DEVELOPING LOCAL INSTRUCTION THEORY FOR LEARNING PERMUTATION USING REALISTIC MATHEMATICS EDUCATION
DOI:
https://doi.org/10.33603/e.v11i4.12148Kata Kunci:
permutation, local instruction theory, design research, realistic mathematics educationAbstrak
Permutation is fundamental topic in combinatorics that support students’ understanding of probability, statistics, and mathematical reasoning. However, many students experience difficulties in distinguishing permutation from combination and in applying counting principles in contextual situations. This study aims to develop a local instruction theory (LIT) for learning permutation based on the Realistic Mathematics Education (RME) approach. The research employed design research consisting of three phases: preliminary design, teaching experiment, and retrospective analysis. The participants were senior high school students in Indonesia. Data were collected through observations, student worksheet, interviews, and classroom documentation. The results indicate that the developed learning trajectory supports students in constructing permutation concepts gradually from informal strategies toward formal mathematical representation. The learning trajectory includes contextual exploration, modelling using diagrams and tables, pattern recognition, generalization, and application of permutation formulas. The findings suggest that the developed LIT can facilitate students’ conceptual understanding and mathematical modelling abilities. This study contributes to mathematics education research by providing a theoretically grounded instructional design for teaching permutation.
Referensi
Bakker, A., Cai, J., & Zenger, L. (2021). Future themes of mathematics education research: an international survey before and during the pandemic. Educational Studies in Mathematics, 107(1). https://doi.org/10.1007/s10649-021-10049-w
Batanero, C., Navarro-Pelayo, V., & Godino, J. D. (1997). Effect Of The Implicit Combinatorial Model On Combinatorial Reasoning In Secondary School Pupils. Educational Studies in Mathematics, 32, 181–199.
Cahyadi, M. H., & Noto, M. S. (2023). Desain Bahan Ajar Berbasis Geogebra pada Kemampuan Pemahaman Matematis dengan Materi Geometri Transformasi SMK. Euclid, 10(1), 22. https://doi.org/https://doi.org/10.33603/e.v10i1.8495
Fitriawan, D., Siregar, N., & Sulistyowati, E. (2023). Learning Design For Combinatoric With Realistic Mathematics Education Approach. Jurnal Pendidikan MIPA, 24(3), 594–602. https://doi.org/10.23960/jpmipa/v24i1.pp594-602
Gravemeijer, K., & Cobb. (2006). Educational Design Research.
Gravemeijer, K. P. E., Cobb, P., Bowers, J., & Whitenack, J. (2012). Symbolizing, modeling, and instructional design. In Symbolizing and communicating in mathematics classrooms.
Sari, S. komala. (2017). Pengembangan Desain Pembelajaran Statistika Berbasis IT Menggunakan Pendekatan Realistic Mathematics Education Untuk Kelas VIII SMP. Jurnal Nasional Pendidikan Matematika), 1(2), 290–304.
Lamanna, L., Gea, M. M., & Batanero, C. (2022). Do Secondary School Students’ Strategies in Solving Permutation and Combination Problems Change with Instruction? Canadian Journal of Science, Mathematics and Technology Education, 22(3), 602–616. https://doi.org/10.1007/s42330-022-00228-z
Leung, F. K. S. , Stillman, G. A. , Kaiser, G. , & Wong, K. L. (2021). Mathematical Modelling Education in the Cultural Contexts of West and East. International Perspectives on the Teaching and Learning of Mathematical Modelling. Springer. https://doi.org/https://doi.org/10.1007/978-3-030-66996-6_1
Lockwood, E. (2013). A model of students’ combinatorial thinking. Journal of Mathematical Behavior, 32(2), 251–265. https://doi.org/10.1016/j.jmathb.2013.02.008
Marina Angraini, L. (2020). Desain Didaktis Penalaran Matematis pada Mata Kuliah Konsep Dasar Matematika. Euclid, 7(1), 1–76. https://doi.org/https://doi.org/10.33603/e.v7i1.2638
Meika, I., Suryadi, D., & Darhim. (2019a). Developing Local Instruction Theory for Learning Combinations. Infinity Journal, 8(2), 157–166. https://doi.org/10.22460/infinity.v8i2.p157-166
Meika, I., Suryadi, D., & Darhim, D. (2019b). Analysis of students’ mathematical modelling ability in solving combination problems using local instruction theory teaching materials. Journal of Physics: Conference Series, 1157(4). https://doi.org/10.1088/1742-6596/1157/4/042082
Ningtyas, Y. D. W. K., Galatea, C. K., Ishartono, N., & Adikalan, N. H. (2023). Learning Trajectory for Learning Multiplication Rules with Islamic Values using Realistic Mathematics Education Approach. VYGOTSKY, 5(2), 123. https://doi.org/10.30736/voj.v5i2.835
Nopriana, T., & Dwi Rosita, C. (2018). Desain Bahan Ajar Perbandingan Berbasis Pemahaman Matematis. Jurnal Euclid, 5(2), 1–122. https://doi.org/https://doi.org/10.33603/e.v5i2.1331
Ryandi, R. B., Somakim, S., & Susanti, E. (2018). Learning Combinations Through “Handshake.” International Journal on Emerging Mathematics Education, 2(1), 105. https://doi.org/10.12928/ijeme.v2i1.8693
Somakim, Darmawijoyo, & Eliyati, N. (2018). Learning Design of Combinatory Using Indonesian Realistic Mathematics Education. In Journal of Physics: Conference Series, 160(1).
Somakim, Darmawijoyo, Eliyati, N., & Yulianita. (2019). Design of mathematics learning by using role playing to investigate the self-efficacy ability. Journal of Physics: Conference Series, 1166(1). https://doi.org/10.1088/1742-6596/1166/1/012034
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