Integrasi Soal Nonrutin dalam Perkuliahan Pemecahan Masalah Matematika: Studi Reflektif Pengajaran Integration of Non-Routine Problems in Mathematics Problem-Solving Lectures: A Reflective Study of Teaching
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1701-1711
Digital Object Identifier:
10.58578/yasin.v6i2.9452
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Authors:Ulil Nurul Imanah1*, Fran Susanto2
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Abstract
The low level of university students’ mathematical problem-solving ability remains a challenge in learning, particularly due to the dominance of routine problems, which limits strategic flexibility and hinders the development of metacognitive awareness in dealing with complex problems. This study aims to analyze the impact of integrating non-routine problems, particularly mathematics olympiad problems, into the Mathematical Problem Solving course through a reflective teaching study design. This study used a qualitative approach involving four students in the mathematics education study program over one semester. Data were collected through student worksheets, classroom observations, reflective journals, as well as assessments using a rubric based on heuristic stages encompassing understanding the problem, planning a strategy, carrying out the solution, and reflecting. Data analysis was conducted using an interactive model strengthened by descriptive quantitative indicators. The results showed improvement at all stages of the problem-solving process. The students demonstrated better ability in identifying problem structures, selecting and adjusting strategies, evaluating the effectiveness of solutions, and reflecting on their thinking processes. In addition, there were improvements in strategic flexibility, metacognitive regulation, intellectual perseverance, and the quality of mathematical argumentation. This study concludes that the systematic integration of non-routine problems is effective in developing reflective problem-solving ability. The implications of this study emphasize the importance of using non-routine problems as a pedagogical strategy in mathematics teacher education to develop critical, adaptive, and reflective thinking skills.
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References
Boaler, J. (2016). Mathematical mindsets: Unleashing students’ potential through creative mathematics. Jossey-Bass.
Cai, J., & Lester, F. K. (2017). Problem solving and reasoning in mathematics education. Journal for Research in Mathematics Education, 48(2), 1–14.
Depaepe, F., De Corte, E., & Verschaffel, L. (2015). Students’ non-routine mathematical problem solving. ZDM Mathematics Education, 47(6), 1–12.
Hendriana, H., Johanto, T., & Sumarmo, U. (2018). The role of problem-based learning to improve students’ mathematical problem-solving ability and self-confidence. Journal on Mathematics Education, 9(2), 291–300. https://doi.org/10.22342/jme.9.2.5394.291-300
Henningsen, M., & Stein, M. K. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematics Education, 28(5), 524–549. https://doi.org/10.2307/749690
Hiebert, J., & Grouws, D. A. (2007). The effects of classroom mathematics teaching on students’ learning. In F. K. Lester, Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 371–404). Information Age Publishing.
Juandi, D., Tamur, M., & Paloloang, B. (2020). Meta-analysis: The effect of problem-based learning on students’ mathematical literacy ability in Indonesia. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(4), 851–864. https://doi.org/10.24127/ajpm.v9i4.3049
Kapur, M. (2016). Examining productive failure. Educational Psychologist, 51(2), 289–299. https://doi.org/10.1080/00461520.2016.1155457
Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM Mathematics Education, 49, 937–949. https://doi.org/10.1007/s11858-017-0867-3
Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (2nd ed.). Pearson.
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed.). SAGE.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all.
Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9–28. https://doi.org/10.1007/s10649-019-09903-9
OECD. (2019). PISA 2018 results (Volume I): What students know and can do. OECD Publishing. https://doi.org/10.1787/5f07c754-en
Polya, G. (1973). How to solve it (2nd ed.). Princeton University Press.
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press.
Schoenfeld, A. H. (2016). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics (Reprint). Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Silver, E. A. (2015). Mathematical problem solving: An overview. Journal of Mathematical Behavior, 37, 1–15.
Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum. Journal of Mathematical Behavior, 24(3–4), 341–350.
Stylianides, A. J. (2018). Argumentation in mathematics education: Research and practice. Educational Studies in Mathematics, 98(3), 1–18.
Sumarmo, U. (2013). Berpikir dan disposisi matematik serta pembelajarannya. UPI Press.
Yeo, K. K. (2017). Students’ difficulties in mathematical problem solving. Journal of Mathematical Behavior, 45, 1–12.
Zimmerman, B. J. (2002). Becoming a self-regulated learner: An overview. Theory Into Practice, 41(2), 64–70. https://doi.org/10.1207/s15430421tip4102_2