Effectiveness of the Multi-Representation Discourse Learning Model on Mathematical Problem-Solving Ability and Self-Confidence
https://doi.org/10.51574/kognitif.v5i3.842
Keywords:
Multi-Representation Discourse, Mathematical Problem-Solving, Self-Confidence, Quasi-Experimental DesignAbstract
This study investigated the effectiveness of the Multi-Representation Discourse (DMR) learning model in improving students’ mathematical problem-solving skills and self-confidence. A quasi-experimental pretest–posttest control group design was applied to 55 students selected through cluster random sampling from a population of 194. Data were collected using observation sheets, problem-solving tests, and self-confidence questionnaires, and analyzed with descriptive and inferential statistics. The results revealed that the DMR model was effectively implemented and significantly enhanced both mathematical problem-solving abilities and self-confidence compared to conventional instruction. Beyond its practical effectiveness, this study contributes to the theoretical discourse by demonstrating the value of multi-representation integration in mathematics learning, and provides empirical evidence that discourse-oriented strategies can strengthen both cognitive and affective outcomes. These findings underscore the potential of the DMR model as a pedagogical innovation for advancing mathematics education.
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Ayalon, M., & Wilkie, K. J. (2020). Investigating peer ‑ assessment strategies for mathematics pre ‑ service teacher learning on formative assessment. Journal of Mathematics Teacher Education, 0123456789. https://doi.org/10.1007/s10857-020-09465-1
Borji, V., Erfani, H., & Font, V. (2020). A combined application of APOS and OSA to explore undergraduate students’ understanding of polar coordinates. International Journal of Mathematical Education in Science and Technology, 51(3), 405–423. https://doi.org/10.1080/0020739X.2019.1578904
Çekmez, E. (2020). What generalizations do students achieve with respect to trigonometric functions in the transition from angles in degrees to real numbers? Journal of Mathematical Behavior, 58(February), 100778. https://doi.org/10.1016/j.jmathb.2020.100778
Charalambous, C. Y., Hill, H. C., Chin, M. J., & McGinn, D. (2020). Mathematical content knowledge and knowledge for teaching: exploring their distinguishability and contribution to student learning. In Journal of Mathematics Teacher Education (Vol. 23, Issue 6). Springer Netherlands. https://doi.org/10.1007/s10857-019-09443-2
Chronaki, A., & Planas, N. (2018). Language diversity in mathematics education research: a move from language as representation to politics of representation. ZDM - Mathematics Education, 50(6), 1101–1111. https://doi.org/10.1007/s11858-018-0942-4
Csíkos, C., & Szitányi, J. (2020). Teachers’ pedagogical content knowledge in teaching word problem solving strategies. ZDM - Mathematics Education, 52(1), 165–178. https://doi.org/10.1007/s11858-019-01115-y
Ding, M., & Li, X. (2014). Transition from concrete to abstract representations: The distributive property in a Chinese textbook series. Educational Studies in Mathematics, 87(1), 103–121. https://doi.org/10.1007/s10649-014-9558-y
Fiallo, J., & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 96(2), 145–167. https://doi.org/10.1007/s10649-017-9755-6
Finesilver, C. (2022). Beyond categories: dynamic qualitative analysis of visuospatial representation in arithmetic. Educational Studies in Mathematics, 110(2), 271–290. https://doi.org/10.1007/s10649-021-10123-3
Fredriksen, H. (2021). Exploring Realistic Mathematics Education in a Flipped Classroom Context at the Tertiary Level. International Journal of Science and Mathematics Education, 19(2), 377–396. https://doi.org/10.1007/s10763-020-10053-1
Gulkilik, H., Moyer-Packenham, P. S., Ugurlu, H. H., & Yuruk, N. (2020). Characterizing the growth of one student’s mathematical understanding in a multi-representational learning environment. Journal of Mathematical Behavior, 58(March 2019), 100756. https://doi.org/10.1016/j.jmathb.2020.100756
Herbel-Eisenmann, B. A., & Otten, S. (2011). Mapping mathematics in classroom discourse. Journal for Research in Mathematics Education, 42(5), 451–485. https://doi.org/10.5951/jresematheduc.42.5.0451
Hernandez-Martinez, P., Rogovchenko, S., Rogovchenko, Y., & Treffert-Thomas, S. (2024). “The theorem says…”: Engineering students making meaning of solutions to Ordinary Differential Equations. Journal of Mathematical Behavior, 73(November 2022), 101116. https://doi.org/10.1016/j.jmathb.2023.101116
Hitt, F., Saboya, M., & Zavala, C. C. (2017). Rupture or continuity: The arithmetico-algebraic thinking as an alternative in a modelling process in a paper and pencil and technology environment. Educational Studies in Mathematics, 94(1), 97–116. https://doi.org/10.1007/s10649-016-9717-4
Ingram, J., Andrews, N., & Pitt, A. (2019). When students offer explanations without the teacher explicitly asking them to. Educational Studies in Mathematics, 101(1), 51–66. https://doi.org/10.1007/s10649-018-9873-9
Ivars, P., Fernández, C., & Llinares, S. (2020). A Learning Trajectory as a Scaffold for Pre-service Teachers’ Noticing of Students’ Mathematical Understanding. International Journal of Science and Mathematics Education, 18(3), 529–548. https://doi.org/10.1007/s10763-019-09973-4
Kobiela, M., & Lehrer, R. (2019). Supporting dynamic conceptions of area and its measure. Mathematical Thinking and Learning, 21(3), 178–206. https://doi.org/10.1080/10986065.2019.1576000
Lee, H. S., Sanei, H., Famularo, L., Masters, J., Bradshaw, L., & Schellman, M. (2023). Validating a concept inventory for measuring students’ probabilistic reasoning: The case of reasoning within the context of a raffle. Journal of Mathematical Behavior, 71(June), 101081. https://doi.org/10.1016/j.jmathb.2023.101081
Montenegro, P., Costa, C., & Lopes, B. (2018). Transformations in the Visual Representation of a Figural Pattern. Mathematical Thinking and Learning, 20(2), 91–107. https://doi.org/10.1080/10986065.2018.1441599
Moreno-Arotzena, O., Pombar-Hospitaler, I., & Barragués, J. I. (2021). University student understanding of the gradient of a function of two variables: an approach from the perspective of the theory of semiotic representation registers. Educational Studies in Mathematics, 106(1), 65–89. https://doi.org/10.1007/s10649-020-09994-9
Muslimin, Indra Putri, R. I., Zulkardi, & Aisyah, N. (2020). Learning integers with realistic mathematics education approach based on islamic values. Journal on Mathematics Education, 11(3), 363–384. https://doi.org/10.22342/JME.11.3.11721.363-384
Öçal, M. F., Şen, C., Güler, G., & Kar, T. (2020). The investigation of prospective mathematics teachers’ non-algebraic solution strategies for word problems. International Journal of Mathematical Education in Science and Technology, 51(4), 563–584. https://doi.org/10.1080/0020739X.2019.1597936
Paoletti, T., Stevens, I. E., Acharya, S., Margolis, C., Olshefke-Clark, A., & Gantt, A. L. (2024). Exploring and promoting a student’s covariational reasoning and developing graphing meanings. Journal of Mathematical Behavior, 74(April), 101156. https://doi.org/10.1016/j.jmathb.2024.101156
Patahuddin, S. M., Ramful, A., Lowrie, T., & Bholoa, A. (2022). Subtleties in spatial visualization maneuvers: Insights from numerical solutions. Journal of Mathematical Behavior, 67(June 2021), 100988. https://doi.org/10.1016/j.jmathb.2022.100988
Swidan, O. (2020). A learning trajectory for the fundamental theorem of calculus using digital tools. International Journal of Mathematical Education in Science and Technology, 51(4), 542–562. https://doi.org/10.1080/0020739X.2019.1593531
Swidan, O., & Fried, M. (2021). Focuses of awareness in the process of learning the fundamental theorem of calculus with digital technologies. Journal of Mathematical Behavior, 62(June 2020), 100847. https://doi.org/10.1016/j.jmathb.2021.100847
Ultan Segal, S. (2009). Action Research in Mathematics Education: a Study of a Master’s Program for Teachers. Unpublished Thesis, April, 231. http://scholarworks.montana.edu/xmlui/bitstream/handle/1/2237/SegalS0509.pdf?sequence=1
Ulusoy, F., & Çakıroğlu, E. (2020). Exploring prospective teachers’ noticing of students’ understanding through micro-case videos. Journal of Mathematics Teacher Education, 0123456789. https://doi.org/10.1007/s10857-020-09457-1
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020a). Word problems in mathematics education: a survey. ZDM - Mathematics Education, 52(1). https://doi.org/10.1007/s11858-020-01130-4
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020b). Word problems in mathematics education: a survey. ZDM - Mathematics Education, 52(1). https://doi.org/10.1007/s11858-020-01130-4

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