Students’ reasoning patterns in solving statistical data problems at the junior high school level: An APOS perspective
DOI:
https://doi.org/10.29408/jel.v12i1.30955Keywords:
APOS theory, cognitive development, mathematical reasoning, problem-solving, student thinking patternsAbstract
Many students face challenges in reasoning through statistical data problems; however, little is known about how their thinking processes develop through different cognitive stages. A qualitative descriptive design was employed to explore students’ reasoning patterns in solving statistical data problems through the lens of Action, Process, Object, and Schema (APOS) theory. This study was conducted with seventh-grade students at a public junior high school in Kulon Progo, Indonesia. Data were collected through written tests and semi-structured interviews and were analyzed using coding techniques aligned with the APOS indicators. The results show that students with correct answers demonstrated conceptual reasoning and progressed through all APOS stages, whereas those with incorrect answers showed fragmented understanding and failed to complete the cognitive sequence. This study contributes to mathematics education by extending the APOS theory to statistical data representation at the secondary level.
References
Agustina, R., Rahmawati, Y., Irfan, M., Suryadinata, N., & Parwitasari, I. P. (2025). Solving geometry problems using inquiry stages: How are students’ spatial abilities? The International Journal of Science, Mathematics and Technology Learning, 32(2), 149–165. https://doi.org/10.18848/2327-7971/CGP/v32i02/149-165
Borji, V., Martínez-Planell, R., & Trigueros, M. (2025). University Students’ Understanding of Directional Derivative: An APOS Analysis. International Journal of Research in Undergraduate Mathematics Education, 11(1), 116–145. https://doi.org/10.1007/s40753-023-00225-z
Chew, S. L., & Cerbin, W. J. (2021). The cognitive challenges of effective teaching. The Journal of Economic Education, 52(1), 17–40. https://doi.org/10.1080/00220485.2020.1845266
Dubinsky, E., & McDonald, M. A. (2002). APOS: A constructivist theory of learning in undergraduate mathematics education research. In D. Holton, M. Artigue, U. Kirchgräber, J. Hillel, M. Niss, & A. Schoenfeld (Eds.), The Teaching and Learning of Mathematics at University Level (Vol. 7, pp. 275–282). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47231-7_25
Irfan, M., Nusantara, T., Subanji, S., & Sisworo, S. (2020). Students know the concept but are incorrect in solving the proportional problem: How does it happen? The International Journal of Science, Mathematics and Technology Learning, 27(2), 1–12. https://doi.org/10.18848/2327-7971/CGP/v27i02/1-12
Jäder, J., & Johansson, H. (2025). Exploring students’ conceptual understanding through mathematical problem solving: Students’ use of and shift between different representations of rational numbers. Research in Mathematics Education, 1–18. https://doi.org/10.1080/14794802.2025.2456840
Lenz, K., Reinhold, F., & Wittmann, G. (2024). Transitions between conceptual and procedural knowledge profiles. Patterns in understanding fractions and indicators for individual differences. Learning and Individual Differences, 116, 102548. https://doi.org/10.1016/j.lindif.2024.102548
Mukuka, A., Balimuttajjo, S., & Mutarutinya, V. (2020, 2020). Applying the SOLO taxonomy in assessing and fostering students’ mathematical problem-solving abilities Proceedings of the 28th Annual Conference of the Southern African Association for Research in Mathematics, Science and Technology Education,
Nilimaa, J. (2023). New Examination Approach for Real-World Creativity and Problem-Solving Skills in Mathematics. Trends in Higher Education, 2(3), 477–495. https://doi.org/10.3390/higheredu2030028
OECD. (2019). PISA 2018 Results (Volume I): What Students Know and Can Do. OECD. https://doi.org/10.1787/5f07c754-en
Olivares, D., Lupiáñez, J. L., & Segovia, I. (2021). Roles and characteristics of problem solving in the mathematics curriculum: A review. International Journal of Mathematical Education in Science and Technology, 52(7), 1079–1096. https://doi.org/10.1080/0020739X.2020.1738579
Pratiwi, S. A., & Widjajanti, D. B. (2020). Contextual problem in mathematical problem solving: Core ability in Realistic Mathematics Education. Journal of Physics: Conference Series, 1613(1), 012018. https://doi.org/10.1088/1742-6596/1613/1/012018
Sun, C., Shute, V. J., Stewart, A., Yonehiro, J., Duran, N., & D'Mello, S. (2020). Towards a generalized competency model of collaborative problem solving. Computers & Education, 143, 103672. https://doi.org/10.1016/j.compedu.2019.103672
Trigueros, M., Badillo, E., Sánchez-Matamoros, G., & Hernández-Rebollar, L. A. (2024). Contributions to the characterization of the schema using APOS theory: Graphing with derivative. ZDM – Mathematics Education, 56(6), 1093–1108. https://doi.org/10.1007/s11858-024-01615-6
Ugalde, L., Santiago-Garabieta, M., Villarejo-Carballido, B., & Puigvert, L. (2021). Impact of interactive learning environments on learning and cognitive development of children with special educational needs: A literature review. Frontiers in Psychology, 12, 674033. https://doi.org/10.3389/fpsyg.2021.674033
Umam, K., Susandi, A. D., Irfan, M., Awang, M. L. B., Susanti, E. N., & Supandi. (2025). Mathematical creative thinking skills: Using APOS theory to identify student errors in solving contextual problems. Humanities, Arts and Social Sciences Studies, 25(1), 10–20. https://doi.org/10.69598/hasss.25.1.269211
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2026 Betty Kusumaningrum, Muhammad Irfan, Yova Ayu Puspita, Esti Harini, Elyas Djufri, Luc Bergman
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International 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
