression for Geometric Transformations. ETS Research Report Series.
  15. Geitz, G., & de Geus, J. (2019). Design-based education, sustainable teaching, and learning. Cogent Education.
  16. Greer, B., Mukhopadhyay, S., Nelson-Barber, S., & Powell, A. B. (2009). Culturally responsive mathematics education. In Culturally Responsive Mathematics Education.
  17. Hariastuti, R. M., Negeri, U., Universitas, S., & Banyuwangi, P. (2021). Indonesian traditional dance: ethnomathematics on culture as a basis of learning mathematics in elementary schools. İlköğretim Online, 20(1), 936–947.
  18. Harper, S. (2003). Enhancing elementary pre-service teachers’ knowledge of geometric transformations through the use of dynamic geometry computer software. SITE 2003--Society for Information Technology & Teacher Education International Conference.
  19. Hermiati, K., Suprihatiningsih, S., & Annurwanda, P. (2021). Visual Thinking Ability of Mathematics Education Students on Geometry Transformation Learning Material. AlphaMath : Journal of Mathematics Education.
  20. Isnawan, M. G., & Wicaksono, A. B. (2018). Model Desain Pembelajaran Matematika. Indonesian Journal of Mathematics Education.
  21. Iyengar, M. K. (2015). Bharatanatyam and Mathematics: Teaching Geometry Through Dance. Journal of Fine and Studio Art.
  22. Khusniati, M., Parmin, & Sudarmin. (2017). Local wisdom-based science learning model through reconstruction of indigenous science to improve student’s conservationist character. Journal of Turkish Science Education.
  23. Kohar, A. W., Wardani, A. K., & Fachrudin, A. D. (2019). Profiling context-based mathematics tasks developed by novice PISA-like task designers. Journal of Physics: Conference Series.
  24. Lester, F. K. (2007). Second handbook of research on mathematics teaching and learning: a project of the National Council of Teachers of Mathematics. Mathematics Teaching.
  25. Lumpkin, A. (2020). Effective Teaching and Learning—A Five-Step Process. Journal of Education and Culture Studies.
  26. Ma’Rifah, N., Widada, W., Aida, A., Yulfitri, Y., & Effendi, J. (2019). The students’ mathematics understanding through ethnomathematics based on kejei dance. Journal of Physics: Conference Series, 1318(1).
  27. Maryati, M., & Pratiwi, W. (2019). Etnomatematika: Eksplorasi dalam Tarian Tradisional pada Pembukaan ASIAN GAMES 2018. FIBONACCI: Jurnal Pendidikan Matematika Dan Matematika.
  28. McCuthen. (2006). Teaching Dance as Art in Education. Human Kinetics.
  29. McKenney, S., & Reeves, T. C. (2014). Educational design research. In Handbook of Research on Educational Communications and Technology: Fourth Edition.
  30. Mulwa, E. C. (2015). Difficulties encountered by students in the learning and usage of mathematical terminology: A critical literature review. Journal of Education and Practice.
  31. Nuraida, I., & Amam, A. (2019). Hypothethical Learning Trajectory in Realistic Mathematics Education to Improve the Mathematical Communication of Junior High School Students. Infinity Journal.
  32. Prahmana, R. C. I., & D’Ambrosio, U. (2020). Learning geometry and values from patterns: Ethnomathematics on the batik patterns of yogyakarta, indonesia. Journal on Mathematics Education.
  33. Putri, R. I. I., & Zulkardi. (2017). Fraction in shot-put: A learning trajectory. AIP Conference Proceedings.
  34. Putri, R. I. I., & Zulkardi. (2020). Designing piSA-like mathematics task using Asian games context. Journal on Mathematics Education.
  35. Putri, R. I. I., & Zulkardi, -. (2018). Noticing Students’ Thinking and Quality of Interactivity During Mathematics Learning.
  36. Radiusman, R., Wardani, K. S. K., Apsari, R. A., Nurmawanti, I., & Gunawan, G. (2021). Ethnomathematics in Balinese Traditional Dance: A Study of Angles in Hand Gestures. Journal of Physics: Conference Series.
  37. Rawani, D., Ilma Indra Putri, R., & Susanti, E. (2023). The Reflective Teaching Practices using PMRI and Collaborative Learning. Jurnal Pendidikan Matematika, 17(1), 69–88.
  38. Rawani, D., Putri, R. I. I., & Hapizah. (2019). PISA-like mathematics problems: Using taekwondo context of Asian games. Journal on Mathematics Education.
  39. Sari, A., & Putri, R. I. I. (2021). Inductive Reasoning Ability of Students Using the Palembang Songket Fabric Context in Rotational Learning in Grade IX. Jurnal Pendidikan Matematika.
  40. Seah, W. T. (2018). Improving Mathematics Pedagogy Through Student/Teacher Valuing: Lessons from Five Continents.
  41. Sembiring, R. K., Hadi, S., & Dolk, M. (2008). Reforming mathematics learning in Indonesian classrooms through RME. ZDM - International Journal on Mathematics Education.
  42. Siemon, D. (2021). Learning progressions/trajectories in mathematics: Supporting reform at scale. Australian Journal of Education.
  43. Simon, M. A., & Tzur, R. (2004). Explicating the Role of Mathematical Tasks in Conceptual Learning: An Elaboration of the Hypothetical Learning Trajectory. Mathematical Thinking and Learning.
  44. Susanti, E., Hapizah, H., Meryansumayeka, M., & Irenika, I. (2019). Mathematical thinking of 13 years old students through problem-solving. Journal of Physics: Conference Series.
  45. Thaqi, X., & Gimenez, J. (2012). Prospective Teacher ’ S Understanding of. 10(3), 2328–2335.
  46. Trung, N. T., Thao, T. P., & Trung, T. (2019). Realistic mathematics education (RME) and didactical situations in mathematics (DSM) in the context of education reform in Vietnam. Journal of Physics: Conference Series.
  47. Uygun, T. (2020). An inquiry-based design research for teaching geometric transformations by developing mathematical practices in dynamic geometry environment. Mathematics Education Research Journal.
  48. Van den Heuvel-Panhuizen, M., & Drijvers, P. (2014). Realistic Mathematics Education. In Encyclopedia of Mathematics Education.
  49. Wilson, P. H., Sztajn, P., Edgington, C., & Myers, M. (2015). Teachers’ Uses of a Learning Trajectory in Student-Centered Instructional Practices. Journal of Teacher Education.
  50. Yanik, H. B., & Flores, A. (2009). Understanding rigid geometric transformations: Jeff’s learning path for translation. Journal of Mathematical Behavior.
  51. Yuanita, P., Zulnaidi, H., & Zakaria, E. (2018). The effectiveness of Realistic Mathematics Education approach: The role of mathematical representation as mediator between mathematical belief and problem solving. PLoS ONE.
  52. Zulkardi. (2002). Developing A Learning Environment on Realistic Mathematics Education for Indonesian Student Teachers. Thesis University of Twente, Enschede. - With Refs. - With Summary in Ducth ISBN 90 365 18 45 8 Subject.
  53. Zulkardi, & Putri, R. I. I. (2019). New School Mathematics Curricula, PISA and PMRI in Indonesia.
  54. Zulkardi, Z., Putri, R. I. I., & Wijaya, A. (2020). Two Decades of Realistic Mathematics Education in Indonesia.

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