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Learning Transformation Geometry (TG) needs a more informal approach to concern situational problems. This study aims to develop actionable knowledge of TG in the form of design related to context and yet general enough to use digital manipulative activities in new situations. We propose such knowledge in the form of conjectured Local Instructional Theory (LIT) in the framework of design research methodological framework. The designed learning activities were based on Realistic Mathematics Education (RME) principles and used batik as the context and van Hiele’s mode of geometric thought. In addition, the CorelDraw software is used as a tool to transform batik-making activities into a digital manipulative environment. The design consists of a pre-assessment and four learning activities. The data were analyzed retrospectively in accordance with the HLT. The analysis of the data described above and the justification of the processes during the teaching experiment indicate a compelling trajectory for students learning transformation geometry for this specific context and the prospect for future studies.


Batik Design Research Local Instructional Theory Realistic Mathematics Education

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How to Cite
Sahara, S., Dolk, M., Hendriyanto, A., Kusmayadi, T. A., & Fitriana, L. (2024). Transformation geometry in eleventh grade using digital manipulative batik activities. Journal on Mathematics Education, 15(1), 55–78.


  1. Ada, T., & Kurtuluş, A. (2010). Students’ misconceptions and errors in transformation geometry. International Journal of Mathematical Education in Science and Technology, 41(7), 901-909.
  2. Badan Standar Kurikulum dan Asesmen Pendidikan. (2022). Capaian Pembelajaran Mata Pelajaran Matematika Fase A - Fase F. Kementrian Pendidikan Dan Kebudayaan Riset Dan Teknologi Republik Indonesia, 1–36.
  3. Bakker, A. (2004). Design research in statistics education: On symbolizing and computer tools. In Igitur-Archive.Library.Uu.Nl.
  4. Bakker, A., & Smit, J. (2018). Design Research in Education (pp. 255–271). Routledge.
  5. Cobb, P., Zhao, Q., & Visnovska, J. (2008). Learning from and Adapting the Theory of Realistic Mathematics education. Éducation Et Didactique, 2–1, 105–124.
  6. Crowley, M. (1987). The van Hiele model of the development of geometric thought. Learning and Teaching Geometry, K-12, 1–16. van Hiele Model of the Development of Geometric Thought.pdf
  7. Depdiknas. (2006). Permendiknas No 22 Tahun 2006 Tentang Standar Isi. Jakarta: Depdiknas.
  8. Evbuomwan, D. (2013). An investigation into the difficulties faced by Form C students in the learning of transformation geometry in Lesotho secondary schools. Doctoral Dissertation. South Africa: University of South Africa.
  9. Freudenthal, H. (1973). The Case of Geometry. In: Mathematics as an Educational Task. Dordrecht: Springer.
  10. Gast, R. H. (1971). The High School Geometry Controversy: Is Transformation Geometry the Answer? The Mathematics Teacher, 64(1), 37–40.
  11. Gravemeijer, K. (2020). Emergent Modeling: an RME Design Heuristic Elaborated in a Series of Examples. Journal of the International Society for Design and Development in Education, 4(13), 1–31.
  12. Gravemeijer, K., & Cobb, P. (2006). Educational Design Research Educational Design Research. Netherlands Institute for Curriculum Development: SLO, 11.
  13. Gravemeijer, K., & Stephan, M. (2002). Emergent Models as an Instructional Design Heuristic. In: Gravemeijer, K., Lehrer, R., Van Oers, B., Verschaffel, L. (eds). Symbolizing, Modeling and Tool Use in Mathematics Education. Mathematics Education Library, vol 30. Springer, Dordrecht.
  14. Hasanah, U. (2023). Innovation of Mathematics Learning Models and Media in Elementary Schools in Kurikulum Merdeka Belajar. KnE Social Sciences, 255–265.
  15. Hollebrands, K. F. (2003). High school students’ understandings of geometric transformations in the context of a technological environment. The Journal of Mathematical Behavior, 22(1), 55-72.
  16. Isnanto, R. R., Hidayatno, A., & Zahra, A. A. (2020, June). Fractal batik motifs generation using variations of parameters in julia set function. In 2020 8th International Conference on Information and Communication Technology (ICoICT) (pp. 1-6). IEEE.
  17. Martin, G. E. (2012). Transformation geometry: An introduction to symmetry. Springer Science & Bussiness Media.
  18. Mashingaidze, S. (2012). The teaching of geometric (isometric) transformations at secondary school level: What approach to use and why? Asian Social Science, 8(15), 197–210.
  19. Mbusi, N. (2015). Misconceptions and Related Errors Displayed By Pre-Service Foundation Phase Teachers in Transformation Geometry. Luneta, 386–400.
  20. NCTM. (2020). NCTM Standards ( 2020 ) – Secondary ( Initial Preparation ). NCTM Standards - Positions, 1–6.
  21. Ngirishi, H., & Bansilal, S. (2019). An exploration of high school learners’ understanding of geometric concepts. Problems of Education in the 21st Century, 77(1), 82–96.
  22. Noerhasmalina., & Khasanah, B. A. (2023). The geometric contents and the values of local batik in Indonesia. Jurnal Elemen, 9(1), 211-226.
  23. Plomp, T. (2013). Introduction to Educational Design Research: An Introduction. An Introduction to Educational Design Research - Part A, 11–50.
  24. 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, 11(3), 439–456.
  25. Pratikno, Y., Hermawan, E., & Arifin, A. L. (2022). Human Resource ‘Kurikulum Merdeka’from Design to Implementation in the School: What Worked and What not in Indonesian Education. Jurnal Iqra’: Kajian Ilmu Pendidikan, 7(1), 326–343.
  26. Putri, R. I. I., & Dolk, M., Zulkardi, Z. (2015). Professional Development of Pmri Teachers for. IndoMS-JME : Journal on Mathematics Education, 6(1), 11–19.
  27. Rellensmann, J., Schukajlow, S., & Leopold, C. (2020). Measuring and investigating strategic knowledge about drawing to solve geometry modelling problems. ZDM, 52, 97-110.
  28. Simon, M. A. (1995). Reconstructing Mathematics Pedagogy from a Constructivist Perspective. Journal for Research in Mathematics Education, 26(2), 114–145.
  29. Simon, M. A., Placa, N., Avitzur, A., & Kara, M. (2018). Promoting a concept of fraction-as-measure: A study of the Learning Through Activity research program. Journal of Mathematical Behavior, 52(March), 122–133.
  30. Sinclair, N., & Bruce, C. D. (2015). New opportunities in geometry education at the primary school. ZDM Mathematics Education, 47(3), 319–329.
  31. Toole, T. O. (2001). Building Powerful Understanding by Connecting Informal and Formal Knowledge. 384–391.
  32. Treffers, A. (1987). Integrated column arithmetic according to progressive schematisation. Educational studies in Mathematics, 18(2), 125-145.
  33. Trimurtini., Waluya, S. B., Sukestiyarno, Y. L., & Kharisudin, I. (2021). A Systematic Review on Geometric Thinking: A Review Research Between 2017-2021. European Journal of Educational Research, 11(1), 69–81.
  34. Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. In CDASSG Project.
  35. Van den Heuvel-panhuizen, M., Drijvers, P., Education, M., Sciences, B., & Goffree, F. (2020). Encyclopedia of Mathematics Education. Encyclopedia of Mathematics Education.
  36. Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic press.
  37. Vojkuvkova, I. (2012). The van Hiele model of geometric thinking. WDS’12 Proceedings of Contributed Papers, 1, 72-75.
  38. Walukow, M. R., Naharia, O., Wullur, M. N., Sumual, S. D. M., & Monoarfa, H. (2023). Implementation of Merdeka Belajar Policy: Constraints in the Pancasila Students Profile Strengthening Project. International Journal of Multidisciplinary Approach Research and Science, 1(02), 104–116.
  39. Zidan, M. R., & Qamariah, Z. (2023). A Literature study on the implementation of merdeka curriculum. Jurnal Riset Rumpun Ilmu Bahasa, 2(2), 153–167.
  40. Zulkardi. (2002). Developing A Learning Environment On Realistic Mathematics Education For Indonesian Student Teacher (Doctoral disertation, University of Twente, Enschede). 1–218.

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