Kesulitan Siswa dalam Membuktikan Masalah Kesamaan dan Ketidaksamaan Matematika Menggunakan Induksi Matematika

I Wayan Puja Astawa, I Gusti Putu Sudiarta, I Nengah Suparta

Abstract


Mathematical similarities and inequalities are common mathematical statements related to numbers whose truth can be proven by mathematical induction. Proving by mathematical induction involves two main steps, namely the basic step and the induction step. The study of mathematical induction related to similarity and inequality is very important and is still relatively limited in quantity. This study aims to determine whether there are significant differences in students' ability to prove mathematical statements using mathematical induction on mathematical similarities and inequalities problems and identify misconceptions. The study was conducted with a mixed method. A sample of 117 students from two high schools in the city of Singaraja was selected by a random cluster technique to obtain quantitative data. Meanwhile, the research subjects were two students selected based on the misconceptions shown to obtain qualitative data. Quantitative data on the ability to prove the similarity and inequality problems using mathematical induction was collected by written tests and qualitative data on misconceptions were collected by interview. Quantitative data were analyzed by a paired group t-test and by z test for proportions. Meanwhile, qualitative data were analyzed by content analysis of students' works to identify their misconceptions. The results showed that proving the mathematical induction of the inequality problem was more difficult than proving the similarity problem. This difficulty occurs both in the basic step and the induction step. Misconceptions arise due to the fallacy of analogies and interpretations of mathematical notation.

Keywords


equality; inequality; mathematical induction; misconception

Full Text:

PDF

References


Andrew, L. (2007). Reasons why students have difficulties with mathematical induction. Retrieved from files.eric.ed.gove/fulltext/ED495959.pdf.

Ashkenazi, Y., & Itzkovitch, E. (2014). Proof by mathematical induction. International Journal of Innovation and Research in Educational Sciences, 1(3), 186–190.

Avital, S., & Libeskind, S. (1978). Mathematical induction in the classroom: Didactical and mathematical issues. Educational Studies in Mathematics, 9(4), 429–438. https://doi.org/10.1007/BF00410588.

Baker, J. (1996). Student’s difficulties with proof by mathematical induction. Paper Presented at Annual Meeting of the American Educational Research Association. New York.

Dogan, H. (2016). Mathematical induction: deductive logic perspective. European Journal of Science and Mathematics Education, 4(3), 315–330.

Ernest, P. (1984). Mathematical induction: A pedagogical discussion. Educational Studies in Mathematics, 15(2), 173–189. https://doi.org/10.1007/BF00305895.

Gruver, J. D. (2010). Growth in students’ conceptions of mathematical induction. Retrieved from All Theses and Dissertations. 2166 website: https://scholarsarchive.byu.edu/etd/2166.

Harel, G. (2002). The development of mathematical induction as a proof scheme: a model for DNR-Based Instruction. In S. R. Campbell & R. Zaskis (Eds.), Learning and Teaching Number Theory: Research in Cognition and Instruction (pp. 185–212). New Jersey: Ablex Publishing Corporation.

Hine, G. (2017). Proof by mathematical induction: Professional practice for secondary teachers. In V. Barker, T. Spencer, & K. Manuel (Eds.), Capital Maths. Proceedings of the 26th Biennial Conference of the Australian Association of Mathematics Teachers (pp. 117–124). Retrieved from https://www.aamt.edu.au/Library/Conference-proceedings.

Kong, C. M. (2003). Mastery of mathematical induction among junior college. The Mathematics Educator, 7(2), 37–54.

Lowenthal, F., & Eisenberg, T. (1992). Mathematical induction in school: an illusion of rigor? School Science and Mathematics, 92(5), 233–238. https://doi.org/10.1111/j.1949-8594.1992.tb15580.x.

Movshovitz-Hadar, N. (1993). Mathematical induction: a focus on the conceptual framework. School Science and Mathematics, 93(8), 408–417. https://doi.org/10.1111/j.1949-8594.1993.tb12271.x.

Öhman, L.-D. (2016). A beautiful proof by induction. Journal of Humanistic Mathematics, 6(1), 73–85. https://doi.org/10.5642/jhummath.201601.06.

Permendikbud nomor 24 tahun 2016 tentang Kompetensi Inti dan Kompetensi Dasar Pelajaran pada Kurikulum 2013 pada Pendidikan Dasar dan Pendidikan Menengah. (2016). Jakarta: Kemdikbud.

Segal, J. (1998). Learners’ difficulties with induction proofs. International Journal of Mathematical Education in Science and Technology, 29(2), 159–177. https://doi.org/10.1080/0020739980290201.

Strauss, A., & Corbin, J. (1990). Basics of qualitative research: Grounded theory procedures and techniques. Thousand Oaks, CA: Sage Publications, Inc.

Supardi. (2016). Aplikasi statistik dalam penelitian konsep statistik yang lebih komprehensip. Jakarta: Change Publication.


Article Metrics

Abstract view : 0 times
PDF - 0 times

Refbacks

  • There are currently no refbacks.


Copyright (c) 2020 Jurnal Elemen

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


 Creative Commons License
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

View My Stats