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Proses metakognisi mahasiswa calon guru matematika dalam memecahkan masalah piramida hitung
Daniel Supriyadi, Program Studi Pendidikan Matematika, Universitas Kristen Satya Wacana Salatiga, Indonesia
Abstract
Metakognisi merupakan salah satu faktor penentu keberhasilan seseorang dalam memecahkan masalah. Penelitian kualitatif ini bertujuan untuk mendeskripsikan proses metakognisi mahasiswa calon guru matematika dalam menyelesaikan soal Piramida Hitung (Pitung) yang merupakan permasalahan non rutin terkait operasi bilangan bulat. Subyek penelitian adalah tiga mahasiswa Pendidikan Matematika Universitas Kristen Satya Wacana Salatiga angkatan 2019. Kriteria pemilihan subyek yaitu: mahasiswa yang berhasil memecahkan tiga tantangan dalam Pitung (tepat dua operasi hitung, tepat tiga operasi hitung, dan tepat empat operasi hitung), komunikatif, dan bersedia menjadi subyek. Data dikumpulkan melalui tes tertulis, think aloud, dan wawancara. Hasil penelitian menunjukkan bahwa proses metacognitive awareness (menyadari pengetahuan dan pengalaman terdahulu, menyadari pola strategi yang dibuat, dan menggunakan informasi pada soal untuk penyelesaian masalah), metacognitive regulation (membuat perencanaan, merevisi langkah penyelesaian, memikirkan dan menemukan jawaban lain), dan metacognitive evaluation (menilai kapasitas berpikir, menilai hasil pekerjaan, dan menilai pemahaman diri sendiri) terjadi saat proses pemecahan masalah dengan bentuk beragam untuk setiap subjeknya. Selain itu, metakognisi juga membantu subyek dalam membuat strategi penyelesaian menjadi lebih efektif.
The process of metacognition of prospective mathematics teachers in solving number pyramid problems
Abstract
Metacognition was one of the determining factors for a person’s success in problem-solving. This qualitative research aimed to describe prospective teachers’ metacognition process in solving the Number Pyramid or Piramida Hitung (Pitung) problem, non-routine problems related to integer operations. The subjects were three mathematics education students of Universitas Kristen Satya Wacana Salatiga, Indonesia. The criteria for selecting subjects, namely: students were succeeded in solving three challenges in the Pitung (exactly two-number operations, three-number operations, and four-number operations), communicative, and willing to be the subject. Data were collected using the written test, think aloud, and interviews. The results showed that process of metacognitive awareness (be aware of previous knowledge and experience, be aware of the pattern of strategies created, and use the information in problems for problem-solving); metacognitive regulation (made plans, revised completion steps, think about, and found others answers); and metacognitive evaluation (assessed thinking capacity, assessed work results, and assessed self-understanding) occurred during the problem-solving process in various forms for each subject. Also, metacognitive helped the subjects in making the completion strategy more effective.
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Aljaberi, N. M. (2015). University students’ learning styles and their ability to solve mathematical problems. International Journal of Business and Social Science, 6(41), 152–165. https://ijbssnet.com/journals/Vol_6_No_4_1_April_2015/18.pdf
Amir, M. F., & Kusuma W, M. D. (2018). Pengembangan perangkat pembelajaran berbasis masalah kontekstual untuk meningkatkan kemampuan metakognisi siswa sekolah dasar. Journal of Medives, 2(1), 117–128. https://doi.org/10.31219/osf.io/bpqas
Anggo, M. (2011). Pelibatan metakognisi dalam pemecahan masalah matematika. Edumatica: Jurnal Pendidikan Matematika, 1(1), 25–32. https://doi.org/10.22437/edumatica.v1i01.188
Barbacena, L. B., & Norina, R. S. (2013). Metacognitive model in mathematical problem solving. BU Faculty E-Journal, 1(1), 1–9.
Barrera-Mora, F., & Rodriguezt, R. (2013). Cognitive processes developed by students when solving mathematical problems within technological environments. The Mathematics Enthusiast, 10(1), 109–136.
Caballero, A., Blanco, L. J., & Guerrero, E. (2011). Problem solving and emotional education in initial primary teacher education. Eurasia Journal of Mathematics, Science & Technology Education, 7(4), 281–292. https://doi.org/10.12973/ejmste/75206
Elita, G. S., Habibi, M., Putra, A., & Ulandari, N. (2019). Pengaruh pembelajaran problem based learning dengan pendekatan metakognisi terhadap kemampuan pemecahan masalah matematis. Mosharafa: Jurnal Pendidikan Matematika, 8(3), 447–458. https://doi.org/10.31980/mosharafa.v8i3.517
Flavell, J. H. (1979). Metacognition and cognitive monitoring a new area of cognitive–developmental inquiry. American Psychologist, 34(10), 906–911. https://psycnet.apa.org/doi/10.1037/0003-066X.34.10.906
Foshay, R., & Kirkley, J. (2003). Principles for teaching problem solving: Technical paper #4. The Roach Organization.
Gartmann, S., & Freiberg, M. (1995). Metacognition and mathematical problem solving: Helping students to ask the right questions. The Mathematics Educator, 6(1). 9–13.
Hmelo-silver, C. E. (2004). Problem-based learning: What and how do students learn? Educational Psychology Review, 16(3), 235–266. https://doi.org/10.1023/B:EDPR.0000034022.16470.f3
In’am, A., Saad, N., & Ghani, S. A. (2012). A metacognitive approach to solving algebra problems. International Journal of Independent Research and Studies, 1(4), 162–173. https://ssrn.com/abstract=2164892
Indarini, E., Sadono, T., & Onate, M. E. (2013). Pengetahuan metakognitif untuk pendidik dan peserta didik. Satya Widya, 29(1), 40–46. https://doi.org/10.24246/j.sw.2013.v29.i1.p40-46
Kilpatrick, J., Swaffword, J., & Findell, B. (2001). Adding it up: Helping children learn mathematics. National Academy Press.
Kuzle, A. (2013). Patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment patterns of metacognitive behavior during mathematics problem-solving in a dynamic geometry environment. International Electronic Journal of Mathematics Education, 8(1), 20–40.
Lee, M., & Baylor, A. L. (2006). Designing metacognitive maps for web-based learning. Journal of Educational Technology & Society, 9(1), 344–348. https://www.jstor.org/stable/jeductechsoci.9.1.344
Lesh, R., & Doerr, H. M. (2003). Book review: Beyond constructivism, models and modeling perspectives on mathematics problem solving, learning, and teaching. ZDM–Mathematics Education, 35(6), 325–329.
Livingstone, J. A. (2003). Metacognition: An overview. https://files.eric.ed.gov/fulltext/ED474273.pdf
Magiera, M. T., & Zawojewsky, J. S. (2011). Characterizations of social-based and self-based contexts associated with students’ awareness, evaluation, and regulation of their thinking during small-group mathematical modeling. Journal for Research in Mathematics Education, 42(5), 23–47. https://doi.org/10.5951/jresematheduc.42.5.0486
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook (2nd ed.). Sage.
Mohd, N., Farah, T., & Tengku, P. (2011). The effects of attitude towards problem solving in mathematics achievements. Australian Journal of Basic and Applied Sciences, 5(12), 1857–1862. http://www.ajbasweb.com/old/ajbas/2011/December-2011/1857-1862.pdf
Mousoulides, N., Sriraman, B., & Christou, C. (2007). From problem solving to modelling. Nordic Studies in Mathematics Education, 12(1), 23–47.
NCTM. (2000). Principles and standards for school mathematics. Author.
Nool, N. R. (2012). Exploring the metacognitive processes of prospective mathematics teachers during problem solving. International Conference on Education and Management Innovation (Vol. 30, pp. 302–306).
Novferma, N. (2016). Analisis kesulitan dan self-efficacy siswa smp dalam pemecahan masalah matematika berbentuk soal cerita. Jurnal Riset Pendidikan Matematika, 3(1), 76. https://doi.org/10.21831/jrpm.v3i1.10403
Ozsoy, G., & Ataman, A. (2009). The effect of metacognitive strategy training on mathematical problem solving achievement. International Electronic Journal of Elementary Education, 1(2), 67–82.
Pimta, S., Tayruakham, S., & Nuangchalerm, P. (2009). Factors influencing mathematic problem-solving ability of sixth grade students. Journal of Social Sciences, 5(4), 381–385. https://doi.org/10.3844/jssp.2009.381.385
Polya, G. (1973). How to solve it (2nd ed.). Princeton University Press.
Purnomo, D., Nusantara, T., Subanji, S., & Rahardjo, S. (2014). Proses metakognisi matematis siswa dalam pemecahan masalah. Prosiding Seminar Nasional Matematika dan Pendidikan Matematika, 5(1), 67–76. http://prosiding.unirow.ac.id/index.php/snmpm/article/view/11
Rahmawati, N. T., & Sugianto, S. (2016). Analisis kemampuan berpikir kreatif matematik ditinjau dari kesadaran metakognisi siswa pada pembelajaran SSCS berbantuan Schoology. Unnes Journal of Mathematics Education Research, 5(1), 24–31. https://journal.unnes.ac.id/sju/index.php/ujmer/article/view/12913
Retnowati, E., Fathoni, Y., & Chen, O. (2018). Mathematics problem solving skill acquisition: Learning by problem posing or by problem solving? Cakrawala Pendidikan, 37(1). 1–10. https://doi.org/10.21831/cp.v37i1.18787
Rizkiani, A., & Septian, A. (2019). Kemampuan metakognitif siswa SMP dalam pembelajaran matematika dengan menggunakan pendekatan realistic mathematics education (RME). UNION: Jurnal Pendidikan Matematika, 7(2), 275–284. http://dx.doi.org/10.30738/union.v7i2.4557
Schneider, W., & Artelt, C. (2010). Metacognition and mathematics education. ZDM–Mathematics Education, 42(2), 149–161. https://doi.org/10.1007/s11858-010-0240-2
Schoenfeld, A. H. (1992). Learning to think mathematically: Problem solving, metacognition, and sense making in mathematics. Journal of Education, 196(2), 1–38. https://doi.org/10.1177/002205741619600202
Schraw, G., & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19(4), 460–475. https://doi.org/10.1006/ceps.1994.1033
Setyadi, D. (2018). Proses metakognisi mahasiswa dalam memecahkan masalah matematika (studi kasus pada mahasiswa pendidikan matematika UKSW). Kreano: Jurnal Matematika Kreatif-Inovatif, 9(1), 93–99. https://doi.org/10.15294/kreano.v9i1.13505
Suryaningtyas, S., & Setyaningrum, W. (2020). Analisis kemampuan metakognitif siswa SMA kelas XI program IPA dalam pemecahan masalah matematika. Jurnal Riset Pendidikan Matematika, 7(1), 74–87. https://doi.org/10.21831/jrpm.v7i1.16049
Tampi, W., Subanji, S., & Sisworo, S. (2016). Proses metakognisi siswa dalam pemecahan masalah aljabar berdasarkan taksonomi SOLO. Jurnal Pendidikan: Teori, Penelitian, dan Pengembangan, 1(11), 2118–2125. https://doi.org/10.29313/ethos.v0i0.1669
Utami, R. W., & Wutsqa, D. U. (2017). Analisis kemampuan pemecahan masalah matematika dan self-efficacy siswa SMP negeri di Kabupaten Ciamis. Jurnal Riset Pendidikan Matematika, 4(2), 166. https://doi.org/10.21831/jrpm.v4i2.14897
Wilson, J. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25–48. https://doi.org/10.1007/BF03217394
DOI: https://doi.org/10.21831/jrpm.v7i2.36732
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