Senior high school students’ argumentation in proving mathematical induction based on mathematical abilities

Natasya Ziana Walidah, Elly Susanti

Abstract


Argumentation and proof are two interrelated elements in mathematics, which is one of the important goals in mathematics education. Furthermore, these also need to be supported by students' mathematical abilities, so that it has implications for proving they did. This qualitative research will be explained descriptively which aims to find out senior high school students' argumentation in proving mathematical induction. This research subjects consisted of six senior high school students in Surabaya who had low, medium, and high mathematical abilities. Research data were collected through a written test about proving mathematical induction. Then, the data analysis will be carried out, including: sorting the data, presenting the data, and making conclusions. The results shows that senior high school students who have medium and high mathematical abilities can proving mathematical induction which bring up claims, evidence, and reasoning in their argumentation. Meanwhile, senior high school students who have low mathematical abilities can proving mathematical induction which only bring up claims and evidence in their argumentation.


Keywords


Argumentation, Proving Mathematical Induction, Mathematical Abilities

Full Text:

PDF

References


Aberdein, A. (2009). Mathematics and argumentation. Foundations of Science, 14(1–2), 1. https://doi.org/https://doi.org/10.1007/s10699-008-9158-3

Brown, R. (2017). Using collective argumentation to engage students in a primary mathematics classroom. Mathematics Education Research Journal, 29(2), 183–199. https://doi.org/10.1007/s13394-017-0198-2

CadwalladerOlsker, T. (2011). What do we mean by mathematical proof? Journal of Humanistic Mathematics, 1(1), 33–60. https://doi.org/10.5642/jhummath.201101.04

Cervantes-Barraza, J. A., Hernandez Moreno, A., & Rumsey, C. (2020). Promoting mathematical proof from collective argumentation in primary school. School Science and Mathematics, 120(1), 4–14. https://doi.org/10.1111/ssm.12379

Firmasari, S., & Sulaiman, H. (2019). Kemampuan pembuktian matematis mahasiswa menggunakan induksi matematika. Journal Of Medives: Journal Of Mathematics Education IKIP Veteran Semarang, 3(1), 1–9. https://doi.org/https://doi.org/10.31331/medivesveteran.v3i1.642

González-Howard, M., & McNeill, K. L. (2019). Teachers’ framing of argumentation goals: Working together to develop individual versus communal understanding. Journal of Research in Science Teaching, 56(6), 821–844. https://doi.org/10.1002/tea.21530

González-Howard, M., McNeill, K. L., Marco-Bujosa, L. M., & Proctor, C. P. (2017). ‘Does it answer the question or is it French fries?’: an exploration of language supports for scientific argumentation. International Journal of Science Education, 39(5), 528–547. https://doi.org/10.1080/09500693.2017.1294785

Hapipi, S. A., & Turmuzi, M. (2019). PROFIL ARGUMENTASI MAHASISWA DALAM MELAKUKAN PEMBUKTIAN PADA TOPIK ANALSISIS KOMPLEKS. Mandalika Mathematics and Educations Journal, 1(1), 41–52. https://doi.org/http://dx.doi.org/10.29303/jm.v1i1.1243

Hine, G. (2017). Proof by mathematical induction: Professional practice for secondary teachers. 26th Biennial Conference of the Australian Association of Mathematics Teachers, 1–8.

Karsenty, R. (2014). Mathematical Ability. In Encyclopedia of Mathematics Education. https://doi.org/10.1007/978-94-007-4978-8_94

Kartini, E. S. (2015). Analisa Kesulitan Pembuktian Matematis Mahasiswa pada Mata Kuliah Analisis Real. SEMIRATA 2015, 1(1), 189–199. https://jurnal.untan.ac.id/index.php/semirata2015/article/view/14066

Knudsen, J., Lara-meloy, T., Stevens, H. S., & Rutstein, D. W. (2014). Advice for mathematical argumentation. Mathematics Teaching in the Middle School. https://doi.org/https://doi.org/10.5951/mathteacmiddscho.19.8.0494

Laamena, C. (2017). Karakteristik Warrant dalam Argumentasi dan Pembuktian Matematis. Seminar Nasional Hasil Penelitian Universitas Kanjuruhan Malang, 296–302. https://semnas.unikama.ac.id/lppm/prosiding/2017/4.PENDIDIKAN/Christina_Penelitian_Pendidikan.pdf

McNeill, K. L. (2011). Elementary students’ views of explanation, argumentation, and evidence, and their abilities to construct arguments over the school year. Journal of Research in Science Teaching. https://doi.org/10.1002/tea.20430

McNeill, K. L., GonzÁlez-Howard, M., Katsh-Singer, R., & Loper, S. (2017). Moving Beyond Pseudoargumentation: Teachers’ Enactments of an Educative Science Curriculum Focused on Argumentation. Science Education. https://doi.org/10.1002/sce.21274

Mcneill, K. L., & Krajcik, J. (2008). Inquiry and Scientific Explanations: Helping Students Use Evidence and Reasoning. In J. Luft, R. Bell, & J. Gess-Newsome (Eds.), Science as inquiry in the secondary setting (pp. 121–134). Arlington, VA: National Science Teachers Association Press.

McNeill, K. L., & Krajcik, J. S. (2012). Supporting grade 5–8 students in constructing explanations in science: The claim, evidence and reasoning framework for talk and writing. New York, NY: Pearson Allyn & Bacon.

McNeill, K. L., & Martin, D. M. (2011). Claims, Evidence, and Reasoning: Demystifying Data During a Unit on Simple Machines. Science and Children, 48(8), 52–56. http://searkscience.pbworks.com/w/file/fetch/70117336/2-Claimsevidence.pdf

Michaelson, M. T. (2008). A literature review of pedagogical research on mathematical induction. Australian Senior Mathematics Journal, 22(2), 57–62. https://doi.org/https://search.informit.org/doi/10.3316/informit.410329014071111

Mikeska, J. N., & Howell, H. (2020). Simulations as practice-based spaces to support elementary teachers in learning how to facilitate argumentation-focused science discussions. Journal of Research in Science Teaching. https://doi.org/10.1002/tea.21659

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook. Third Edition. In The SAGE Handbook of Applied Social Research Methods.

Nizoloman, O. N. (2013). Relationship between Mathematical Ability and Achievement in Mathematics among Female Secondary School Students in Bayelsa State Nigeria. Procedia - Social and Behavioral Sciences, 106. https://doi.org/10.1016/j.sbspro.2013.12.254

Pungkasari, A. M., Purwosetiyono, F. X. D., & Pramasdyahsari, A. S. (2020). Kemampuan Spasial Perception dalam Menyelesaikan Masalah Geometri berdasarkan Teori Van Hiele Ditinjau dari Kemampuan Matematika. Prismatika: Jurnal Pendidikan Dan Riset Matematika, 3(1), 75–86. https://doi.org/https://doi.org/10.33503/prismatika.v3i1.1123

Ruggiero, V. R. (2014). Becoming a critical thinker. USA: Cengage Learning.

Sugiyono. (2015). Sugiyono, Metode Penelitian dan Pengembangan Pendekatan Kualitatif, Kuantitatif, dan R&D , (Bandung: Alfabeta, 2015), 407 1. Metode Penelitian Dan Pengembangan Pendekatan Kualitatif, Kuantitatif, Dan R&D.

Suhendra, M. (2015). ARGUMENTASI MATEMATIK SEBAGAI SEBUAH KOMPETENSI MATEMATIK. Jurnal Pengajaran Matematika Dan Ilmu Pengetahuan Alam, 15(1). https://doi.org/10.18269/jpmipa.v15i1.284

Toulmin, S. E. (2003). The uses of argument: Updated edition. In The Uses of Argument: Updated Edition. https://doi.org/10.1017/CBO9780511840005

Walidah, N. Z., Kusaeri, K., & Yudi, U. (2019). Mengoptimalkan dukungan guru dalam melibatkan siswa menggunakan argumentasi kolektif pada pembelajaran matematika. MaPan, 7(2), 261–280. https://doi.org/10.24252/mapan.2019v7n2a7

Zambak, V. S., & Magiera, M. T. (2020). Supporting grades 1–8 pre-service teachers’ argumentation skills: constructing mathematical arguments in situations that facilitate analyzing cases. International Journal of Mathematical Education in Science and Technology, 51(8). https://doi.org/10.1080/0020739X.2020.1762938




DOI: https://doi.org/10.18860/ijtlm.v4i1.14315

Refbacks

  • There are currently no refbacks.




Copyright (c) 2022 Natasya Ziana Walidah, Elly Susanti

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


International Journal on Teaching and Learning Mathematics is powered by Open Journal Systems

Department of Mathematics Education
Universitas Islam Negeri Maulana Malik Ibrahim Malang

Information:

Address: Jalan Gajayana 50 Malang, Jawa Timur, Indonesia 65144 
Phone/Fax: (0341) 552398
Website: ejournal.uin-malang.ac.id/index.php/ijtlm
View Stats: Web Analytics View IJTLM Stats
Email: ijtlm@uin-malang.ac.id
p-ISSN: 2621-2188
e-ISSN: 2621-2196

Indexed by : 

 
 

 

International Journal on Teaching and Learning Mathematics is licensed under
a Creative Commons Attribution-ShareAlike 4.0 International License.


To ensure the language quality of the manuscript, the authors have to use a professional proofreading service.