Functional thinking and Kolb learning style: Case of solving linear and non-linear pattern problems
Keywords:
functional thinking, generalization, Kolb learning style, linier pattern, non-linear patternAbstract
Functional thinking (FT) is a part of algebraic thinking. Several studies revealed that algebraic thinking is influenced by learning style, and few studies showed FT viewed from learning style. This study aims to describe students’ FT views from Kolb's learning style in solving linear and non-linear pattern tasks. The study used a qualitative approach with a case study method. It involved thirty-one students in 8th grade at an Islamic State junior high school in Mataram, West Nusa Tenggara, Indonesia. Four students were selected as research subjects for analysis of answers and interviews. The Kolb learning style inventory (KLSI) collected research data, tests, and interviews. The instrument consisted of KLSI and FT tests. Data was analyzed by reduction, presenting, and verifying. The finding showed that students with convergent, divergent, and accommodator learning styles can consist of near, far, and formal generalizations and determining inverse in FT. They represented the generalization of the relationship of two quantities symbolically. Meanwhile, students with an assimilator learning style can in FT consisting of near and far generalizations in solving figural and non-figural linear pattern tasks. They can perform formal generalizations and determine inverse-solving figural and non-figural linear pattern tasks. They are also unable to solve figural non-linear pattern tasks.References
Abosalem, Y. (2013). The relationship between the learning styles of students in grades five and six and their held misconceptions about dividing fractions based on kolb’s model (Issue June). British University in Dubai.
Akinyode, B. F., & Khan, T. H. (2016). Students’ learning style among planning students in nigeria using kolb’s learning style inventory. Indian Journal of Science and Technology, 9(47), 1–13. https://doi.org/10.17485/ijst/2015/v8i1/107129
Amit, M., & Neria, D. (2008). Rising to the challenge: using generalization in pattern problems to unearth the algebraic skills of talented pre-algebra students. ZDM Mathematics Education, 40(2), 111–129. https://doi.org/10.1007/s11858-007-0069-5
Biza, I., Hewitt, D., Watson, A., & Mason, J. (2020). Generalization strategies in finding the nth term rule for simple quadratic sequences. International Journal of Science and Mathematics Education, 18(6), 1105–1126. https://doi.org/10.1007/s10763-019-10009-0
Blanton, M., & Kaput, J. J. (2004). Elementary grades students’ capacity for functional thinking. Proceedings of the 28th Conference of the International Group for the Psychology of Mathematics Education, 2, 135–142.
Cohen, L., Manion, L., & Morrison, K. (2000). Research methods in education (5th edition). Routledge.
Creswell, J. W. (2012). Educational research: Planning, conducting, and evaluating quantitative and qualitative research (fourth). Pearson Education.
DePorter, B., & Hernacki, M. (2000). Quantum learning. PT Kaifa.
Erdogan, F., & Gul, N. (2023). Reflections from the generalization strategies used by gifted students in the growing geometric pattern task. Journal of Gifted Education and Creativity, 9(4), 369–385. https://dergipark.org.tr/en/pub/jgedc/issue/74010/1223156
Fraenkel, J. R., Wallen, N. E., & Hyun, H. H. (2012). How to design and evaluate research in education. McGraw-Hill.
Ganesen, P., Osman, S., Abu, M. S., & Kumar, J. A. (2020). The relationship between learning styles and achievement of solving algebraic problems among lower secondary school students. International Journal of Advanced Science and Technology, 29(9 Special Issue), 2563–2574.
Hajaro, U., Nayazik, A., & Kusumawati, R. (2021). Analysis of david kolb’s learning style according to mathematical representation ability. Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 5(2), 403–416. https://doi.org/10.31331/medivesveteran.v5i2.1709
JilardiDamavandi, A., Mahyuddin, R., Elias, H., Daud, S. M., & Shabani, J. (2011). Academic achievement of students with different learning styles. International Journal of Psychological Studies, 3(2), 186–192. https://doi.org/10.5539/ijps.v3n2p186
Kolb, D. . (1984). Experiential learning: Experience as the source of learning and development. Prentice-Hall.
Lannin, J. K. (2003). Developing algebraic reasoning through generalization. Mathematics Teaching in the Middle School, 8(7), 342–348.
Lannin, J. K. (2005). Generalization and Justification: The Challenge of Introducing Algebraic Reasoning Through Patterning Activities. Mathematical Thinking and Learning, 7(3), 231–258. https://doi.org/DOI: 10.1207/s15327833mtl0703_3
Lannin, J. K., Barker, D. D., & Townsend, B. E. (2006). Recursive and explicit rules: How can we build student algebraic understanding? Journal of Mathematical Behavior, 25(4), 299–317. https://doi.org/10.1016/j.jmathb.2006.11.004
Loo, R. (1999). Confirmatory factor analyses of kolb’s learning style inventory (LSI-1985). British Journal of Educational Psychology, 69(2), 213–219. https://doi.org/10.1348/000709999157680
Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. SAGE Publications Inc.
NCTM. (2000). Principless and Standards for School Mathematics. NCTM.
Oliveira, H., Polo-Blanco, I., & Henriques, A. (2021). Exploring prospective elementary mathematics teachers’ knowledge: A focus on functional thinking. Journal on Mathematics Education, 12(2), 257–278. https://doi.org/10.22342/jme.12.2.13745.257-278
Orhun, N. (2007). An investigation into the mathematics achievement and attitude towards mathematics with respect to learning style according to gender. International Journal of Mathematical Education in Science and Technology, 38(3), 321–333. https://doi.org/10.1080/00207390601116060
Rahmah, K., Inganah, S., Darmayanti, R., Sugianto, R., & Ningsih, E. F. (2022). Analysis of mathematics problem solving ability of junior high school students based on APOS theory viewed from the type of kolb learning style. IndoMATH: Indonesia Mathematics Education, 5(2), 109–122.
Ratnaningsih, N., Hidayat, E., & Santika, S. (2019). Mathematical problem-solving skills of students based on the Kolb learning style through creative problem-solving learning. International Journal of Innovation, Creativity and Change, 9(1), 177–186.
Rivera, F. D. (2010). Visual templates in pattern generalization activity. Educational Studies in Mathematics, 73(3), 297–328. https://doi.org/10.1007/s10649-009-9222-0
Rohmanawati, E., Kusmayadi, T. A., & Fitriana, L. (2021). Student’s mathematical communication ability based on Kolb’s learning styles of assimilator and accommodator type. International Conference on Mathematics and Science Education (ICMScE) 2020 on Journal of Physics: Conference Series, 1806(1),012091. https://doi.org/10.1088/1742-6596/1806/1/012091
Siregar, A. P., Juniati, D., & Sulaiman, R. (2017). Profil berpikir fungsional siswa SMP dalam menyelesaikan masalah matematika ditinjau dari perbedaan jenis kelamin [Functional thinking profile of junior high school students in solving mathematics problem based on gender]. Jurnal Review Pembelajaran Matematika, 2(2), 144–152. https://doi.org/10.15642/jrpm.2017.2.2.144-152
Smith, E. (2008). Representational thinking as a framework for introducing functions in the elementary curriculum. In J. Kaput, D. Carraher, & M. Blanton (Eds.), Algebra in the early grades (pp. 95–132). Lawrence Erlbaum/Taylor & Francis Group & NCTM.
Stephens, A. C., Fonger, N., Strachota, S., Isler, I., Blanton, M., Knuth, E., & Gardiner, A. M. (2017). A learning progression for elementary students’ functional thinking a learning progression for elementary students’ functional. Mathematical Thinking and Learning, 19(3), 143–166. https://doi.org/10.1080/10986065.2017.1328636
Sujadi, A. A., Arigiyati, T. A., Kusumaningrum, B., & Utami, T. (2019). The correlation of motivation, activeness, and learning style with mathematical learning achievement. International Conference on Technology, Education and Science, 54–58.
Syawahid, M. (2021). Berpikir fungsional siswa SMP dalam menyelesaikan soal matematika berbasis konteks [Functional thinking of junior high school in solving mathematics problem based context]. Universitas Negeri Malang.
Syawahid, M. (2022). Elementary students’ functional thinking in solving context-based linear pattern problems. Beta: Jurnal Tadris Matematika, 15(1), 37–52. https://doi.org/10.20414/betajtm.v15i1.497
Tanıslı, D. (2011). Functional thinking ways in relation to linear function tables of elementary school students. The Journal of Mathematical Behavior, 30, 206–223. https://doi.org/10.1016/j.jmathb.2011.08.001
Warren, E. A., Cooper, T. J., & Lamb, J. T. (2006). Investigating functional thinking in the elementary classroom: Foundations of early algebraic reasoning. Journal of Mathematical Behavior, 25, 208–223. https://doi.org/10.1016/j.jmathb.2006.09.006
Wicaksono, A. B., Chasanah, A. N., & Sukoco, H. (2021). Kemampuan pemecahan masalah geometri berbasis budaya ditinjau dari gender dan gaya belajar [Geometrical Problem solving abilities cultural-based viewed from gender and learning style]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(1), 240-251. https://doi.org/10.24127/ajpm.v10i1.3256
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with the Jurnal Elemen agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under Creative Commons Attribution-ShareAlike 4.0 International License (CC BY-SA 4.0).
- Authors are able to enter into separate, additional contractual arrangements for the distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
Jurnal Elemen is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License
