Keywords
modeling problems
arithmetic relationship
How to Cite
Abstract
Algebraic thinking is important for developing students' mathematical generalization abilities, and identifying patterns, shapes, and symbols. This study uses a qualitative descriptive approach that aims to describe the profile of students' algebraic thinking in solving modeling problems. The subjects of this study were 158 fifth-grade students in two private schools in Surakarta, Central Java. The data collection instrument used was six test questions related to the modeling component adopted from Ralston. Prior to use, the instrument was validated by 3 elementary school mathematics learning experts and tested on 10 students who were not the subject of the study. Based on the test results, there were 12 students who scored in the high category. This study focuses on analyzing the algebraic thinking profile of students with high categories. The results showed that high-category subjects were able to demonstrate understanding related to modeling indicators in algebraic thinking, namely understanding the meaning of the equal sign (=) as an equivalence relationship, using variables to solve problems in the form of equations, and understanding the relationships between arithmetic operations. However, a small number of subjects still experience calculation errors and understanding errors in algebraic operations. Hence, it can be concluded that subjects with high categories are able to demonstrate algebraic thinking skills in the modeling component
References
Afonso, D., & Mc Auliffe, S. (2019). Children’s capacity for algebraic thinking in the early grades. African Journal of Research in Mathematics, Science and Technology Education, 23(2), 219–232. https://doi.org/10.1080/18117295.2019.1661661
Apsari, R. A., Putri, R. I. I., Sariyasa, Abels, M., & Prayitno, S. (2020). Geometry representation to develop algebraic thinking: A recommendation for a pattern investigation in pre-algebra class. Journal on Mathematics Education, 11(1), 45–58. https://doi.org/10.22342/jme.11.1.9535.45-58
Blanton, M. L., & Kaput, J. J. (2011). Functional thinking as a route into algebra in the elementary grades. 5–23. https://doi.org/10.1007/978-3-642-17735-4_2
Eriksson, H., & Eriksson, I. (2021). Learning actions indicating algebraic thinking in multilingual classrooms. Educational Studies in Mathematics, 106(3), 363–378. https://doi.org/10.1007/s10649-020-10007-y
Eriksson, H., & Sumpter, L. (2021). Algebraic and fractional thinking in collective mathematical reasoning. Educational Studies in Mathematics, 108(3), 473–491. https://doi.org/10.1007/s10649-021-10044-1
Eriksson, I., & Tabachnikova, N. (2022). “Learning models”: Utilising young students’ algebraic thinking about equations. Lumat, 10(2), 215–238. https://doi.org/10.31129/LUMAT.10.2.1681
Harti, L. S., & Agoestanto, A. (2019). Analysis of algebraic thinking ability viewed from the mathematical critical thinking ablity of junior high school students on problem based learning A R T I C L E I N F O. Unnes Journal of Mathematics Education, 8(2), 119–127. https://doi.org/10.15294/ujme.v8i2.32060
Kamol, N., & Har, Y. B. (2010). Upper primary school students’ algebraic thinking. Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia, July, 289–296. https://files.eric.ed.gov/fulltext/ED520911.pdf
Kieran, C. (2004). Algebraic thinking in the early grades : What is it? Mathematics Educator, 8(1), 139–151.
Kriegler, S. (2007). Just what is algebraic thinking? Introduction to algebra :Teacher handbook, 1–11.
Lew, H.-C. (2004). Developing algebraic thinking in early grades: Case study of korean elementary school mathematics 1. The Mathematics Educator, 8(1), 88–106.
Patton, B. (2012). Analyzing algebraic thinking using “Guess My Number” problems. International Journal of Instruction, 5(1), 5–22.
Permatasari, D., Azka, R., & Fikriya, H. (2021). Exploring students’ algebraic thinking in generational activities and their difficulties. Beta: Jurnal Tadris Matematika, 14(1), 53–68. https://doi.org/10.20414/betajtm.v14i1.418
Pitta-Pantazi, D., Chimoni, M., & Christou, C. (2020). Different types of algebraic thinking: an Empirical study focusing on middle school students. International Journal of Science and Mathematics Education, 18(5), 965–984. https://doi.org/10.1007/s10763-019-10003-6
Pourdavood, B. R., McCarthy, K., & McCafferty, T. (2020). The impact of mental computation on children’s mathematical communication, problem solving, reasoning, and algebraic thinking. Athens Journal of Education, 7(3), 241–254. https://doi.org/10.30958/aje.7-3-1
Rahmawati, A. W., Juniati, D., & Lukito, A. (2019). Algebraic Thinking profiles of junior high schools’ pupil in mathematics problem solving. International Journal of Trends in Mathematics Education Research, 2(4), 202–206. https://doi.org/10.33122/ijtmer.v2i4.137
Ralston, N. C. (2013). The Development and validation of a diagnostic assessment of algebraic thinking skills for students in the elementary grades. Retrieved from: http://hdl.handle.net/1773/23606
Sibgatullin, I. R., Korzhuev, A. V., Khairullina, E. R., Sadykova, A. R., Baturina, R. V., & Chauzova, V. (2022). A systematic review on algebraic thinking in education. Eurasia Journal of Mathematics, Science and Technology Education, 18(1), 1–15. https://doi.org/10.29333/EJMSTE/11486
Somasundram, P. (2021). The role of cognitive factors in year five pupils’ algebraic thinking: a structural equation modelling analysis. Eurasia Journal of Mathematics, Science and Technology Education, 17(1), 1–12. https://doi.org/10.29333/ejmste/9612
Töman, U., & Gökburun, Ö. (2022). What was and is algebraic thinking skills at different education levels? World Journal of Education, 12(4), 8. https://doi.org/10.5430/wje.v12n4p8
Utomo, D. P. (2020). The pattern of a relational understanding of fifth-grade students on integer operations. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(2), 119–129. https://doi.org/10.23917/jramathedu.v5i2.9545
Veloso, M. G., Landanganon, L., Lamanilao, R., & Elipane, L. (2021). Integration of Ignatian values in the development of algebraic thinking via utilization of quasi-variables: A lesson study. International Journal of Evaluation and Research in Education, 10(4), 1298–1305. https://doi.org/10.11591/IJERE.V10I4.21583
Venenciano, L. C. H., Yagi, S. L., Zenigami, F. K., & Dougherty, B. J. (2020). Supporting the development of early algebraic thinking, an alternative approach to number. Investigations in Mathematics Learning, 12(1), 38–52. https://doi.org/10.1080/19477503.2019.1614386
Wettergren, S. (2022). Identifying and promoting young students’ early algebraic thinking. Lumat, 10(2), 190–214. https://doi.org/10.31129/LUMAT.10.2.1617
Windsor, W. (2010). Algebraic thinking : A problem solving approach. Proceedings of the 33rd Annual Conference of the Mathematics Education Research Group of Australasia, 33, 665–672. Retrieved from: https://research-repository.griffith.edu.au/bitstream/handle/10072/36557/67823_1.pdf?sequence=1&isAllowed=y
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