Study of Didactic Transposition: Exploration of Taught Knowledge in Revealing Learning Obstacles for Madrasah Students
Keywords:
Didactic Transposition, Learning Obstacle, Taught KnowledgeAbstract
Didactic transposition helps bridge the gap between formal mathematical knowledge and classroom instruction, ensuring more effective material delivery aligned with students’ needs. The purpose of this study was to explore how linear equations of one variable are taught to eighth-grade students at Madrasah Tsanawiyah based on the didactic transposition approach. This study focuses on the knowledge transfer stage of a didactic transposition study on linear equations of one variable, using qualitative research with a descriptive method. The study’s results showed that the presentation of material in the teaching and learning process led to a shift in understanding of linear equations of one variable from the concept of linear equations of one variable in a didactic context. Incomplete explanations of linear equations with one variable cause learning obstacles. Ontogenic obstacles arise from students’ cognitive limitations, epistemic obstacles from conceptual complexity, and didactic obstacles from ineffective teaching strategies. This study is conducted because didactic transposition can bridge the gap between formal mathematical knowledge and classroom instruction, yet it may also create learning obstacles. The findings can help improve teaching strategies by addressing conceptual gaps and learning obstacles, making mathematics instruction more effective for students at Madrasah Tsanawiyah.
References
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Ball, D. L., Thames, M. H., and Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational studies in mathematics, 79(1), 127-147. https://doi.org/10.1007/s10649-011-9333-2
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Ishak, H., Ardiana, A., Bakar, M. T., and Saputra, L. R. (2025). Analysis of Students’ Learning Obstacles in The Differential Equations Course Reviewed from Their Problem-Solving Ability. IJORER: International Journal of Recent Educational Research, 6(1), 139-153. https://doi.org/10.46245/ijorer.v6i1.738
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Asquith, P., Stephens, A. C., and Knuth, E. J. (2007). “Middle School Mathematics Teachers’ Knowlegde of Students’ Understanding of Core Algebraic Concepts: Equal Sign and Variable.” Journal of Mathematical Thinking and Learning, 9(3), 249-272. https://doi.org/10.1080/10986060701360910
Atteh, E., Andam, E. A., Amoako, J., Obeng–Denteh, W., and Wiafe, F. (2018). The Impact of Using Balance Model in Teaching Linear Equation. Archives of Current Research International, 11(3), 1–12. https://doi.org/10.9734/ACRI/2017/35310
Bakar, M. A. A., Ghani, A. T. A., and Abdullah, M. L. (2024). Discover Teacher’s Knowledge on Neuroscience and Mathematics Learning Relevancy via Fuzzy Conjoint Analysis: Study Case in Southern Malaysia. Malaysian Journal of Mathematical Sciences, 18(4). https://doi.org/10.47836/mjms.18.4.02
Ball, D. L., Thames, M. H., and Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554
Beswick, K. (2012). Teachers’ beliefs about school mathematics and mathematicians’ mathematics and their relationship to practice. Educational studies in mathematics, 79(1), 127-147. https://doi.org/10.1007/s10649-011-9333-2
Casi, R., and Garzetti, M. (2024). You Need a Map to Navigate a Teacher Education Programme: Analyzing the Informal Math Project through Conjecture Mapping. La matematica e la sua didattica, 32(2), 209-233. https://doi.org/10.6092/issn.3035-2940/20711
Chevallard Yves and Bosch, M. (2014). Didactic Transposition in Mathematics Education. In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 170–174). Springer Netherlands. https://doi.org/10.1007/978-94-007-4978-8_48
Chevallard Yves and Bosch, M. (2019). Anthropological Theory of the Didactic (ATD). In S. Lerman (Ed.), Encyclopedia of Mathematics Education (pp. 1–8). Springer International Publishing. https://doi.org/10.1007/978-3-319-77487-9_100034-1
De Mello, L. A. (2019). A propose of rules defining as a didactic transposition should occur or be achieved - the generalized didactic transposition theory. Retrieved from https://api.semanticscholar.org/CorpusID:214697563
Elkjær, M., and Thomsen, L. A. (2022). Adapting the balance model for equation solving to virtual reality. Digital Experiences in Mathematics Education, 8(2), 127-156. https://doi.org/10.1007/s40751-022-00103-4
Fardian, D., Suryadi, D., and Prabawanto, S. (2024). Students’ learning obstacles in solving mathematical proficiency tasks: A hermeneutic phenomenological study focused on algebra. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(2), 593–618 https://doi.org/10.15294/36aygs91
Fauzi, K. M. A., Hia, Y., Darari, M. B., and Siagian, M. D. (2024). Efforts to overcome students’ learning difficulties in geometry: A didactic design of creative thinking skills through metacognitive approaches. Beta: Jurnal Tadris Matematika, 17(2), 159-182. https://doi.org/10.20414/Betajtm.V17i2.648
Goos, M., Carreira, S., & Namukasa, I. K. (2023). Mathematics and interdisciplinary STEM education: Recent developments and future directions. ZDM–Mathematics Education, 55(7), 1199-1217. https://doi.org/10.1007/s11858-023-01533-z
Gupta, A., and Elby, A. (2011). Beyond epistemological deficits: Dynamic explanations of engineering students’ difficulties with mathematical sense-making. International Journal of Science Education, 33(18), 2463-2488. https://doi.org/10.1080/09500693.2010.551551
Hamash, M., Ghreir, H., and Tiernan, P. (2024). Breaking through barriers: A systematic review of extended reality in education for the visually impaired. Education Sciences, 14(4), 365. https://doi.org/10.3390/educsci14040365
Harisman, Y., Kusnandi, K., Kusumah, Y. S., and Noto, M. S. (2019). The Teachers’ Experience Background and Their Profesionalism. Infinity Journal, 8(2), 129-142. https://doi.org/10.22460/infinity.v8i2.p129-142
Hasina, A. N., Septiani, N., and Saripudin, S. N. R. (2021). Using a Contextual Approach to Improve Student Learning Outcomes in PLSV Material. Jurnal Riset Pendidikan Dan Inovasi Pembelajaran Matematika, 4(2), 93–102. https://doi.org/10.26740/jrpipm.v4n2.p93-102
Hendriyanto, A., Suryadi, D., Juandi, D., Dahlan, J. A., Hidayat, R., Wardat, Y., ... and Muhaimin, L. H. (2024). The Didactic Phenomenon: Deciphering Students’ Learning Obstacles in Set Theory. Journal on Mathematics Education, 15(2), 517-544. http://doi.org/10.22342/jme.v15i2.pp517-544
Ishak, H., Ardiana, A., Bakar, M. T., and Saputra, L. R. (2025). Analysis of Students’ Learning Obstacles in The Differential Equations Course Reviewed from Their Problem-Solving Ability. IJORER: International Journal of Recent Educational Research, 6(1), 139-153. https://doi.org/10.46245/ijorer.v6i1.738
Jupri, A., Drijvers, P., and van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710. https://doi.org/10.1007/s13394-013-0097-0
Kadarisma, G., and Amelia, R. (2018, December). Epistemological obstacles in solving equation of straight-line problems. In International Conference on Mathematics and Science Education of Universitas Pendidikan Indonesia (Vol. 3, pp. 905-910). Retrieved from http://science.conference.upi.edu/proceeding/index.php/ICMScE/issue/view/3
Kenney, S., & Ntow, F. D. (2024). Unveiling the Errors Learners Make When Solving Word Problems Involving Algebraic Task. Sage Open, 14(4). https://doi.org/10.1177/21582440241299245
Kluth, V., and Ag Almouloud, S. (2020). Didactic Transposition in Chevallard: primordial concepts and theorizing for the Antropological Theory of Didactics. Revista Eletrônica de Educação Matemática, 15, 22. https://doi.org/10.5007/1981-1322.2020.e72961
Lhachimi, M. Y., Mamouni, M. I., and Achtaich, N. (2022). The Didactic Balance: Simulation and Experimentation. Journal of Higher Education Theory and Practice, 22(9), 156-166. https://doi.org/10.33423/jhetp. v22i9
Lisnawati, L., and Nirmala, S. D. (2024). The Effectiveness of Differentiated Learning Strategies on Elementary Students’ Mathematical Critical Thinking Ability. AL-ISHLAH: Jurnal Pendidikan, 16(3), 3882-3895. https://doi.org/10.35445/alishlah.v16i3.5746
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. Zdm, 49(6), 937-949. https://doi.org/10.1007/s11858-017-0867-3
Malmqvist, J., Hellberg, K., Möllås, G., Rose, R., and Shevlin, M. (2019). Conducting the Pilot Study: A Neglected Part of the Research Process? Methodological Findings Supporting the Importance of Piloting in Qualitative Research Studies: International Journal of Qualitative Methods, 18, 1–11. https://doi.org/10.1177/1609406919878341
Maudy, S. Y., Suryadi, D., and Mulyana, E. (2017, August). Contextualizing symbol, symbolizing context. In AIP Conference Proceedings (Vol. 1868, No. 1, p. 050029). https://doi.org/10.1063/1.4995156
Mello, L. A. de. (2020). The Unification of Didactic Transposition Theory with the Didactic Situation Theory of Brousseau. Teacher Education and Curriculum Studies, 4(4), 65–75. https://doi.org/10.11648/j.tecs.20190404.12
Mengistie, S., M. (2020). Enhancing Students’ Understanding of Linear Equation With One Variable Through Teaching. International Journal of Trends in Mathematics Education Research, 3 (2), 69-80. https://doi.org/10.33122/ijtmer.v3i2.148
Moru, E. K. (2007). Talking with the Literature on Epistemological Obstacles. For the Learning of Mathematics, 27(3), 34–37. Retrieved from http://www.jstor.org/stable/40248586
Nadira, N., Muhammad, A., Tiew, F., Sian Hoon, T., Singh, P., Singh, A., Walida, S. El, & Faradiba, S. S. (2023). An Analysis of Students’ Understanding of Algebraic Concepts. Jurnal Pendidikan Sains Dan Matematik Malaysia, 13(2), 86–95. https://doi.org/10.37134/JPSMM.VOL13.2.8.2023
Namkung, J. M., and Bricko, N. (2021). The effects of algebraic equation solving intervention for students with mathematics learning difficulties. Journal of Learning Disabilities, 54(2), 111-123. 10.1177/0022219420930814
Nansiana, M. N., Usodo, B., and Fitriana, L. (2024). Analysis of Epistemological Obstacles Experienced by Indonesian Junior High School Students in Solving Mathematical Literacy Problems viewed from Algebraic Thinking Skills. Jurnal Pendidikan Progresif, 14(2), 1334-1354. https://doi.org/10.23960/jpp. v14.i2.202495
Ntow, F. D., Adom, G., Essel, S., & Kenney, S. (2024). Students’ Understanding of the Equal Sign when Solving Arithmetic Tasks. African Journal of Educational Studies in Mathematics and Sciences, 20(2), 293–306. Retrieved from https://www.ajol.info/index.php/ajesms/article/view/284576
Numonova, M. (2024). Visual Aids in Enhancing the Learning Process In English Language In A Private School (Akhmad Education). Qo‘Qon Universiteti Xabarnomasi, 13, 309–312. https://doi.org/10.54613/ku.v13i.1086
Nurhamsiah, H. and Dian, A. (2016). Analysis of Students’ Difficulties in Learning Algebraic Forms Related to Concepts and Principles in Junior High School. Khatulistiwa, 5(2), 20-28. http://dx.doi.org/10.26418/jppk.v5i2.13675
Nurjanah, P., and Angraini, L. M. (2024). Analysis of Students’ Mathematical Problem-Solving in Translating Story Problems into Mathematical Models. Progressive of Cognitive and Ability, 3(4), 230-250. https://doi.org/10.56855/jpr.v3i4.1105
Panjaitan, M. A., and Juandi, D. (2024). Analysis of Problems in Learning Mathematics Based on Difficulties, Errors, and Misconceptions in the Material of Equations and Inequality Absolute Values of One Variable: Systematic Literature Review. KnE Social Sciences, 316-324. 10.18502/kss. v9i13.15932
Pauji, I., Suryadi, D., Setambah, M. A. B. B., and Hendriyanto, A. (2023). Learning Obstacle in the Introduction to Number: A Critical Study Within Didactical Design Research Framework. Indonesian Journal of Science and Mathematics Education, 6(3), 430-451. http://dx.doi.org/10.24042/ijsme.v6i3.19792
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