Skema Berpikir Mahasiswa Ketika Mengostruksi Bukti Matematis
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Abstract
Kemampuan konstruksi bukti merupakan kemampuan yang sangat penting dan harus dimiliki oleh siapa saja yang terlibat dengan matematika dan pendidikan matematika, seperti mahasiswa pendidikan matematika. Walaupun kemampuan mengonstruksi bukti sangat penting banyak hasil penelitian yang menyatakan bahwa mahasiswa mengalami kesulitan dalam mengonstruksi Untuk itu perlu ditelusuri proses berpikir mahasiswa ketika mengonstruksi bukti matematis. Bagaimana struktur skema mahasiswa ketika berupaya menyelesaikan masalah pembuktian. Gambaran struktur skema mahasiswa diperoleh dengan mnggunakan metode penelitian kualitatif, dengan memberikan masalah pembuktian kepada mahasiswa. Mereka diminta mengerjakan konstruksi bukti dengan metoda think aloud. Jika masih ada hal yang belum terungkap dari proses berpikir mahasiswa dilanjutkan dengan wawancara. Berdasarkan hasil temuan dan analisis data diperoleh 5 model struktur skema mahasiswa ketika mengonstruksi bukti matematis, yaitu (1) kelengkapan skema, (2) ketidaklengkapan skema, (3) ketidakterhubungan skema, (4) ketidaksesuaian skema dan (5) ketidakmatangan skema.
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NETTI, Syukma Netti Syukma et al.
Skema Berpikir Mahasiswa Ketika Mengostruksi Bukti Matematis.
Prosiding SI MaNIs (Seminar Nasional Integrasi Matematika dan Nilai-Nilai Islami), [S.l.], v. 1, n. 1, p. 547-556, july 2017.
Available at: <http://conferences.uin-malang.ac.id/index.php/SIMANIS/article/view/148>. Date accessed: 16 apr. 2024.
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Mathematics Education
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References
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[2] Arbib, A. M. 1990. A Piagetian Perspective on Mathematical Construction. Synthesis. July 1990, Volume 84, Issue 1, pp 43–58 doi:10.1007/BF00485006
[3] Creswell, J.W. 2012. Educational Research: Planning, Conducting and Evaluating Quantitative and Qualitatitive Research, Fourth edition , Boston, Amsterdam , Delhi. Pearson.
[4] Dreyfus, T. 1999. Why Johnny Can`t Prove (with apologies to Morris Kline) Educational Studies in Mathematics.vol. 38. pp. 85-109 DOI: 10.1023/A:1003660018579
[5] Gholamazad, S., Liljedahl, P., & Zazkis, R. 2003. One Line Proof: What can Go Wrong? dalam Pateman, N., (Eds) Proceedings of the 27th Conference of the International Group for the Psychology of Mathematics Education, 2, pp. 437-444. Honolulu. HI.
[6] Harel & Sowder. 1998. Harel, G., Sowder. L. 1998. Students’ Proof Schemes: Results from exploratory studies. In E. Dubinsky, A. H. Soenfeld and J.J. Kaput (eds), Issues in mathematics education: Vol.7. Research in collegiate mathematics education, III, American Mathematical Society, Providence, RI, USA, 234-283
[7] Heinze, A & Reiss, K. 2004. Reasoning and Proof: Methodological Knowledge as a Component of Proof Competence. Procceding of the Third Conference of the European Society for Research in Mathematics Education 28 February-3 March 2003. Thematic Group 4.
[8] Kaasila, R & Pehkonen, E & Hellinen, A. 2009. Finnish pre-service teachers’ and upper secondary students’ understanding of division and reasoning strategies used Published online: 16 September 2009 Springer Science + Business Media B.V. Educ Stud Math 73:247–261 DOI 10.1007/s10649-009-9213-1
[9] Netti, S. Nusantara, T., Subanji, Abadyo & Anwar, L. 2016. The Failure to Construct Proof Based on Assimilation and Accommodation Framework from Piaget. International Education Studies; Vol. 9, No. 12; 2016
[10] Plaxco, D.B. 2011. Relationship Between Students` Proof Schemes and Defiitions. Thesis faculty of the Virginia Polytechnic Institute and State University. Tidak dipublikasikan. online. http://scholar.lib.vt.edu/theses/available/etd-05172011-121003/unrestricted/Plaxco_DB_T_2011.pdf diakses September 2015.
[11] Selden, A. & Selden, J .2009. Understanding the Proof Construction Process. artikel http://www.researchgate.net/publication/268630244 diakses 20 November 2015
[12] Selden, A. & Selden, J. 1995. Unpacking the Logic of Mathematical Statements. Educational Studies in Mathematics 29; 123-151. Kluwer Academic Publishers. Netherlands.
[13] Selden, A. & Selden, J. 1987. Errors and Misconception in College level Theorema Proving. in Novak, D. J (Eds) Proccedings of the Second International seminar on Misconception and Educational Strategies In Science and Mathematics. Vol III. Cornell University. July p. 457-470.
[14] Selden, A. & Selden, J. 2008. Overcoming students’ difficulties in learning to understand and construct proofs. In M. Carlson & C. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics (pp.95-110). Washington, DC: Mathematical Association of America.
[15] Selden, J., Benkhalti, A & Annie Selden. 2014. An Analysis Of Transition-To-Proof Course Students’ Proof Constructions With A View Towards Course Redesign (online) : https://www.researchgate.net/publication/268278836. Diakses Desember 2016.
[16] Selden, A. & Selden, J. 2015. A Theoretical Perspective for Proof Construction. CERME 9 Proceeding. (didownload melalui www.researchgate.net tanggal 12 Pembuari 2016.
[17] Subanji & Nusantara, T. 2015. Teori Konstruksi Konsep dan Pemecahan Masalah Matematika. Malang. UM Press
[18] Subanji & Nusantara, T. 2017. Teori Defragmentasi Struktur Berpikir dalam Mengonstruksi Konsep dan Pemecahan Masalah Matematika. Malang.UM Press.
[19] Skemp, R. Richard. 1982. The Psychology of Learning Mathematics. Great Britain. Harell Watson & Vinely Ltd.
[20] Stylianides, Gabriel J. & Stylianides, Andreas J. 2009. Ability to Construct Proofs and Evaluate One’s Own Constructions in Fou-Lai Lin, Feng-Jui Hsieh Gila Hanna, Michael de Villiers (Eds) Proceeding ICMI 19th The Department of Mathematics, National Taiwan Normal University Taipei, Taiwan. 2-166
[21] Stemberg, R.J & Stenberg, K. 2012. Cognitive Psychology. Sixth edition. Wadsworth, Cengage Learning.
[22] Tabach, M & Levenson, E & Barkai, R & Tsamir, P. Tirosh, D & Dreyfus, T 2009. Teachers’ Knowledge of Students’ Correct and IncorrectProof Constructions in Fou-Lai Lin, Feng-Jui Hsieh Gila Hanna, Michael de Villiers (Eds) Proceeding ICMI 19th The Department of Mathematics, National Taiwan Normal University Taipei, Taiwan.
[23] Tall. D. 2002. The Psychology of Advanced Mathematical Thinking. Dalam Tall. D (Ed), Advanced Mathematical Thinking (hlm. 4-20). New York: Kluwer Academic Publishers
[24] Weber, K. 2004. A Framework for Describing the Processes that Undergraduates Use to Construct Proofs. Proccedings of the 28th Confrence of the International Group for the Psychology of Mathematics Education. Vol 4. pp. 425-432.
[25] Weber, K. 2001. Student difficulty in constructing proofs: the need for strategic knowledge. Educational Studies in Mathematics, 48, 101-119.
[26] Weber, K. 2006 . Investigating and teaching the processes used to construct proofs. In F. Hitt, G. Harel & S. Hauk (Eds.), Research in Collegiate Mathematics Education. VI (pp.197-232). Providence: RI: American Mathematical Society. DOI: 10.1090/cbmath/013/07