Tahapan Berpikir Mahasiswa dalam Mengonstruksi Bukti Matematis
DOI:
https://doi.org/10.33477/mp.v6i1.437Abstract
Abstrak Mengonstruksi bukti matematis merupkan bentuk khusus dari pemecahan masalah sehingga perlu proses berpikir yang sedikit berbeda. Penelitian ini bertujuan untuk merumuskan tahapan berpikir mahasiswa dalam menelesaikan masalah pembuktian. Metoda penelitian yang digunakan adalah metoda kualitatif. Pengumpulan data dilakukan dengan memberikan satu masalah pembuktian kepada 10 orang mahasiswa. Mahasiswa diminta melakukan think aloud ketika sedang berupaya mengonstruksi bukti. Semua aktifitas di rekap dengan camera video. Hasil kerja yang dianalisis adalah yang hasil konstruksi bukti yang valid. Temuan dari penelitian ini adalah ada 5 tahapan berpikir mahasiswa ketika berupaya menghasilkan konstruksi bukti yang valid, yaitu (1) memahami masalah pembuktian, (2) membuat koneksi dan menyeleksi, (3) Menemukan ide utama,(4) merangkai bukti dan menimpulkan, dan (5) melakukan refleksi. Kata kunci: konstruksi bukti, proses berpikir, fungsi komposisi. Abstract Constructing mathematical proofs is a special case of problem solving so it needs a slightly different thinking process. This study aims to formulate the stages of student thinking in solving the problem of proof. The research method used is qualitative method. Data collection was done by giving two models of proof problem to 17 students. Students were asked to think aloud while trying to construct of proof. All activities were recaps with video camera. The results of the analyzed work were those of valid proof construction. The findings of this study were five stages of student thinking when attempt to construct a valid construction proof, namely (1) understanding the problem of proof, (2) making connections and selecting, (3) finding the main idea, (4) assembling evidence and concluding, and (5) doing reflection. Keywords: Constructing proof, thinking process, composition functionReferences
Arbib, A.M. (1990). A Piagetian Perspective on Mathematical Construction. Synthesis, Volume 84, Issue 1, pp 43–58 doi:10.1007/BF00485006.
Benkhalti, A & Selden, A, & Selden, J (2016). Proof Frameworks--A Way to Get Started, (online) https://www.researchgate.net/publication/299532808 diakses April 2016 DOI: 10.13140/RG.2.1.4160.9368
Creswell, J.W. (2012). Educational Research: Planning, Conducting and Evaluating Quantitative and Qualitatitive Research, Fourth edition , Boston, Amsterdam , Delhi. Pearson.
Dreyfus, T & Gabel, M. (2017). Affecting the Flow of a Proof by Creating Presence-Case Study in Number theory. Educational Studies Mathematics. Vol 96 Issue 2 pp 187-205. Spinger
Furinghetti, F., & Morselli, F. (2009). Every unsuccessful problem solver is unsuccessful in his or her own way: Affective and cognitive factors in proving. Educational Studies of Mathematics, 70, 71-90.
Mason, J., Burton, L.,Stacey, K. (2010). Thinking Mathematically. Edisi kedua. Prentice Hall. Harlow
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
Polya, G. (1973). How To Solve It. Edisi kedua. Cetakan kedua. Princeton University Press ISBN 0-691-08097-6.
Selden, A & Selden, J. (1996). The Role Of Logic In The Validation Of Mathematical Proofs.presented at the DIMACS Symposium on Teaching Logic and Reasoning, Rutgers University,25 - 26 July 1996.
Selden, A. & Selden, J. (2003). Validations of proofs written as texts: Can undergraduates tell whether an argument proves a theorem? Journal for Researchin Mathematics Education, 34, 4-36.
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.
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.
Selden, A. (2004). How Students Learn to Construct and Understand Proofs Presented in AAAS Symposium The Changing Nature of Proof in Mathematics: Past, Present, Future, February di New Mexico State University.
Selden, A. & Selden, J. (2015). A Theoretical Perspective for Proof Construction. CERME 9 Proceeding. (didownload melalui www.researchgate.net tanggal 12 Pebruari 2016.
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.
Weber, K. (2001). Student difficulty in constructing proofs: the need for strategic knowledge. Educational Studies in Mathematics, 48, 101-119.
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.
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.
