STUDENTS' THINKING PROCESS IN SOLVING MATHEMATICAL PROOF PROBLEM

Authors

  • Fauziah Hakim Universitas Sulawesi Barat
  • Murtafiah Murtafiah Universitas Sulawesi Barat

DOI:

https://doi.org/10.33477/mp.v8i1.1251

Keywords:

mathematical proof, problem solving, thinking process

Abstract

TThis research aimed to describe students’ thinking process in solving mathematical proof problem. The subjects in this research were Mathematics Education Study Program students in Universitas Sulawesi Barat who were taking Abstract Algebra course on academic year of 2019/2020 and were grouped into 3 proving ability categories, high, medium, and low. For each category, two subjects were chosen to be interviewed in order to obtain a description of students' thinking processes. From the results of tests and interviews, it was found that in the entry phase, high and medium category subjects were able to find the right initial verification procedure, whereas low category subjects were not yet able. In the attack phase, high category subjects were able to complete the process of proof to the final stage very systematically, medium category subjects were able to use the properties and theorems but still have difficulty achieving the right end result, while low category subjects try to use the properties and theorems but are not related to the verification process. In the review phase, high category subjects were able to explain the procedure outline again, category subjects were trying to supplement the shortcomings of the procedure, and low category subjects realized the importance of the initial proof process.

Author Biographies

Fauziah Hakim, Universitas Sulawesi Barat

Lecturer at Mathematics Education Study Program Universitas Sulawesi Barat

Murtafiah Murtafiah, Universitas Sulawesi Barat

Lecturer at Mathematics Education Study Program Universitas Sulawesi barat

References

Abdussakir. (2014). Proses Berpikir Mahasiswa dalam Menyusun Bukti Matematis dengan Strategi Semantik. Malang: Pascasarjana Program Studi Pendidikan Matematika, Universitas Negeri Malang. Dissertation: Not Published.

Cresswell, J.W. (2015). Riset Pendidikan: Perencanaan, Pelaksanaan, dan Evaluasi Riset Kualitatif & Kuantitatif. Yogyakarta: Pustaka Pelajar. (Original edition published in 2015 by Pearson Education, Inc. New Jersey Upper Saddle River).

Hanna, G., Barbeau, E. (2010). Proofs as Bearers of Mathematical Knowledge in Explanation and Proof in Mathematics: Philosophical and Educational Perspectives. 85 - 99.

Hasan, B. (2016). Proses Berpikir Mahasiswa dalam Mengkonstruksi Bukti Menggunakan Induksi Matematika Berdasarkan Teori Pemrosesan Informasi. APOTEMA: Jurnal Pendidikan Matematika. 33 - 40.

İmamoğlu. (2015). Proof Construction and Evaluating of Prospective Mathematics Educators. European Journal of Science and Mathematics Education. 130 - 144.

Kartini, E.S. (2015). Analisa Kesulitan Pembuktian Matematis Mahasiswa pada Mata Kuliah Analisis Real. SEMIRATA 2015. 189 - 199.

Lesseig, K., Hine, G., Gwi Soo Na, Boardman, K. (2019). Perceptions on Proof and Teaching of Proof: A Compariosn Across Preservice Secondary Teachers in Australia, USA, and Korea. Mathematics Education Research Journal.

Mason, J., Burton, L., Stacey, K. (2010). Thinking Mathematically Second Edition. England: Pearson Education Limited.

Muliawati, N.E. (2018). Proses Berpikir Mahasiswa dalam Memecahkan Masalah Pembuktian Grup Berdasarkan Langkah Polya. Jurnal Pendidikan dan Pembelajaran Matematika. 32 - 42.

Nurrahmah, A., Karim, A. (2018). Analisis Kemampuan Pembuktian Matematis pada Mata Kuliah Teori Bilangan. Jurnal Edumath. 21 - 29.

Ozdemir, E., Ovez, F.T.D. (2012). A Research on Proof Perceptions and Attitudes towards Proof and Proofing: Some Implications for Elementary Mathematics Prospective Teachers. Procedia Social and Behavioral Sciences. 2121 - 2125.

Rahardjo, M. (2017). Studi Kasus dalam Penelitian Kualitatif: Konsep dan Prosedurnya. Malang: Not Published.

Ross, K. (1998). Doing and Proving: The Place of Algorithms and Proof in School Mathematics. American Mathematical Monthly. 252 - 255.

Schoenfeld. (1994). What Do We Know About Mathematics Curricula?. Journal of Mathematical Behavior. 55 - 80.

Stefanowicz, A. (2014). Proof and Mathematical Reasoning. Birmingham: University of Birmingham Mathematics Support Centre.

Suryabrata, S. (2012). Psikologi Pendidikan. Jakarta: Raja Grafindo Persada.

Yohani, D.D., Sujadi, I., Usodo, B. (2016). Proses Berpikir Mahasiswa Pendidikan Matematika dalam Pemecahan Masalah Pembuktian Tahun Akademik 2014/2015. JMEE. 79 - 90.

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Published

2020-06-30