TRANSPOSISI DIDAKTIK KONSEP TURUNAN FUNGSI: PRADETEKSI LEARNING OBSTACLE PADA SISWA SMA
Keywords:
konsep turunan, learning obsctacle, transposisi DidaktikAbstract
Abstrak
Penelitian ini bertujuan untuk menganalisis transposisi didaktik internal dan eksternal konsep turunan fungsi pada siswa SMA. Penelitian ini adalah penelitian kualitatif yang merupakan studi awal dari serangkaian proses penelitian desain didaktik (DDR). Penelitian transposisi didaktik ini merupakan bagian dari tahap pertama dalam penelitian DDR yakni analisis prospektif, yaitu 1) analisis buku teks matematika kelas XII dalam bentuk analisis prakseologi buku teks dan 2) analisis situasi didaktik dalam bentuk hasil wawancaran dengan guru dan analisis buku catatan siswa dalam bentuk analisis prakseologi didaktik guru. Hasil penelitian menunjukkan bahwa baik buku teks maupun situasi didaktik pembelajaran guru keduanya belum sistematis karena sajian pengetahuan dalam keduanya tidak sesuai urutannya dengan sajian pengetahuan dalam buku matematika scientific knowledge dan belum epistemik karena siswa tidak dilibatkan secara langsung untuk mengkontruksi pengetahuaannya sendiri untuk mendapatkan pengetahuan yang justified true belief sehingga berpeluang membuat siswa mengalami learning obstacle (LO), baik itu LO epistemik, LO ontogenik, maupun LO didaktik. Penelitian ini diharapkan memberikan kontribusi untuk memperluas kajian transposisi didaktik pada materi kalkulus sekolah yang berpeluang menimbulkan learning obstacle pada siswa dan kelanjutannya digunakan sebagai referensi dalam merancang desain didaktik baru pada materi turunan fungsi di sekolah menengah atas.
Kata Kunci: konsep turunan, learning obstacle, transposisi Didaktik,
Abstract
This study aims to analyze the internal and external didactic transposition of the concept of derivative functions in high school students. This research is a qualitative study which is the initial study of a series of didactic design research (DDR) processes. This didactic transposition research is part of the first stage in the DDR research, namely prospective analysis, namely 1) analysis of grade XII mathematics textbooks in the form of textbook praxeology analysis and 2) analysis of didactic situations in the form of interview results with teachers and analysis of student notebooks in the form of teacher didactic praxeology analysis. The results of the study indicate that both textbooks and the didactic situation of teacher learning are not systematic because the presentation of knowledge in both is not in accordance with the sequence of presentation of knowledge in scientific knowledge mathematics books and is not epistemic because students are not directly involved in constructing their own knowledge to obtain knowledge that is justified true belief so that it has the potential to make students experience learning obstacles (LO), both epistemic LO, ontogenic LO, and didactic LO. This study is expected to contribute to expanding the study of didactic transposition in school calculus material that has the potential to cause learning obstacles in students and its continuation is used as a reference in designing new didactic designs on function derivative material in high school.
Keywords: derivative concept, didactic Transposition,, learning obstacle.
References
Abou-Hayt, A. 2026. A critical look at the anthropological theory of the didactic. Research in Mathematics Education, 28(1), 3–24. https://doi.org/10.1080/14794802.2024.2344754
Aniswita, A., Sepriyanti, N., & Medika, G. H. (2024). Unravelling undergraduate mathematics students’ understanding of derivatives. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 9(4), 262–272. https://doi.org/10.23917/jramathedu.v9i4.11267
Azzahra, N., Isnaini, P., Nur Karimah Nst, S., & Natalia, C. (2025). Analisis Miskonsepsi Turunan Fungsi pada Buku Matematika SMA : Definisi Turunan, Visual Grafik, dan Contoh Soal. Pendas : Jurnal Ilmiah Pendidikan Dasar, 10(3), 260–271. https://doi.org/https://doi.org/10.23969/jp.v10i03.33292
Bintara, A., & Prabawanto, S. (2024). Learning Obstacles of Junior High School Students on the Concept of Triangle. International Conference On Mathematics And Science Education, KnE Social Sciences, 500–509. https://doi.org/10.18502/kss.v9i13.15952
Bosch, M., & Gascón, J. (2014). Introduction to the Anthropological Theory of the Didactic (ATD). Dalam Networking of Theories as a Research Practice in Mathematics Education, Advances in Mathematics Education (hlm. 67–83). Springer International Publishing Switzerland. https://doi.org/10.1007/978-3-319-05389-9_5
Bressoud, D., Ghedamsi, I., Martinez-Luaces, V., & Törner, G. (2016). Teaching and Learning of Calculus ICME-13 Topical Surveys (13 ed.). Springer Nature. http://www.springer.com/series/14352
Byerley, C. (2019). Calculus students’ fraction and measure schemes and implications for teaching rate of change functions conceptually. Journal of Mathematical Behavior, 55. https://doi.org/10.1016/j.jmathb.2019.03.001
Chandra, F. E., Suryadi, D., Dahlan, J. A., Hayuningrat, S., & Rahman, S. (2025). Derivative in Indonesian textbook curricula: A praxeological analysis of learning obstacles in Indonesian mathematics textbooks. Eurasia Journal of Mathematics, Science and Technology Education, 21(5). https://doi.org/10.29333/ejmste/16256
Chevallard, Y. (2019). Introducing The Anthropological Theory of The Didactic: An Attempt At A Principled Approach. Hiroshima Journal Of Mathematics Education, 12, 71–114.
https://doi.org/10.24529/hjme.1205
DÃaz, J. L. (2024). Integrating the anthropological theory of didactics in multivariate calculus education: Challenges, pedagogical shifts, and innovative activities. International Electronic Journal of Mathematics Education, 19(1). https://doi.org/10.29333/iejme/14142
Fardian, D., Suryadi, D., & Prabawanto, S. (2025). A praxeological analysis of linear equations in Indonesian mathematics textbooks: Focusing on systemic and epistemic aspect. Journal on Mathematics Education, 16(1), 225–254. https://doi.org/10.22342/jme.v16i1.pp225-254
Fitriasari, P., Suryadi, D., Nurlaelah, E., Suhendra, S., Hermanto, H., & Ningsih, Y. L. (2026). A didactical transposition study on secondary students’ number sense of integers. Frontiers in Education, 11. https://doi.org/10.3389/feduc.2026.1739073
Ismayanti, S., Jatisunda, M. G., & Hoon, T. S. (2025). Didactic transposition of trigonometric ratios: A comparative study of school and university textbooks. Journal on Mathematics Education, 16(4), 1283–1312. https://doi.org/10.22342/jme.v16i4.pp1283-1312
Mutia, Kartono, Dwijanto, & Wijayanti. (2023). Students’ Mathematical Creative Thinking Obstacle and Scaffolding in Solving Derivative Problems. Journal of Higher Education Theory and Practice, 23(17). https://doi.org/10.33423/jhetp.v23i17.6540
Ozaltun-Celik, A. (2021). A calculus student’s understanding of graphical approach to the derivative through quantitative reasoning. LUMAT, 9(1), 892–916. https://doi.org/10.31129/LUMAT.9.1.1663
Prihandhika, A., Prabawanto, S., Turmudi, T., & Suryadi, D. (2020). Epistemological Obstacles: An Overview of Thinking Process on Derivative Concepts by APOS Theory and Clinical Interview. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032028
Quezada, V. nica D. az. (2020). Difficulties and performance in mathematics competences: Solving problems with derivatives. International Journal of Engineering Pedagogy, 10(4), 35–53. https://doi.org/10.3991/ijep.v10i4.12473
Syaputra, M., Juandi, D., Kusnandi, K., & Ayuningtias Elsa, H. (2024). Exploring Student Errors in Solving Derivative Problems: A Systematic Literature Review. Jurnal Pendidikan MIPA, 25(4), 1693–1704. https://doi.org/10.23960/jpmipa/v25i4.pp1693-1704
Sawitri, Z. A., Fuadiah, N. F., & Tanzimah. (2020). Analisis Learning Obstacle pada Materi Volume Limas. Indiktika: Jurnal Inovasi Pendidikan Matematika, 3, 16–25. https://jurnal.univpgri-palembang.ac.id/index.php/indiktika/article/view/4930
Siagian, M. D., Suryadi, D., Nurlaelah, E., & Sufyani, P. (2022). Investigation of Secondary Students’ Epistemological Obstacles in the Inequality Concept. Mathematics Teaching Research Journal Fall, 14(4), 106–128. https://eric.ed.gov/?id=EJ1361657
Suryadi, D. (2023). Jalan Epistemik Menghasilkan Pengetahuan melalui Didactical Design Research (DDR). Pusat Pengembangan DDR Indonesia (PUSBANGDDRINDO).
Tesfamicael, S. A., & Lundeby, Ø. A. (2019). A comparative study of Norwegian and Ethiopian textbooks: The case of relations and functions using anthropological theory of didactics (ATD). Universal Journal of Educational Research, 7(3), 754–765. https://doi.org/10.13189/ujer.2019.070315
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2015). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 89(1), 41–65. https://doi.org/10.1007/s10649-015-9595-1
Zamanabadi, S., & Rafiepour, A. (2026). Application of Anthropological Theory oF Didactic in Teaching of Mathematics. Mathematics and Society 11(1), 25–41. https://doi.org/10.22108/msci.2025.143082.1718
Published
Issue
Section
License
Authors who publish with AKSIOMA: Jurnal Program Studi Pendidikan Matematika agree to the following terms:
Creative Commons License
AKSIOMA:Â Jurnal Program Studi Pendidikan Matematika is licensed under a Creative Commons Attribution 4.0 International License.
This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. AKSIOMA offers all authors of journal articles allows their research openly available, free access and time restrictions.
All articles published Open Access will be immediately and permanently free for everyone to read and download. Under the CC-BY license, authors retain ownership of the copyright for their article, but authors grant others permission to use the content of publications in AKSIOMA in whole or in part provided that the original work is properly cited. Users (redistributors) of AKSIOMA are required to cite the original source, including the author's names, AKSIOMA as the initial source of publication, year of publication, volume number and DOI (if available).
