Profile of Students' Conceptual Understanding of Geometric Transformation Material Reviewed from Students' Learning Readiness
DOI:
https://doi.org/10.30587/didaktika.v32i1.11400Keywords:
understanding of mathematical concepts, Learning readiness, geometric transformationAbstract
This study aims to describe students' conceptual understanding of geometric transformation material in the explanation and application aspects, viewed from their learning readiness. The type of research used is descriptive qualitative with 3 students in the medium learning readiness category selected from 35 students in grade XI.8 of SMAN 1 Gresik. The selection of subjects with developing learning readiness, because in each class is dominated by students with that level of readiness. Data collection was carried out through cognitive diagnostic assessments to determine the level of student learning readiness, especially mastery of prerequisite materials. Formative tests in the form of Student Worksheets and application tests to obtain conceptual understanding data supported by semi-structured interview guidelines. Data analysis techniques refer to qualitative research types, which include data reduction, data presentation, and drawing conclusions. The results showed that students with developing learning readiness were able to meet all indicators in the explanation aspect (accurate, justified, systematic), but in the application aspect only some students met the effective indicator, and only one student met the fluent indicator. The subject with the best ability showed mastery of geometric transformation steps in a structured and logical manner, while the other subjects still experienced difficulties in calculating matrices and applying concepts fluently. The results of this study recommend that teachers provide more problems to apply mathematical concepts after students discover them through guided discovery activities. Conceptual understanding significantly influences application skills, so learning that begins with students' own construction of concepts will contribute to a strong conceptual understanding.
References
Armutcu, Y., & Bal, A. P. (2023). The Effect of Mathematical Modelling Activities on Students’ Mathematical Modelling Skills in the Context of STEM Education. International Journal of Contemporary Educational Research, 10(1). https://doi.org/10.33200/ijcer.1131928
Aseptianova, A., Nawawi, S., & Pesisa, L. (2019). Analisis Pemahaman Konsep Siswa Pada Materi Pencemaran Lingkungan Di Sma Negeri 4 Palembang. Bioilmi: Jurnal Pendidikan, 5(1), 59–65. https://doi.org/10.19109/bioilmi.v5i1.3540
Asterhan, C. S. C., & Resnick, M. S. (2020). Refutation texts and argumentation for conceptual change: A winning or a redundant combination? Learning and Instruction, 65. https://doi.org/10.1016/j.learninstruc.2019.101265
Azizah, N., Budiyono, B., & Siswanto, S. (2021). Students’ Conceptual Understanding In Terms Of Gender Differences. Journal of Mathematics and Mathematics Education, 11(1). https://doi.org/10.20961/jmme.v11i1.52746
Barta, A., Fodor, L. A., Tamas, B., & Szamoskozi, I. (2022). The development of students critical thinking abilities and dispositions through the concept mapping learning method – A meta-analysis. In Educational Research Review (Vol. 37). https://doi.org/10.1016/j.edurev.2022.100481
Braithwaite, D. W., & Sprague, L. (2021). Conceptual Knowledge, Procedural Knowledge, and Metacognition in Routine and Nonroutine Problem Solving. Cognitive Science, 45(10). https://doi.org/10.1111/cogs.13048
Dessie, E., Gebeyehu, D., & Eshetu, F. (2024). Motivation, conceptual understanding, and critical thinking as correlates and predictors of metacognition in introductory physics. Cogent Education, 11(1). https://doi.org/10.1080/2331186X.2023.2290114
Don, H. J., Goldwater, M. B., & Livesey, E. J. (2023). Cognition of relational discovery: why it matters for effective far transfer and effective education? In Frontiers in Psychology (Vol. 14). https://doi.org/10.3389/fpsyg.2023.957517
Etikan, I., Musa, S. abubakar, & Alkassim, R. S. (2016). Comparison of Convenience Sampling and Purposive Sampling. American Journal of Theoretical and Applied Statistics, 5(1), 1. https://doi.org/10.11648/j.ajtas.20160501.11
Eviana, M. (2023). Penerapan Pembelajaran Berdiferensiasi Untuk Meningkatkan Pemahaman Konsep Luas Permukaan Bangun Ruang Dan Mengatasi Kejenuhan Pada Siswa Kelas Vi a Sdi Labat Kota Kupang Tahun Pelajaran 2021/2022. Jurnal Lazuardi, 6(1), 1–23. https://doi.org/10.53441/jl.vol6.iss1.79
Fauziyah, N., & Rahma, Z. N. (2025). Analysis of student’s mathematical problem-solving ability with moderate learning readiness based on Polya’s theory. Research and Development in Education (RaDEn), 5(1). https://doi.org/10.22219/raden.v5i1.39567
Fauziyah, N., & Wahyunita, E. N. (2025). Constructing the Concept of Geometric Transformation through APOS Theory: A Perspective on Learning Readiness. Edumatica : Jurnal Pendidikan Matematika, 15(2). https://doi.org/10.22437/edumatica.v15i2.43166
Gusteti, M. U., & Neviyarni. (2022). Pembelajaran Berdiferensiasi Pada Pembelajaran Matematika Di Kurikulum Merdeka. Jurnal Ilmiah Pendidikan Matematika, Matematika Dan Statistika, 3(3), 170–184. https://doi.org/10.46306/lb.v3i3.180
Hidayat, S. R., & Warmi, A. (2024). Analisis Kesulitan Belajar Matematika Siswa SMP Dalam Menyelesaikan Soal Cerita SPLDV Syiva Restiani Hidayat Attin Warmi Analysis of Middle School Students ’ Mathematics Learning Difficulties in Solving SPLDV Story Problems pelajaran yang ditetapkan oleh. 6379, 484–495.
Jäder, J., & Johansson, H. (2025). Exploring students’ conceptual understanding through mathematical problem solving: students’ use of and shift between different representations of rational numbers. Research in Mathematics Education. https://doi.org/10.1080/14794802.2025.2456840
Jannah, R., Fauziyah, N., & Huda, S. (2022). Analisis Pemahaman Konsep Matematika Smp Dalam Pembelajaran Berdiferensiasi Pada Proses Berdasarkan Perbedaan Gaya Belajar. AdMathEdu : Jurnal Ilmiah Pendidikan Matematika, Ilmu Matematika Dan Matematika Terapan, 12(2).
Komariyah, S., Afifah, D. S. N., & Resbiantoro, G. (2018). Analisis Pemahaman Konsep Dalam Memecahkan Masalah Matematika Ditinjau Dari Minat Belajar Siswa. SOSIOHUMANIORA: Jurnal Ilmiah Ilmu Sosial Dan Humaniora, 4(1), 1–8. https://doi.org/10.30738/sosio.v4i1.1477
Lestari, D. P., & Palupi, E. L. W. (2023). Representasi Matematis Siswa dalam Menyelesaikan Masalah Teorema Pythagoras berdasarkan Tahapan Polya Ditinjau dari Perbedaan Gender. MATHEdunesa, 12(2). https://doi.org/10.26740/mathedunesa.v12n2.p588-610
Makramalla, M., Coles, A., le Roux, K., & Wagner, D. (2025). Mathematics education for sustainable futures: a strengths-based survey of the field to invite further research action. Educational Studies in Mathematics, 119(3). https://doi.org/10.1007/s10649-025-10389-x
Mayasari, D., & Habeahan, N. L. S. (2021). the Ability of Students’ Conceptual Understanding in Completing Story Problems on Mathematics. Jurnal Pendidikan Matematika Dan IPA, 12(2), 123. https://doi.org/10.26418/jpmipa.v12i2.43354
Miles, M. B., Huberman, A. M., & Saldaña, J. (2016). Qualitative Data Analysis: A Methods Sourcebook (3rd ed.). In Educacao e Sociedade (Vol. 1, Issue 1).
Miles, M., Huberman, A., & Saldaña, J. (2018). Qualitative data analysis: A methods sourcebook.
Nugraha, M. G., Kidman, G., & Tan, H. (2024). Interdisciplinary STEM education foundational concepts: Implementation for knowledge creation. Eurasia Journal of Mathematics, Science and Technology Education, 20(10). https://doi.org/10.29333/ejmste/15471
Qomari, M. N., Lestari, S. A., & Fauziyah, N. (2022). Learning Trejectory pada Pembelajaran Berdiferensiasi Materi Keliling Bangun Datar Berdasarkan Perbedaan Gaya Belajar. DIDAKTIKA: Jurnal Pemikiran Pendidikan, 28(2(1)), 29–41. https://doi.org/10.30587/didaktika.v28i2(1).4399
Rahadi, I. W. S., Wikanta, I. M. I. A., Suardika, K. W., & Umam, E. K. (2023). Panduan
Pembelajaran Matematika dengan Pendekatan Understanding by Design (M. Hidayat & M. A. U. Islamiah (eds.)). Penerbit P4I, 2023.
Rajadurai, R., & Ganapathy, H. (2023). Effect of use of metacognitive instructional strategies in promoting mathematical problem solving competence amongst undergraduate students in facing competitive examination. Cogent Social Sciences, 9(1). https://doi.org/10.1080/23311886.2023.2173103
Safitri, S., Muharrami, L. K., Hadi, W. P., & Wulandari, A. Y. R. (2021). Faktor Penting Dalam Pemahaman Konsep Siswa Smp: Two-Tier Test Analysis. Natural Science Education Research, 4(1), 45–55. https://doi.org/10.21107/nser.v4i1.8150
Salsabila, A. N. A., Fauziyah, N., & Huda, S. (2024). Pengembangan Media Pembelajaran Matematika Berbasis Android dalam Pembelajaran Berdiferensiasi di SMPN 1 Mantup. Ideguru: Jurnal Karya Ilmiah Guru, 9(2), 925–931. https://doi.org/10.51169/ideguru.v9i2.990
Santos-Trigo, M. (2024). Problem solving in mathematics education: tracing its foundations and current research-practice trends. ZDM - Mathematics Education, 56(2). https://doi.org/10.1007/s11858-024-01578-8
Sugiyono. (2012). Metode Penelitian Kuantitatif, Kualitatif, dan R&D (17th ed.). Alfabeta.
Tomlinson, C. A. (2017). Differentiated instruction. In Fundamentals of Gifted Education Routledge., 279–292.
Vlachopoulos, D., & Makri, A. (2024). A systematic literature review on authentic assessment in higher education: Best practices for the development of 21st century skills, and policy considerations. Studies in Educational Evaluation, 83. https://doi.org/10.1016/j.stueduc.2024.101425
Wiggins, G., & McTighe, J. (2005). Understanding By Design.
Wong, S. S. H. (2023). Deliberate Erring Improves Far Transfer of Learning More Than Errorless Elaboration and Spotting and Correcting Others’ Errors. Educational Psychology Review, 35(1). https://doi.org/10.1007/s10648-023-09739-z
Yanti, R., Laswadi, L., Ningsih, F., Putra, A., & Ulandari, N. (2019). Penerapan pendekatan saintifik berbantuan geogebra dalam upaya meningkatkan pemahaman konsep matematis siswa. AKSIOMA: Jurnal Matematika Dan Pendidikan Matematika, 10(2), 180–194. https://doi.org/10.26877/aks.v10i2.4399
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