An Analysis of Students’ Mathematical Reasoning in Solving Probability Problems Judging from Learning Styles: The Converger
DOI:
https://doi.org/10.15359/ru.38-1.32Keywords:
Mathematical Reasoning, Probability Problem, Learning StylesAbstract
[Background] Several challenges are encountered by students when attempting to solve probability problems, one of which relates to reasoning about the given problem scenario. This phenomenon may arise due to variations in students’ learning styles. [Objective] Thus, the current study aimed to examine students’ reasoning abilities when dealing with probability problems, focusing on those with converging learning styles. [Method] This study employed a qualitative method, involving two students with a converging learning style who were invited to solve reasoning tasks. Three instruments were utilized: learning style questionnaire, mathematical reasoning tasks, and semi-structured interviews. The research data was analyzed through data reduction and display. [Results] The study’s findings revealed that, in solving probability problems, convergers (students with a converging learning style) primarily relied on imitative reasoning. These students demonstrated four patterns. First, they accurately and comprehensively articulated known information from a question and correctly identified the question being asked. Second, they possessed a conceptual understanding of probability but provided inaccurate explanations regarding arithmetic sequences. Although they could devise problem-solving strategies, their articulation of these strategies lacked precision. Third, they utilized the concept of probability and employed problem-solving strategies to solve the given problem and explain the steps involved in reaching the solution. Four, they derived answers from problem-solving strategies and drew accurate conclusions, often exhibiting a tendency to trust their answers and subsequently verify them. [Conclusions] Students with converging learning styles predominantly used imitative reasoning when solving probability problems.
References
Adu-Gyamfi, K., Stiff, L. V., & Bossé, M. J. (2012). Lost in Translation: Examining Translation Errors Associated With Mathematical Representations. School Science and Mathematics, 112(3), 159–170. https://doi.org/10.1111/j.1949-8594.2011.00129.x
Boesen, J., Lithner, J., & Palm, T. (2010). The relation between types of assessment tasks and the mathematical reasoning students use. Educational Studies in Mathematics, 75(1), 89–105. https://doi.org/10.1007/s10649-010-9242-9
Gasteiger, H., Bruns, J., Benz, C., Brunner, E., & Sprenger, P. (2020). Mathematical pedagogical content knowledge of early childhood teachers: a standardized situation-related measurement approach. ZDM - Mathematics Education, 52(2), 193–205. https://doi.org/10.1007/s11858-019-01103-2
Granberg, C., & Olsson, J. (2015). ICT-supported problem solving and collaborative creative reasoning: Exploring linear functions using dynamic mathematics software. Journal of Mathematical Behavior, 37, 48–62. https://doi.org/10.1016/j.jmathb.2014.11.001
Hackenberg, A. J., & Lee, M. Y. (2015). Relationships between students’ fractional knowledge and equation writing. Journal for Research in Mathematics Education, 46(2), 196–243. https://doi.org/10.5951/jresematheduc.46.2.0196
Herbert, S., & Pierce, R. (2012). Revealing educationally critical aspects of rate. Educational Studies in Mathematics, 81(1), 85–101. https://doi.org/10.1007/s10649-011-9368-4
Hirschfeld-Cotton, K. (2008). Mathematical Communication, Conceptual Understanding, and Students’ Attitudes Toward Mathematics. Action Research Projects, 4.
İDİL, Ş., GÜLEN, S., & DÖNMEZ, İ. (2024). What Should We Understand from PISA 2022 Results? Journal of STEAM Education, 7(1). https://doi.org/10.55290/steam.1415261
Ikram, M., Purwanto, Nengah Parta, I., & Susanto, H. (2020). Mathematical reasoning required when students seek the original graph from a derivative graph. Acta Scientiae, 22(6), 45–64. https://doi.org/10.17648/acta.scientiae.5933
Johansson, H. (2016). Mathematical Reasoning Requirements in Swedish National Physics Tests. International Journal of Science and Mathematics Education, 14(6). https://doi.org/10.1007/s10763-015-9636-3
Kang, W. (2015). Implication from Polya and Krutetskii. In S. J. Cho (Ed.), Selected Regular Lectures from the 12th International Congress on Mathematical Education (pp. 405–416). Springer International Publishing Switzerland 2015. https://doi.org/10.1007/978-3-319-17187-6
Khozaei, S. A., Zare, N. V., Moneghi, H. K., Sadeghi, T., & Taraghdar, M. M. (2022). Effects of quantum-learning and conventional teaching methods on learning achievement, motivation to learn, and retention among nursing students during critical care nursing education. Smart Learning Environments, 9(1). https://doi.org/10.1186/s40561-022-00198-7
Lee, K. H. (2017). Convergent and divergent thinking in task modification: a case of Korean prospective mathematics teachers’ exploration. ZDM - Mathematics Education, 49(7), 995–1008. https://doi.org/10.1007/s11858-017-0889-x
Lee, M. Y., & Hackenberg, A. J. (2014). Relationships Between Fractional Knowledge and Algebraic Reasoning: the Case of Willa. International Journal of Science and Mathematics Education, 12(4), 975–1000. https://doi.org/10.1007/s10763-013-9442-8
Lithner, J. (2003). Students ’ Mathematical Reasoning in University Textbook Exercises. Educational Studies in Mathematics, 52(1), 29–55. http://www.jstor.org/stable/3483334
Lithner, J. (2008). A research framework for creative and imitative reasoning. Educational Studies in Mathematics, 67(3), 255–276. https://doi.org/10.1007/s10649-007-9104-2
Lithner, J. (2011). University Mathematics Students’ Learning Difficulties. Education Inquiry, 2(2), 289–303. https://doi.org/10.3402/edui.v2i2.21981
Lithner, J. (2017). Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM - Mathematics Education, 49(6), 937–949. https://doi.org/10.1007/s11858-017-0867-3
Marufi, Ilyas, M., Winahyu, & Ikram, M. (2021). An Implementation of Ethno-STEM to Enhance Conceptual Understanding. Al-Jabar: Jurnal Pendidikan Matematika, 12(1). https://doi.org/10.24042/ajpm.v12i1.7834
Marufi, M., Ilyas, M., Ikram, M., & Kaewhanam, P. (2022). Exploration of high school students ’ reasoning in solving trigonometric function problems. 13(2), 231–249. https://doi.org/10.24042/ajpm.v13i2.12972
Mata-Pereira, J., & da Ponte, J. P. (2017). Enhancing students’ mathematical reasoning in the classroom: teacher actions facilitating generalization and justification. Educational Studies in Mathematics, 96(2), 169–186. https://doi.org/10.1007/s10649-017-9773-4
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third Edit). SAGE Publications, Inc.
Miles, M. B., Huberman, A. M., & Saldaña, J. (2018). Qualitative data analysis: A methods sourcebook. Sage publications.
Morrison, J., Frost, J., Gotch, C., McDuffie, A. R., Austin, B., & French, B. (2020). Teachers’ Role in Students’ Learning at a Project-Based STEM High School: Implications for Teacher Education. International Journal of Science and Mathematics Education, 19(1), 1103-1123. https://doi.org/10.1007/s10763-020-10108-3
OECD. (2018). Programme for International Students Assesment (PISA) Result From PISA 2018.
PISA. (2023). PISA 2022 Results Factsheets Indonesia. The Language of Science Education, 1.
Pitta-Pantazi, D., & Christou, C. (2009). Cognitive styles, dynamic geometry and measurement performance. Educational Studies in Mathematics, 70(1), 5–26. https://doi.org/10.1007/s10649-008-9139-z
Putri, N. U., Mukhini, & Jazwinarti. (2014). Kemampuan Penalaran Matematis Siswa Kelas XI Ipa SMAN 2 Painan Melalui Penerapan Pembelajaran Think Pair Square. Jurnal Pendidikan Matematika, 3(1).
Savard, A., & Polotskaia, E. (2017). Who’s wrong? Tasks fostering understanding of mathematical relationships in word problems in elementary students. ZDM - Mathematics Education, 49(6), 823–833. https://doi.org/10.1007/s11858-017-0865-5
Singer, F. M., Voica, C., & Pelczer, I. (2017). Cognitive styles in posing geometry problems: implications for assessment of mathematical creativity. ZDM - Mathematics Education, 49(1), 37–52. https://doi.org/10.1007/s11858-016-0820-x
Szabo, Z. K., Körtesi, P., Guncaga, J., Szabo, D., & Neag, R. (2020). Examples of problem-solving strategies in mathematics education supporting the sustainability of 21st-century skills. Sustainability (Switzerland), 12(23), 1–28. https://doi.org/10.3390/su122310113
Tohir, M. (2019). Hasil PISA Indonesia Tahun 2018 Turun Dibanding Tahun 2015 (Indonesia’s PISA Results in 2018 are Lower than 2015). Open Science Framework, 2. https://doi.org/10.31219/osf.io/pcjvx
Published
Issue
Section
License
Copyright (c) 2024 Shared by Journal and Authors (CC-BY-NC-ND)
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors who publish with this journal agree to the following terms:
1. Authors guarantee the journal the right to be the first publication of the work as licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
2. Authors can set separate additional agreements for non-exclusive distribution of the version of the work published in the journal (eg, place it in an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
3. The authors have declared to hold all permissions to use the resources they provided in the paper (images, tables, among others) and assume full responsibility for damages to third parties.
4. The opinions expressed in the paper are the exclusive responsibility of the authors and do not necessarily represent the opinion of the editors or the Universidad Nacional.
Uniciencia Journal and all its productions are under Creative Commons Atribución-NoComercial-SinDerivadas 4.0 Unported.
There is neither fee for access nor Article Processing Charge (APC)
