A Didactical Design of Teaching Decimal Numbers for Fourth-Grade Elementary Students
DOI:
https://doi.org/10.37640/jip.v17i2.2458Keywords:
Decimal Numbers, Hypothetical Learning Trajectory, Learning ObstaclesAbstract
Learning obstacles to decimal concepts at the elementary level can hinder students' mathematical development in subsequent grades. A common difficulty lies in interpreting decimal values, which requires a well-structured instructional design to minimize these barriers. This study aims to develop a didactic design for teaching decimals based on an analysis of learning barriers and learning trajectories. Using Didactical Design Research (DDR), this study was conducted through three stages: prospective analysis, metapedadidactic analysis, and retrospective analysis. Data were collected through interviews, tests, documentation, and video recordings. Initially, learning barriers in ontogenic, epistemological, and didactic aspects were identified in fifth-grade students who had already learned decimals. Based on these findings, a Hypothetical Learning Trajectory was developed and implemented with 19 fourth-grade students who had not yet learned decimals. The results showed that the didactic design significantly improved students' ability to interpret decimals and strengthened their understanding of decimal operations. These findings underscore the importance of addressing learning obstacles in instructional design and recommend the integration of the DDR approach in mathematics teaching to enhance conceptual understanding from an early stage.
Downloads
References
Agustianingsih, A., Lusiana, L., & Kesumawati, N. (2021). Pengembangan Bahan Ajar Materi Kubus Berdasarkan Pendekatan Open Ended Berbantuan Geogebra. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(3), 1787–1796. https://doi.org/10.24127/ajpm.v10i3.4014
Andrews-Larson, C., Wawro, M., & Zandieh, M. (2017). A hypothetical learning trajectory for conceptualizing matrices as linear transformations. International Journal of Mathematical Education in Science and Technology, 48(6), 809–829. https://doi.org/10.1080/0020739X.2016.1276225
Baroody, A. J., Clements, D. H., & Sarama, J. (2022). Lessons Learned from 10 Experiments That Tested the Efficacy and Assumptions of Hypothetical Learning Trajectories. Education Siences, 12(195). https://doi.org/https://doi.org/10.3390/educsci12030195
Brousseau, G. (2002). Theory Of Didactical Situation In Mathematics. Kluwer Academic Publisher.
Deswita, D. (2016). Penerapan Metode Mind Maping untuk Meningkatkan Hasil Belajar Siswa Kelas 5 Mata Pelajaran Matematika di Sekolah Dasar. Jurnal Ilmu Pendidikan (JIP) STKIP Kusuma Negara, 8(1), 81–88.
Durkin, K., & Rittle-Johnson, B. (2015). Diagnosing Misconceptions: Revealing Changing Decimal Fraction Knowledge. Learning and Instruction, 37, 21–29. https://doi.org/https://doi.org/10.1016/j.learninstruc.2014.08.003
Fuadiah, N. F. (2016). Miskonsepsi Sebagai Hambatan Belajar Siswa Dalam Memahami Matematika. Jurnal Ilmu Pendidikan (JIP) STKIP, 7(2), 87.
Fuadiah, N. F. (2017). Hypothetical Learning Trajectory Pada Pembelajaran Bilangan Hypothetical L Earning T Rajectory of Negative Numbers Based on Theory of. Mosharafa, 6(1), 13–24. https://doi.org/https://doi.org/10.31980/mosharafa.v6i1.425
Fuadiah, N. F. (2021). Theory Of Didactical Situation (TDS), Kajian Karakteristik dan Penerapannya dalam Pembelajaran Matematika. Jurnal Pendidikan Matematika: Judika Education, 4(2), 160–169. https://doi.org/https://doi.org/10.31539/judika.v4i2.3054
Hendrik, A. I., Ekowati, C. K., & Samo, D. D. (2020). Kajian Hypothetical Learning Trajectories dalam Pembelajaran Matematika di Tingkat SMP. Fraktal: Jurnal Matematika Dan Pendidikan Matematika, 1(1), 1–11. https://doi.org/10.35508/fractal.v1i1.2683
Kuswidyanarko, A., & Pratama, A. (2020). Efektivitas Model Pembelajaran Cooperative Script dan Think Pair Share Berbantuan Worksheet Berbasis Karakter Pada Materi Pokok Bangun Datar. DWIJA CENDEKIA: Jurnal Riset Pedagogik, 4(1), 153–161. https://doi.org/10.20961/jdc.v4i1.41128
Lantakay, C. N., Senid, P. P., Blegur, I. K. S., & Samo, D. D. (2023). Hypothetical Learning Trajectory: Bagaimana Perannya dalam Pembelajaran Matematika di Sekolah Dasar? Griya Journal of Mathematics Education and Application, 3(2), 384–393. https://doi.org/10.29303/griya.v3i2.329
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). Thousand Oaks, CA: SAGE Publications
Muliaman, A. (2021). Efektivitas Model Project Based Learning Berorientasi eXe Learning dan Motivasi terhadap Hasil Belajar pada Materi Laju Reaksi. Jurnal Ilmu Pendidikan (JIP) STKIP Kusuma Negara, 13(1), 51–57. https://doi.org/10.37640/jip.v13i1.956
Downloads
Published
Issue
Section
License
Copyright (c) 2026 Nyiayu Fahriza Fuadiah, Nyiayu Fahriza Fuadiah, Yunika Lestaria Ningsih
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Authors agree that this article remains permanently open access under the terms of the Creative Commons Attribution-ShareAlike 4.0 International License
