AKTIVITAS PENALARAN KONTROVERSIAL MAHASISWA DALAM MENYELESAIKAN MASALAH ALJABAR
Kata Kunci:
aktivitas penalaran kontroversial, masalah kontroversial matematis, aljabarAbstrak
Penelitian ini bertujuan mengidentifikasi aktivitas penalaran kontroversial mahasiswa dalam menyelesaikan masalah kontroversial matematis yang terdapat pada materi persamaan aljabar. Penelitian deskriptif ini dilakukan terhadap 76 mahasiswa semester 6 program studi Pendidikan Matematika salah satu universitas swasta di Malang. Data penalaran kontroversial diperoleh dari hasil pekerjaan mahasiswa menggunakan instrumen tes dan wawancara. Analisis data dan interpretasi makna temuan diperoleh melalui analisis teks data. Hasil penelitian menunjukkan bahwa penalaran kontroversial mahasiswa dalam menyelesaikan masalah kontroversial matematis pada persamaan aljabar memiliki aktivitas eksplorasi, kontradiksi, refleksi, dan klarifikasi. Pada aktivitas eksplorasi, subjek mengenali komponen-komponen masalah. Pada aktivitas kontradiksi, subjek menemukan komponen yang menyebabkan pertentangan. Pada aktivitas refleksi subjek menelusuri kembali penyebab pertentangan, dan akhirnya subjek mengklarifikasi untuk menemukan solusi. Dengan demikian, dosen pengampu dan mahasiswa dapat mengembangkan model pembelajaran yang melibatkan aktivitas penalaran kontroversial untuk keberhasilan pembelajaran selanjutnya.
Referensi
Al-Mutawah, M. A., Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual understanding, procedural knowledge and problem-solving skills in mathematics: High school graduates work analysis and standpoints. International Journal of Education and Practice. https://doi.org/10.18488/journal.61.2019.73.258.273
Didi?, M. G., Ba?, S., & Erba?, A. K. (2011). Students’ reasoning in quadratic equations with one unknown. The Seventh Congress of the European Society for Research in Mathematics Education. https://doi.org/10.1111/j.1365-294X.2008.04000.x
El Walida, S., Cholis, S., Subanji, & Sisworo. (2022). A portrait of controversial mathematics problems and students’ metacognitive awareness: A case of Indonesia. Journal of Higher Education Theory and Practice, 22(12), 51–62. https://doi.org/10.33423/jhetp.v22i12
Gurat, M. . (2018). Mathematical problem-solving strategies among student teachers. ERIES Journal, 11(3), 53–64. https://doi.org/10.7160/ eriesj.2018.110302
Jäder, J., Lithner, J., & Sidenvall, J. (2019). Mathematical problem solving in textbooks from twelve countries. International Journal of Mathematical Education in Science and Technology. https://doi.org/10.1080/0020739X.2019.1656826
Kang, S., Scharmann, L. C., & Noh, T. (2004). Reexamining the role of cognitive conflict in science concept learning. Research in Science Education, 34, 71–96. https://doi.org/10.1023/B:RISE.0000021001.77568.b3
Malatjie, F., & Machaba, F. (2019). Exploring mathematics learners’ conceptual understanding of coordinates and transformation geometry through concept mapping. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/EJMSTE/110784
Mueller, M., & Yankelewitz, D. (2014). Fallacious argumentation in student reasoning: Are there benefits? European Journal of Science and Mathematics Education, 2(1), 27–38.
NCTM. (2014). Procedural Fluency in Mathematics. National Council of Teachers of Mathematics.
Reiss, K., & Törner, G. (2007). Problem solving in the mathematics classroom: The German perspective. ZDM - International Journal on Mathematics Education. https://doi.org/10.1007/s11858-007-0040-5
Rolka, K., & Liljedahl, P. (2007). The role of cognitive conflict in belief changes. 31st Conference of the International Group for the Psychology of Mathematics Education.
Rosyadi, A. A. P., Sa’dijah, C., Susiswo, & Rahardjo, S. (2022). High order thinking skills: Can it arise when a prospective teacher solves a controversial mathematics problem? Journal of Physics: Conference Series, 2157(1), 012038. https://doi.org/10.1088/1742-6596/2157/1/012038
Skemp, R. R. (1978). Relational understanding and instrumental understanding. The Arithmetic Teacher.
Star, J. R., & Stylianides, G. J. (2013). Procedural and onceptual knowledge: Exploring the gap between knowledge type and knowledge quality. Canadian Journal of Science, Mathematics and Technology Education. https://doi.org/10.1080/14926156.2013.784828
Subanji, Rosyadi, A. A. P., & Emanuel, E. P. L. (2021). Levels of controversial reasoning of the pre-service teachers to solve mathematical problems. Journal of Southwest Jiaotong University, 56(4), 643–658. https://doi.org/10.35741/issn.0258-2724.56.4.55
Tall, D. (1977). Cognitive conflict and the learning of mathematics. The International Group for the Psychology of Mathematics Education.
Watson, J. M. (2002). Inferential reasoning and the influence of cognitive conflict. Educational Studies in Mathematics, 225–256. https://doi.org/10.1023/A:1023622017006
Watson, Jane M. (2007). The role of cognitive conflict in developing students’ understanding of average. Educational Studies in Mathematics. https://doi.org/10.1007/s10649-006-9043-3
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Hak Cipta (c) 2024 Sikky El Walida, Fadhila Kartika Sari, Yuli Ismi Nahdiyati Ilmi, Gusti Firda Khairunnisa
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