Bagaimana Berpikir Kreatif Termanifestasi dalam Komunikasi Matematis Siswa pada Penyelesaian Masalah Geometri Dua Dimensi: Perspektif Commognitive
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Abstract
Mathematical communication skills and creative thinking are two essential aspects of mathematics learning; however, studies examining how creative thinking is manifested within mathematical communication remain limited. This study aims to describe how creative thinking is manifested in students’ mathematical communication when solving two-dimensional geometry problems from a commognitive perspective. This research employed a qualitative approach with a single-case study design. The research subject was one student who demonstrated a variety of strategies in solving contextual 2D geometry problems. Data were collected through written tasks and semi-structured interviews, and were analyzed based on the components of commognitive discourse, namely the use of mathematical terms, visual representations, argumentative narratives, and solution patterns. The findings indicate that creative thinking is manifested through variations in representation, flexibility of strategies, originality in constructing arguments, and elaboration of mathematical explanations. These findings suggest that creativity can be identified through the structure of students’ mathematical communication and contribute theoretically to the integration of creativity within mathematical discourse analysis.
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References
Fujita, T., Kaur, B., & Jones, K. (2020). Students’ reasoning in geometry: Recent developments and emerging issues. ZDM–Mathematics Education, 52(1), 1–13. https://doi.org/10.1007/s11858-020-01136-5
Granberg, C., & Olsson, J. (2021). Creativity and reasoning in mathematics: An empirical analysis of students’ solution strategies. Journal of Mathematical Behavior, 62, 100846.
Herbel-Eisenmann, B., Steele, M. D., & Cirillo, M. (2017). (Developing) teacher discourse moves: A framework for professional development. For the Learning of Mathematics, 37(2), 29–34.
Hodges, T. E., & Cady, J. A. (2019). Supporting students’ mathematical communication through problem-solving discourse. Journal of Mathematical Behavior, 53, 1–14.
Jones, K. (2018). The development of geometry learning. In T. Dreyfus dkk. (Eds.), Developing Research in Mathematics Education (pp. 45–62). Routledge.
Kattou, M., Kontoyianni, K., Pitta-Pantazi, D., & Christou, C. (2013). Connecting mathematical creativity to mathematical ability. ZDM–Mathematics Education, 45(2), 167–181.
Kontorovich, I. (2019). The role of multiple solution tasks in developing mathematical creativity. Educational Studies in Mathematics, 100(3), 243–259.
Kontorovich, I., & Koichu, B. (2020). Multiple-solution tasks as a mechanism for fostering mathematical creativity. Educational Studies in Mathematics, 104(1), 1–20.
Leikin, R. (2018). Creativity in mathematics education: Theoretical considerations and empirical findings. ZDM–Mathematics Education, 50(1–2), 1–12.
Leikin, R. (2021). When practice needs theory: Theoretical underpinnings of creativity in mathematics education. ZDM–Mathematics Education, 53(2), 289–301.
Leikin, R., & Pitta-Pantazi, D. (2013). Creativity and mathematics education: The state of the art. ZDM–Mathematics Education, 45(2), 159–166.
Lithner, J. (2017). Principles for designing mathematical tasks that enhance creative reasoning. ZDM–Mathematics Education, 49(6), 937–949.
Moschkovich, J. N. (2021). Beyond academic language: Reframing language and mathematical learning. Educational Studies in Mathematics, 108(12), 7–24.
Nachlieli, T., & Tabach, M. (2019). Discursive shifts in mathematics classrooms: A commognitive perspective. Educational Studies in Mathematics, 101(2), 251–268.
OECD. (2019). OECD future of education and skills 2030: OECD learning compass 2030. OECD Publishing.
OECD. (2022). PISA 2022 results (Volume I): The state of learning and equity in education. OECD Publishing.
Planas, N. (2018). Language as resource: A key notion for understanding the complexity of mathematics learning. Educational Studies in Mathematics, 98(3), 215–229.
Planas, N., & Schütte, M. (2020). The role of language in mathematics education research: Moving toward a communicational turn. ZDM–Mathematics Education, 52(1), 1–12.
Retnawati, H., Djidu, H., Kartianom, Apino, E., & Anazifa, R. D. (2018). Teachers’ knowledge about higher-order thinking skills and its learning strategy. Problems of Education in the 21st Century, 76(2), 215–230.
Sfard, A. (2018). Learning, discourses, and mathematics education. Cambridge University Press.
Sinclair, N., Pimm, D., & Skelin, M. (2016). The mathematics of visual thinking. ZDM–Mathematics Education, 48(1–2), 1–5. https://doi.org/10.1007/s11858-016-0785-8
Singer, F. M., Sheffield, L. J., Freiman, V., & Brandl, M. (2017). Research on and activities for mathematically gifted students. ZDM–Mathematics Education, 49(1), 1–13.
Sriraman, B. (2017). The characteristics of mathematical creativity. ZDM–Mathematics Education, 49(1), 1–13.
Stylianides, G. J., & Stylianides, A. J. (2020). Geometry for reasoning and proof. Journal of Mathematical Behavior, 59, 100794.
UNESCO. (2021). Reimagining our futures together: A new social contract for education. UNESCO Publishing.
Wijaya, A., van den Heuvel-Panhuizen, M., & Doorman, M. (2018). Opportunity-to-learn context-based tasks provided by mathematics textbooks. Educational Studies in Mathematics, 98(3), 301–320.
Vale, I., Barbosa, A., Borralho, A., Cabrita, I., & Fonseca, H. (2021). Fostering mathematical creativity in school contexts: Recent research developments. Mathematics Education Research Journal, 33(4), 1–23.