KnE Social Sciences

ISSN: 2518-668X

The latest conference proceedings on humanities, arts and social sciences.

Students' Errors in Constructing Mathematical Proofs by Direct Method

Published date: Apr 26 2024

Journal Title: KnE Social Sciences

Issue title: International Conference on Mathematics and Science Education (ICMScE 2022): Learning Models and Teaching Approaches

Pages: 651–659

DOI: 10.18502/kss.v9i13.15969

Authors:

Herizal .herizal_mathedu@unimal.ac.idDepartment of Mathematics Education, Universitas Malikussaleh, Jl. Cot Teungku Nie, Reuleut, Aceh Utara 24355, Indonesia

Marhami .Department of Mathematics Education, Universitas Malikussaleh, Jl. Cot Teungku Nie, Reuleut, Aceh Utara 24355, Indonesia

Nurul AkmalDepartment of Tadris Mathematics, IAIN Lhokseumawe, Jl. Medan-Banda Aceh, Alue Awe- Muara Dua, Lhokseumawe 24352, Indonesia

Abstract:

In mathematics, there are several methods for proving mathematical statements, two of them are direct method and indirect method. Both the methods were included in the mathematics curriculum at senior high school level as a learning topic. It implied that the teachers or pre-service teachers must master these methods. In addition, learning advanced mathematics courses also needed the ability of mathematical proving. The direct method was often used in proving mathematical statements. This descriptive qualitative study was conducted to examine what errors were written by the students in constructing mathematical proofs by direct method. Two basic problems (mathematical statements) were administered to 13 college students. They were pre-service mathematics teachers in one of the public universities in Aceh, Indonesia, and were asked to prove the statements by direct method. The data were analyzed by using Miles and Huberman step. The results showed that there were three main errors, (1) errors in using definition correctly, (2) errors in algebraic process, and (3) proving by examples. It concluded that the students must be accustomed to mathematical proving activities to avoid errors in constructing mathematical proofs.

Keywords: constructing mathematical proofs, direct method, students’ errors

References:

[1] Kemendikbud. “Peraturan menteri pendidikan nasional RI no. 22 tahun 2006. tentang standar isi kurikulum pendidikan dasar dan menengah.” Departemen Pendidikan Nasional. p. 2006.

[2] Principles N. “Standards for school mathematics reston, va natl.,” Counc. Teach. Math. p. 2000.

[3] Doruk M, Kaplan A. “Prospective mathematics teachers’ difficulties in doing proofs and causes of their struggle with proofs,” 1st International Eurasian Educational Research Congress. pp. 315–328, 2015.

[4] Rav Y. “Why do we prove theorems?” philosophia mathematica. vol. 7, no. 1, pp. 5–41, 1999. https://doi.org/10.1093/philmat/7.1.5.

[5] Hersh R. Proving is convincing and explaining. Educ Stud Math. 1993;24(4):389–99.

[6] Herizal H, Suhendra S, Nurlaelah E. The ability of senior high school students in comprehending mathematical proofs. Journal of Physics: Conference Series. Institute of Physics Publishing; 2019. https://doi.org/10.1088/1742-6596/1157/2/022123.

[7] Coe R, Ruthven K. Proof practices and constructs of advanced mathematics students. Br Educ Res J. 1994;20(1):41–53.

[8] Güler G, Dikici R. Examining prospective mathematics teachers’ proof processes for algebraic concepts. Int J Math Educ Sci Technol. 2014;45(4):475–97.

[9] Weber K. Student difficulty in constructing proofs: the need for strategic knowledge. Educ Stud Math. 2001;48(1):101–19.

[10] Moore RC. Making the transition to formal proof. Educ Stud Math. 1994;27(3):249–66.

[11] Houston K. How to think like a mathematician: a companion to undergraduate mathematics. Cambridge: Cambridge University Press; 2009. https://doi.org/10.1017/CBO9780511808258.

[12] Mertens DM. Research and evaluation in education and psychology: integrating diversity with quantitative, qualitative, and mixed methods. Sage publications; 2019.

[13] Creswell JW. Research design: qualitative, quantitative, and mixed methods approaches. California: SAGE Publications, Inc; 2014.

[14] Tong DH, Loc NP. Students’ errors in solving mathematical word problems and their ability in identifying errors in wrong solutions. Eur J Educ Stud. 2017;3(6):226–41.

[15] Fei Lai C. Technical report: error analysis in mathematics. Eugene; 2012.

[16] Stavrou SG. Common error and misconceptions in mathematical proving by education undergraduates. Issues in the Undergraduate Mathematics Preparation of School Teachers. 2014;1:1–8.

Download
HTML
Cite
Share
statistics

183 Abstract Views

68 PDF Downloads