Abstraksi Reflektif: Suatu Sudut Pandang Pemecahan Masalah Geometris
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Published:
Oct 31, 2021
Keywords:
reflective abstraction, problem solving, Krulik Rudnick, geometry
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Abstract
This study aims to analyze and describe the process of mathematical reflective abstraction of students with high early mathematics ability in problem solving based on Krulik and Rudnick's steps on geometry material. This research is a case study qualitative research. The research subjects were students of MAN 1 Ngawi who were taken by purposive sampling technique. The data collection technique was done by task-based interviews. The results of the problem solving task and interview data are then presented and analyzed using descriptive analysis. The results of this study indicate that students who are highly capable in every step of problem solving according to the Krulik and Rudnick stages always bring up a complete reflective abstraction which includes recognition, representation, structural abstraction, and structural awareness. Subjects utilize previous knowledge related to trigonometry in solving geometric problems. In reflective abstraction activities, it can be seen how students construct conceptual knowledge, by providing reasons for the decisions made. This is in accordance with the demands of learning in the new normal era, students are required to construct their own mathematical knowledge.
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Masamah, U. (2021). Abstraksi Reflektif: Suatu Sudut Pandang Pemecahan Masalah Geometris. Quadratic: Journal of Innovation and Technology in Mathematics and Mathematics Education, 1(2), 114–124. https://doi.org/10.14421/quadratic.2021.012-06
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References
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[18] Panjaitan, B., Level-Level Abstraksi Reflektif dalam Pemecahan Masalah Matematika, http://repository.uhn.ac.id/handle/123456789/410, 2009.
[19] Piaget, J., & Beth, E. W., “Mathematical Epistemology and Psychology,” (W. Mays, Trans.) Paris: Springer Science Bussiness Media, 1966.
[20] Piaget, J., Genetic Epistemology. New York: The Norton Library, 1971.
[21] Simon, M.A., Tzur, R., Heinz, K., Kinzel, M., Explicating a Mechanism For Conceptual Learning: Elaborating the Construct of Reflective Abstraction. Journal for Research in Mathematics Education National Council of Teachers of Mathematics, Vol. 35, No. 5, 2004, pp. 305-329. https://doi.org/10.2307/30034818
[22] Siswono, T. Y. E., “Penjenjangan Kemampuan Berpikir Kreatif dan Identifikasi Tahap Berpikir Kreatif Siswa dalam Memecahkan dan Mengajukan Masalah Matematika”. Disertasi PPS UNESA. Surabaya: Tidak diterbitkan, 2007.
[23] Solso, L.R., Maclin, H.O., dan Maclin, K. M., Psikologi Kognitif. Jakarta: Erlangga, 2008.
[24] Suparno, P., Teori Perkembangan Kognitif Jean Piaget. Yogyakarta. Kanisius, 2001.
[25] Tall, D., “Using Technology to Support an Embodied Approach Learning Concept in Mathematics”, First Coloquio de Historia e Techologia no Ensino de Matematics at Universidade do Estado do Rio De Janiero, 2002.
[26] Usodo, B., “Karakteristik Intuisi Siswa SMA dalam Memecahkan Masalah Matematika Ditinjau dari Kemampuan Matematika dan Perbedaan Gender,” Jurnal Untad. AKSIOMA, 2012.
[27] Wiryanto, “Level-level Abstraksi dalam Pemecahan Masalah Kalkulus”, Jurnal Pendidikan Teknik Elektro , 03, 80, 2014.
[2] Cifarelli, V., “The Role of Abstraction as a Learning Process in Mathematical Problem Solving. Indiana, USA: Purdue University, 1988.
[3] Djasuli, M., dkk., “Students’ Reflective Abstraction in Solving Number Sequence Problems,” IJME, 12:3, 2017.
[4] Dubinsky, E. “Constructive Aspect of Reflective Abstraction in Advanced Mathematics. Dalam L. P. Steffe (Ed.). Epistemological Foundation of Mathematical Experience (pp. 160-202). New York: Springer, 1991. https://doi.org/10.1007/978-1-4612-3178-3_9
[5] Dubinsky, E., & Lewin, P. “Reflective abstraction and mathematics education: The Genetic Decomposition of Induction and Compactness,” The Journal of Mathematical Behavior, 5(1), 55–92, 1986.
[6] El Walida dan Fuady, “Abstraksi Reflektif Siswa Dalam Memecahkan Masalah Matematika Berdasarkan Gaya Kognitif”, Seminar Nasional Pendidikan Matematika Ahmad Dahlan, 6, 465, 2017.
[7] Fuady, A.. “Berpikir Reflektif dalam Pembelajaran Matematika”. Jurnal Ilmiah Pendidikan Matematika. Vol. 1 No 2. 104-107, 2016.
[8] Gagatsis, A. dan Patronis, T. “Using Geometrical Models in a Process of Reflective Thinking in Learning and Teaching Mathematics. Educational Studies in Mathematics Netherlands, Vol. 21, 29-54, 1990.
[9] Goodson-Espy T., “Reflective Abstraction as an Individual and Collective Learning Mechanism,” Constructivist Foundations, 381-383, 2014.
[10] Goodson-Espy, “T. The Roles of Reification and Reflective Abstraction in the Development of Abstract Thought: Transitions from Arithmetic to Algebra,” Educational Studies in Mathematics 36, 219–245, 1998. https://doi.org/10.1023/A:1003473509628
[11] Hershkowitz et.al (2001 Hershkowitz, R., Schwarz, B., & Dreyfus, T. “Abstraction in Context: Epistemic Action,” Journal for Research in Mathematics Education , 32, 195-222, 2001.
[12] Jonassen, D. H. Learning to Solve Problem. An Intsructional Design Guide. San Fransisco USA: John Wiley & Sons, Inc., 2004.
[13] Kariadinata, R., “Students’ Reflective Abstraction Ability on Linear Algebra Problem Solving and Relationship with Prerequisite Knowledge,” Infinity, 10(1), 1-16, 2021.
[14] Krulik, S. dan Rudnick, J. A., Problem Solving: A Handbook for Teachers. Boston: Allyn & Bacon, 1988.
[15] Mardiyah, U.R. & Budiarto, M.T., “Abstraksi Reflektif dalam Mengonstruk Bangun Segiempat,” MATHEedunesa; Jurnal Ilmiah Pendidikan Matematika Vol. 8 No. 2, 2019, PP. 517-523.
[16] Mustikarini, A. A., ”Level Abstraksi Reflektif Siswa dalam Memecahkan Masalah Matematika Ditinjau dari Gaya Kognitif. Skripsi. UIN Sunan Ampel Surabaya: Tidak Diterbitkan, 2020.
[17] Nurman, T. A. Profil Kemampuan Siswa SMP dalam Memecahkan Masalah Matematika Open Ended Ditinjau dari Perbedaan Tingkat Kemampuan Matematika. PPS UNESA. Surabaya: Tidak diterbitkan, 2008.
[18] Panjaitan, B., Level-Level Abstraksi Reflektif dalam Pemecahan Masalah Matematika, http://repository.uhn.ac.id/handle/123456789/410, 2009.
[19] Piaget, J., & Beth, E. W., “Mathematical Epistemology and Psychology,” (W. Mays, Trans.) Paris: Springer Science Bussiness Media, 1966.
[20] Piaget, J., Genetic Epistemology. New York: The Norton Library, 1971.
[21] Simon, M.A., Tzur, R., Heinz, K., Kinzel, M., Explicating a Mechanism For Conceptual Learning: Elaborating the Construct of Reflective Abstraction. Journal for Research in Mathematics Education National Council of Teachers of Mathematics, Vol. 35, No. 5, 2004, pp. 305-329. https://doi.org/10.2307/30034818
[22] Siswono, T. Y. E., “Penjenjangan Kemampuan Berpikir Kreatif dan Identifikasi Tahap Berpikir Kreatif Siswa dalam Memecahkan dan Mengajukan Masalah Matematika”. Disertasi PPS UNESA. Surabaya: Tidak diterbitkan, 2007.
[23] Solso, L.R., Maclin, H.O., dan Maclin, K. M., Psikologi Kognitif. Jakarta: Erlangga, 2008.
[24] Suparno, P., Teori Perkembangan Kognitif Jean Piaget. Yogyakarta. Kanisius, 2001.
[25] Tall, D., “Using Technology to Support an Embodied Approach Learning Concept in Mathematics”, First Coloquio de Historia e Techologia no Ensino de Matematics at Universidade do Estado do Rio De Janiero, 2002.
[26] Usodo, B., “Karakteristik Intuisi Siswa SMA dalam Memecahkan Masalah Matematika Ditinjau dari Kemampuan Matematika dan Perbedaan Gender,” Jurnal Untad. AKSIOMA, 2012.
[27] Wiryanto, “Level-level Abstraksi dalam Pemecahan Masalah Kalkulus”, Jurnal Pendidikan Teknik Elektro , 03, 80, 2014.