Online didactical design for subtraction fractions: A didactical design research through lesson study activities
DOI:
https://doi.org/10.33830/ijdmde.v1i1.7772Keywords:
fractions, learning barriers, online didactical design, didactical design research, lesson studyAbstract
The COVID-19 pandemic disrupted educational practices worldwide, posing significant challenges for students, particularly in mastering foundational mathematical concepts such as fraction subtraction. In response to the urgent need for effective remote learning strategies, this study aimed to develop and implement an online didactic design to reduce student learning obstacles. Employing a Didactical Design Research (DDR) approach, the design process was supported by lesson study activities at each developmental phase to ensure instructional quality. Participants included 56 students from grades VII and VIII (ages 13 to 18). The researcher served as the primary instrument, supported by additional tools including a fraction test, interview guide, documentation study, and the online didactic design itself. Thematic analysis was used to identify learning barriers, while qualitative analysis assessed the effectiveness of the design implementation. Findings revealed that during the pandemic, students experienced both ontogenic and epistemological learning obstacles in subtracting fractions. However, after the online didactic design was introduced and implemented, these learning barriers were no longer evident. Remaining difficulties were attributed to internal, non-instructional factors, such as limited personal study time, rather than issues related to instructional delivery. This study contributes to the field of mathematics education by providing an empirically grounded model for designing online instruction that addresses specific learning barriers. The findings underscore the importance of aligning didactic design with student learning needs, especially in crisis contexts, and highlight the potential of structured online approaches to support equitable mathematics learning.
References
Alhojailan, M. I., & Ibrahim, M. (2012). Thematic analysis: A critical review of its process and evaluation. West East Journal of Social Sciences, 1(2011), 8–21. https://faculty.ksu.edu.sa/sites/default/files/ta_thematic_analysis_dr_mohammed_alhojailan.pdf
Alsulami, N. M., Isnawan, M. G., Bahri, S., Pakhrurrozi, I., & Santosa, F. H. (2023). Meaning and learning fractions: analysis of learning barriers from a mathematics teacher's perspective. Polyhedron International Journal in Mathematics Education, 1(1), 7-14. https://doi.org/10.59965/pijme.v1i1.2
Arslan, S., Baran, D., & Okumus, S. (2011). Brousseau’s theory of didactical situations in mathematics and an application of adidactical situations. Necatibey Faculty of Education Electronic Journal of Sciene and Mathematics Education, 5(1), 204–224. https://www.academia.edu/813560/Brousseaus_Theory_of_Didactical_Situations_in_Mathematics_and_An_Application_of_Adidactical_Situations
Brousseau, G. (2002). Theory of didactical situations in mathematics. Kluwer Academic Publishers. https://id1lib.org/book/979725/fd6fae
Chen, X. I., & Li, Y. (2010). Instructional coherence in chinese mathematics classroom — a case study of lessons on fraction division. International Journal of Science and Mathematics Education, 8, 711–735. https://doi.org/10.1007/s10763-009-9182-y
Finkelstein, S., Sharma, U., & Furlonger, B. (2019). The inclusive practices of classroom teachers: a scoping review and thematic analysis. International Journal of Inclusive Education, 1–28. https://doi.org/10.1080/13603116.2019.1572232
Fitriati, F., Rosli, R., & Iksan, Z. H. (2023). Enhancing prospective mathematics teachers’ lesson planning skills through lesson study within school university partnership program. Journal on Mathematics Education, 14(1), 69–84. https://doi.org/10.22342/JME.V14I1.PP69-84
Gantina, I., & Herman, T. (2013). The Didactical Design of Fractions Addition Operation Using RME. The 2nd International Conference on Elementary Education, 2, 1779–1790. http://proceedings.upi.edu/index.php/icee/article/download/806/724
Huang, R., & Shimizu, Y. (2016). Improving teaching, developing teachers and teacher educators, and linking theory and practice through lesson study in mathematics: An international perspective. ZDM-Mathematics Education, 48(4), 393–409. https://doi.org/10.1007/s11858-016-0795-7
Isnawan, M. G., & Fakhrina, D. (2023). Perkembangan Kemampuan Pemecahan Masalah dan Motivasi Belajar Murid dalam Pembelajaran Pola Bilangan Geometri Selama Program KDS di SMP NW Mataram. Prosiding Seminar Nasional: Kemitraan Dosen Lembaga Pendidikan Tenaga Kependidikan (LPTK) Dengan Guru Di Sekolah Tahun 2023.
Isnawan, M. G., Sudirman, S., Sukarma, I. K., Wahyuni, F., & Alsulami, N. M. (2023). Optimizing students’ mathematical problem-solving abilities through geoboard-assisted didactic design on triangular number pattern material. Journal of Didactic Mathematics, 4(3), 200-213. https://doi.org/10.34007/jdm.v4i3.2073
Isnawan, M. G., Alsulami, N. M., Rusmayadi, M., Samsuriadi., Sudirman & Yanuarto, W. N. (2023). Analysis of student learning barriers in fractional multiplication: A hermeneutics phenomenology study in higher education. Edumatica: Jurnal Pendidikan Matematika, 13(1), 11–22. https://doi.org/https://doi.org/10.22437/edumatica.v13i01.24190
Isnawan, M. G., Suryadi, D., & Turmudi, T. (2022). How do secondary students develop the meaning of fractions? A hermeneutic phenomenological study. Beta: Jurnal, 15(1), 1–19. https://doi.org/10.20414/betajtm.v15i1.496
Isnawan, M. G., Suryadi, D., Turmudi, T., & Marfuah, M. (2022). Parental obstacles during distance learning mathematics in Indonesia: A phenomenology study. European Journal of Educational Research, 11(2), 873–883. https://doi.org/10.12973/eu-jer.11.2.873
Jarrah, A. M., Wardat, Y., & Gningue, S. (2022). Misconception on Addition and Subtraction of Fractions in Seventh-grade Middle School students. Eurasia Journal of Mathematics, Science and Technology Education, 18(6). https://doi.org/10.29333/ejmste/12070
Joubert, J., Callaghan, R., & Engelbrecht, J. (2020). Lesson study in a blended approach to support isolated teachers in teaching with technology. ZDM-Mathematics Education, 52, 907–925. https://doi.org/10.1007/s11858-020-01161-x
Kasim, F. F. (2017). Desain Didaktis Konsep Operasi Hitung Bilangan Pecahan pada Pembelajaran Matematika SMP [Universitas Pendidikan Matematika]. http://repository.upi.edu/28781/
Marfuah, M., Suryadi, D., Turmudi, T., & Isnawan, M. G. (2022). Providing online learning situations for in-service mathematics teachers’ external transposition knowledge during Covid-19 pandemic: Case of Indonesia. Electronic Journal of E-Learning, 20(1), 69–84. https://doi.org/10.34190/ejel.20.1.2388
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook. In SAGE Publications, Inc. https://id.id1lib.org/book/3593988/83e08f
Muhibban, M., Isnawan, M. G., & Aziz, A. (2023). Android-based Didactical Design for Learning Lines and Angles: An Interpretive Didactical Design Research. Polyhedron International Journal in Mathematics Education, 1(2), 106-118. https://doi.org/10.59965/pijme.v1i2.54
Nowell, L. S., Norris, J. M., White, D. E., & Moules, N. J. (2017). Thematic analysis: Striving to meet the trustworthiness criteria. International Journal of Qualitative Methods, 16, 1–13. https://doi.org/10.1177/1609406917733847
Parwadi, P., Susanta, A., & Muchlis, E. E. (2020). Analisis Kesalahan Siswa dalam Menyelesaikan Soal Matematika Materi Pecahan Kelas VII SMP Negeri 16 Kota Bengkulu. Jurnal Penelitian Pembelajaran Matematika Sekolah (JP2MS), 4(3), 442–454. https://doi.org/10.33369/jp2ms.4.3.442-454
Rianasari, V., & Julie, H. (2018). Secondary School Students’ Construction of Knowledge: the Case of Fractions Division. International Journal of Indonesian Education and Teaching, 2(2), 137–146. https://doi.org/10.24071/ijiet.2018.020205
Rønning, F. (2021). Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations. ZDM-Mathematics Education, 53(2), 305–316. https://doi.org/10.1007/s11858-020-01199-x
Singh, P., Hoon, T. S., Nasir, N. A. M., Han, C. T., Rasid, S. M., & Hoong, J. B. Z. (2021). Obstacles Faced by Students in Making Sense of Fractions. The European Journal of Social & Behavioural Sciences, 30(1), 34–51. https://doi.org/10.15405/ejsbs.287
Sollervall, H., & Iglesia, D. G. de la. (2016). Designing a Didactical Situation with Mobile and Web Technologies. CERME9, 2410–2417. https://hal.archives-ouvertes.fr/hal-01289292
Stewart, W. H., Baek, Y., & Lowenthal, P. R. (2022). From emergency remote teaching (ERT) to sustained remote teaching (SRT): A comparative semester analysis of exchange students’ experiences and perceptions of learning online during Covid-19. Online Learning Journal, 26(2), 170–197. https://doi.org/10.24059/olj.v26i2.2661
Sukarma, I. K., Isnawan, M. G., & Alsulami, N. M. (2024). Research on nonroutine problems: A hybrid didactical design for overcoming student learning obstacles. Human Behavior and Emerging Technologies, 2024, 1–12. https://doi.org/10.1155/2024/5552365
Sulistiawati, S., Suryadi, D., & Fatimah, S. (2015). Desain Didaktis Penalaran Matematis untuk Mengatasi Kesulitan Belajar Siswa SMP pada Luas dan Volume Limas. Kreano, Jurnal Matematika Kreatif-Inovatif, 6(2), 135. https://doi.org/10.15294/kreano.v6i2.4833
Suryadi, D. (2019a). Landasan filosofis penelitian desain didaktis (DDR). Pusat Pengembangan DDR Indonesia.
Suryadi, D. (2019b). Penelitian desain didaktis (DDR) dan implementasinya. Gapura Press.
Wahyu, K. (2021). How students understand smaller fractions divided by greater fractions? Beta: Jurnal Tadris Matematika, 14(1), 85–92. https://doi.org/10.20414/betajtm.v14i1.447
Widiawati, W., & Deniansyah, D. (2022). Desain Pembelajaran Penjumlahan dan Pengurangan Pecahan dengan Konteks Kaplet di Kelas VII. Jurnal Ilmiah Soulmath : Jurnal Edukasi Pendidikan Matematika, 10(1), 53–62. https://doi.org/10.25139/smj.v10i1.4552
Zhang, X., Clements, M. A. K., & Ellerton, N. F. (2014). Conceptual mis(understandings) of fractions: From area models to multiple embodiments. Mathematics Education Research Journal, 27(2), 233–261. https://doi.org/10.1007/s13394-014-0133-8
Zhou, L., Li, F., Wu, S., & Zhou, M. (2020). “School’s out, but class’s on”, the largest online education in the world today: Taking China’s practical exploration during the COVID-19 Epidemic prevention and control as an example. Best Evidence in Chinese Education, 4(2), 501–519. https://doi.org/10.15354/bece.20.ar023
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 R. Didi Kuswara, Essa Eqal Almazroei, Muhamad Galang Isnawan
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
