Rethinking Matrix Instruction: A Mixed-Methods Analysis of Students’ Problem-Solving Skills and Pedagogical Challenges
DOI:
https://doi.org/10.36312/ijece.v4i1.3399Keywords:
Problem-solving ability, Mathematics learning, Matrix topic, Mixed-methods, Pedagogical challengesAbstract
This study aims to analyze students’ problem-solving skills in the matrix topic and to identify instructional constraints that influence the learning process. A mixed-methods approach was employed: the quantitative phase involved an eight-session expository intervention (90 minutes per session) and an assessment consisting of 30 multiple-choice and 5 essay questions (scored 0–100), while the qualitative phase included open-ended interviews with the teacher responsible for matrix instruction. Quantitative findings revealed that most students remained at the basic mastery level, with an average score of 26.82 and a distribution dominated by the “Low” category. Only 3.88% of students reached the “Good” level, and a binomial test confirmed that this proportion was significantly lower than the reference threshold (p < 0.001), reinforcing the conclusion that student performance fell short of expected standards. These findings highlight the urgent need for early diagnosis of foundational algebra skills—such as row-column operations and linear equation manipulation—before introducing more complex matrix concepts. The qualitative analysis revealed that although the teacher still employed expository methods—lectures, question and answer, and open discussions—these strategies were insufficient for fostering deep problem-solving skills. Students often relied on mechanical procedures without conceptual understanding, struggled to connect algebraic notation to real-world contexts, and lost motivation when facing multi-step problems. The combined results suggest that instructional design should shift toward more contextual and concept-exploratory approaches. Strategic steps are recommended, including the adoption of structured problem-solving methods to improve learning outcomes in mathematics. Furthermore, curriculum development should allocate sufficient time and resources to matrix topics, provide professional development for teachers in designing innovative instruction, and ensure access to digital infrastructure that supports mathematical visualization.
References
Agustiningsih, R., & Syamsudin, A. (2019). Authentic assessment model in problem solving learning for kindergarten. https://doi.org/10.2991/iceri-18.2019.56
Ballon, E., Gomez, F., Castro, A., & Linares, M. (2024). Evaluating problem-solving and procedural skills of first-year students in a Peruvian higher education institution. Eurasia Journal of Mathematics Science and Technology Education, 20(2), em2396. https://doi.org/10.29333/ejmste/14154
Bernacki, M., & Walkington, C. (2018). The role of situational interest in personalized learning. Journal of Educational Psychology, 110(6), 864–881. https://doi.org/10.1037/edu0000250
Cabotage, D. (2024). Mathematics vocabulary and problem-solving skills of Grade 4 pupils in Narvacan North District. International Journal for Multidisciplinary Research, 6(3). https://doi.org/10.36948/ijfmr.2024.v06i03.21269
Demirci, N., & ?ahin, F. (2024). The effects of a systematic approach to solve real-life inventive problems in science class. Journal of Turkish Science Education, 20(1). https://doi.org/10.36681/tused.2023.004
Dooren, W. V., Lem, S., Wortelaer, H., & Verschaffel, L. (2019). Improving realistic word problem solving by using humor. The Journal of Mathematical Behavior, 53, 96–104. https://doi.org/10.1016/j.jmathb.2018.06.008
Jiang, P., Zhang, Y., Jiang, Y., & Xiong, B. (2022). Preservice mathematics teachers’ perceptions of mathematical problem solving and its teaching: A case from China. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.998586
Kabael, T., & Baran, A. (2023). An investigation of mathematics teachers’ conceptions of mathematical literacy related to participation in a web-based PISA course. Bart?n University Journal of Faculty of Education, 12(2), 315–324. https://doi.org/10.14686/buefad.1053557
Ke, F., Dai, C., West, L., Pan, Y., & Xu, J. (2023). Using mathematizing supports for applied problem solving in a game-based learning environment. Journal of Educational Computing Research, 62(2), 248–280. https://doi.org/10.1177/07356331231206990
Ke, F., Dai, C., & West, L. (2024). Mathematical experience in game-based problem-solving. Journal of Computer Assisted Learning, 40(3), 1083–1097. https://doi.org/10.1111/jcal.12938
Khalid, M., Saad, S., Hamid, S., Abdullah, M., Ibrahim, H., & Shahrill, M. (2020). Enhancing creativity and problem solving skills through creative problem solving in teaching mathematics. Creativity Studies, 13(2), 270–291. https://doi.org/10.3846/cs.2020.11027
Ling, A., & Mahmud, M. (2023). Challenges of teachers when teaching sentence-based mathematics problem-solving skills. Frontiers in Psychology, 13. https://doi.org/10.3389/fpsyg.2022.1074202
Nahdi, D., Cahyaningsih, U., Jatisunda, M., & Rasyid, A. (2023). Mathematics interest and reading comprehension as correlates of elementary students’ mathematics problem-solving skills. Edukasiana: Jurnal Inovasi Pendidikan, 3(1), 115–127. https://doi.org/10.56916/ejip.v3i1.510
Nortvedt, G. (2018). Policy impact of PISA on mathematics education: The case of Norway. European Journal of Psychology of Education, 33(3), 427–444. https://doi.org/10.1007/s10212-018-0378-9
Ramirez, G., Chang, H., Maloney, E., Levine, S., & Beilock, S. (2016). On the relationship between math anxiety and math achievement in early elementary school: The role of problem solving strategies. Journal of Experimental Child Psychology, 141, 83–100. https://doi.org/10.1016/j.jecp.2015.07.014
Said, Z., Mansour, N., & Abu-Tineh, A. (2023). Integrating technology pedagogy and content knowledge in Qatar’s preparatory and secondary schools: The perceptions and practices of STEM teachers. Eurasia Journal of Mathematics Science and Technology Education, 19(6), em2271. https://doi.org/10.29333/ejmste/13188
Setiawan, H., Handican, R., & Rurisman, R. (2023). Revolutionizing math education: Unleashing the potential of web-based learning media for enhanced mathematical problem solving skills. JDIME, 1(2), 01–11. https://doi.org/10.32939/jdime.v1i2.2978
Simamora, R., Saragih, S., & Hasratuddin, H. (2018). Improving students’ mathematical problem solving ability and self-efficacy through guided discovery learning in local culture context. International Electronic Journal of Mathematics Education, 14(1). https://doi.org/10.12973/iejme/3966
Uji, R., Angga, D., & Rajagukguk, W. (2022). Differences in students’ mathematical communication ability and self-efficacy between open ended and contextual learning approach. Journal of Education and Practice, 13(7), 1–9. https://doi.org/10.7176/jep/13-7-03
Ulandari, L., Amry, Z., & Saragih, S. (2019). Development of learning materials based on Realistic Mathematics Education approach to improve students’ mathematical problem solving ability and self-efficacy. International Electronic Journal of Mathematics Education, 14(2). https://doi.org/10.29333/iejme/5721
Umar, U., & Zakaria, Z. (2022). The effectiveness of the realistic math education (RME) learning method based on manipulative media in improving the problem-solving abilities of elementary school students. Ekspose: Jurnal Penelitian Hukum dan Pendidikan, 21(1), 1369–1376. https://doi.org/10.30863/ekspose.v21i1.3405
Van Dooren, W., Lem, S., Wortelaer, H., & Verschaffel, L. (2019). Improving realistic word problem solving by using humor. The Journal of Mathematical Behavior, 53, 96–104. https://doi.org/10.1016/j.jmathb.2018.06.008
Wangmo, P. (2021). Factors affecting Bhutanese secondary school students’ ability in solving mathematical word problems: A case study. Asian Research Journal of Mathematics, 1–13. https://doi.org/10.9734/arjom/2021/v17i130260
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Rasyidin Rasyidin
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
