MENGATASI KESULITAN MAHASISWA KETIKA MELAKUKAN PEMBUKTIAN MATEMATIS FORMAL

Cecep Anwar HF Santosa

Abstract


ABSTRAK

Melakukan pembuktian matematis formal merupakan hal yang sentral dalam matematika. Ketika seseorang mempunyai dugaan tentang suatu hal, salah satu cara yang paling tepat untuk meyakinkan bahwa hal tersebut benar adalah dengan melakukan pembuktian matematis yang sah. Proses mendefinisikan pembuktian ini berkembang dari masa ke masa sesuai dengan perkembangan jaman. Walaupun belum ada konsensus yang disepakati oleh matematikawan secara keseluruhan tentang apa itu bukti matematis formal, namun proses membuktikan ini merupakan suatu masalah tersendiri ketika bukti matematis dikenalkan saat pembelajaran berlangsung. Kesulitan ini terjadi tidak hanya pada mahasiswa tingkat pertama perkuliahan, namun ternyata mahasiswa program yang lebih tinggi (pascasarjana) pun mengalami kesulitan dalam membuktikan walaupun dengan porsi yang lebih kecil. Jika ditelusuri proses berpikir pembuktian matematikawan ternyata sangat berbeda dengan alur berpikir yang disajikan pada buku-buku teks matematika saat ini. Sehingga terdapat masalah ketika mahasiswa melakukan proses pembuktian. Tulisan ini mencoba untuk menjelaskan pembuktian matematis secara komprehensif dimulai dari sejarah pembuktian sampai dengan masa kini, dan mengeksplorasi kesulitan-kesulitan pembuktian yang telah diteliti oleh para peneliti. Tulisan ini pun mencoba untuk mendiskusikan suatu cara yang paling baik yang dapat dilakukan untuk mengatasi kesulitan ketika mahasiswa dihadapkan pada proses membuktikan. Dimulai dari aspek kognitif, afektif, dan commognition.

ABSTRACT

Doing formal mathematical proof is central in mathematics. When someone has a conjecture about something, one of the most appropriate ways to ensure that we do the right thing is to do a legitimate mathematical proof. The process of defining formal mathematics proof is changing from time to time in accordance with the changing times. Although there has been no consensus reached by mathematicians as a whole about what the formal proof, but the process of proving is another issue when mathematical proof introduced during the learning. This difficulty occurs not only in the first years student in undergraduate, but it turned out to graduted student have difficulty proving althought with smaller portions. If we try to trace mathematicians’ process to do prove, we can see that it turned out very different from the logic presented in mathematics textbooks today. This paper tries to explain in a comprehensive mathematical proof starts from the historical of proofing to the present, and explores the difficulties of proof which has been studied by researchers. This paper attempts to discuss the best way to solve the difficulties when students are faced with proving process. Starting from the cognitive, affective, and commognition.


Keywords


afektif; aspek kognitif; bukti formal; commognition; affective; cognitive aspect; formal proof

Full Text:

PDF

References


Almeida, D. (2003). Engendering proof attitudes: Can the genesis of mathematical knowledge teach us anything? International Journal of Mathematical Education in Science and Technology, 34(4), 479-488

Balacheff, N. (1988). Aspect of proof in pupils’ practice of school mathematics. In D. Pimm (Ed.), Mathematics, Teachers and Children (pp. 216-236). Great Britain: Hodder and Stoughton Educational.

Epp, S. (2003). The role of logic in teaching proof. The American Mathematics Monthly, 110(10), 886-899.

Gowers, W.T. The Language and Grammar in Mathematics. Diunduh dari https://www.dpmms.cam.ac.uk/~wtg10/grammar.pdf tanggal 8 Mei 2013.

Hanna, G. (1991). Mathematical Proof. In David Tall, Advanced Mathematical Thinking (p.54-61). The Netherland: Kluwer Academic Publisher.

Jamison, R.E. (2000). Learning and Language in Mathematics in Language and Learning Across the Disciplines. Diunduh dari wac.coloasate.edu. tanggal 10 Mei 2013.

Kassios, Y. 2009. Formal Proof. Diunduh dari http://www.cs.toronto.edu/~hehner/ aPToP/formal proof-1.pdf tanggal 26 Maret 2012.

Kleiner, I. (1991). Rigor and proof in mathematics: A historical perpective. Mathematics Magazine.

Knuth, E. (2002). Secondary school mathematics teachers’ conception of proof. Dalam Journal for Research in Mathematics Education, 33(5), 379-405.

Martin, W. G,, & Harel, G. (1989). Proof frames of preservice elementary teachers. Journal for Research in Mathematics Education, 20(1), 41 – 51.

Moore, R.C., 1994. Making Transition to Formal Proof. Journal of Educational Studies in Mathematics 27: 249-266. Kluwer Academic Publisher: Netherlands.

NCTM (2000). Principles and Standar for School Mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Remillard, K.S. (2010). Exploring the learning of mathematicak proof by undergraduate mathematics majors through discourse analysis. Proceedings of the 13th Annual Conference in Researh in Undergraduate Mathematics Education.

Ruseffendi, E.T. (2006). Pengantar Kepada Membantu Guru Mengembangkan Kompetensinya dalam Pengajar Matematika untuk Meningkatkan CBSA. Tarsito: Bandung

Sowder, L., & Harel, G. (2003). Case studies of Mathematics majors’ proof understanding, production, and appreciation. Canadian Journal of Science, Mathematics, and Technology, 3, 251-267.

Sriraman, B. 2004. The Characteristics of Mathematical Creativity. The Mathematics Educator, Vol 14, No.1 (19-34).

Van Dormolen, J. (1977). Learning to understand what giving a proof really means. Educational Studies in Mathematics, 8, 27-34.

Vanspronsen, H.D. 2008. Proof Processes Of Novice Mathematics Proof Writers. Dissertation University of Montana, Missoula.

Yerizon (2011). Peningkatan Kemampuan Pembuktian Dan Kemandirian Belajar Matematik Mahasiswa Melalui Pendekatan M-Apos. Disertasi UPI Bandung.




DOI: https://doi.org/10.18269/jpmipa.v18i2.36130

DOI (PDF): https://doi.org/10.18269/jpmipa.v18i2.36130.g15510

Refbacks

  • There are currently no refbacks.


Copyright (c) 2021 Jurnal Pengajaran MIPA

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

JPMIPA http://ejournal.upi.edu/index.php/jpmipa/index is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License

Jurnal Pengajaran Matematika dan Ilmu Pengetahuan Alam (JPMIPA) or Journal of Mathematics and Science Teaching 

All rights reserverd. pISSN 1412-0917 eISSN 2443-3616

Copyright © Faculty of Mathematics and Science Education (FPMIPA) Universitas Pendidikan Indonesia (UPI)

 

View JPMIPA Stats