Email this article Restructuring Conceptual Understanding: The Efficacy of Representation-Based Remedial Learning on Algebraic Misconceptions
), Cut Morina Zubainur(3), Arhamni Hamid(4)
| 
Country:
(1) Department of Mathematics Education, Syiah Kuala University, Indonesia
(2) Department of Mathematics Education, Syiah Kuala University, Indonesia
(3) Department of Mathematics Education, Syiah Kuala University, Indonesia
(4) Department of Educational Evaluation, Sultan Idris Education University, Malaysia
Corresponding Author
Misconceptions remain a major problem in mathematics learning at the junior high school level, particularly in algebraic expressions, which require conceptual understanding and the ability to translate various mathematical representations. This study aims to assess improvements in students' conceptual understanding and analyze changes in the types of misconceptions following the implementation of mathematical representation-based remedial learning. This study used a mixed methods approach with an explanatory sequential design. The subjects comprised 33 eighth-grade students at a public junior high school in Banda Aceh City, Indonesia, selected using purposive sampling. Quantitative data were collected using a three-tier diagnostic test before and after the intervention. In contrast, qualitative data were obtained through semi-structured interviews to deepen and contextualize the quantitative findings. Quantitative analysis was conducted using nonparametric statistics, while qualitative data were analyzed through the stages of data reduction, data presentation, and systematic conclusion drawing. The results of the analysis showed a statistically significant increase in students' conceptual understanding, with normalized gain values in the moderate category. Qualitative findings showed a decrease in misconceptions regarding interpreting algebraic symbols and translating problem language into mathematical models, as well as a shift in the structure of students' understanding when interpreting relationships among representations. However, misconceptions stemming from weaknesses in prerequisite concepts, particularly integer operations, tended to persist after the intervention. Furthermore, the increase in correct answers accompanied by low confidence levels suggests that some students' understanding remains traditional and not yet fully stable. Overall, the results of this study indicate that remedial learning based on mathematical representations is associated with improved conceptual understanding and shifts in certain patterns of misconceptions, and provide practical implications for developing learning strategies that are more adaptive to students' conceptual characteristics.
Keywords: algebraic expressions, conceptual understanding, misconceptions, remedial teaching, mathematical representation.
Adıgüzel, T., Şimşir, F., Çubukluöz, Ö., & Özdemir, B. G. (2018). Türkiye’de matematik ve fen eğitiminde kavram yanılgılarıyla ilgili yapılan yüksek lisans ve doktora tezleri: Tematik bir inceleme, Bayburt Eğitim Fakültesi Dergisi, 13(25), 57–92. https://dergipark.org.tr/en/pub/befdergi/issue/38072/411387
Ainsworth, S. (2021). The multiple representation principle in multimedia learning. The Cambridge Handbook of Multimedia Learning, 464–486. https://doi.org/10.1017/CBO9781139547369.024
Al Rababaha, Y., Yew, W. T., & Meng, C. C. (2020). Misconceptions in school algebra. International Journal of Academic Research in Business and Social Sciences, 10(5), 803–812. https://doi.org/10.6007/ijarbss/v10-i5/7250
Alsrairi, N., & Amjad, F. (2025). Exploring remedial teaching interventions for students facing persistent learning challenges. Lex Localis-Journal of Local Self-Government, 23(11), 47–67. https://doi.org/10.52152/801712
Altınbaş, A. A., Solak, S., & Ertekin, E. (2025). The effect of multiple representations-based and problem-based instruction in linear algebra on pre-service teachers’ dimensions of understanding and self-efficacy perceptions. Journal of Mathematics Teacher Education. https://doi.org/10.1007/s10857-025-09696-0
Arslan, H. O., Cigdemoglu, C., & Moseley, C. (2012). A three-tier diagnostic test to assess pre-service teachers’ misconceptions about global warming, greenhouse effect, ozone layer depletion, and acid rain. International Journal of Science Education, 34(11), 1667–1686. https://doi.org/10.1080/09500693.2012.680618
Ario, M., Suhendra, S., Jupri, A., Nurlaelah, E. (2025). Students’ errors and learning obstacles in solving algebraic word problems: hermeneutic phenomenology. Education Sciences, 15(12), 1674. https://doi.org/10.3390/educsci15121674
Bicer, A. (2021). Multiple representations and mathematical creativity. Thinking Skills and Creativity, 42. https://doi.org/10.1016/j.tsc.2021.100960
Chow, T.-C. F., & Treagust, D. F. (2013). An intervention study using cognitive conflict to foster conceptual change. Journal of Science and Mathematics, 36(1), 44–64. https://espace.curtin.edu.au/bitstream/20.500.11937/42636/2/196406_196406.pdf
Clark, J. M., & Paivio, A. (1987). A dual coding perspective on encoding processes. In M. A McDaniel et al. (Eds.), Imagery and related mnemonic processes (pp. 5–33). New York, NY: Springer-Verlag.
Creswell, J. W., & Plano Clark, V. L. (2018). Designing and conducting mixed methods research (3rd ed.). Thousand Oaks, CA: SAGE.
Chrisnawati, H. E., Pinilih, A. C., Nurhasanah, F., Usodo, B., Sutopo, & Kuswardi, Y. (2024). Marica: a story-based motion-comic learning media to improve students’ mathematical representation. Jurnal Pendidikan Progresif, 14(01), 322–333. https://doi.org/10.23960/jpp.v14.i1.202424
Fitria, A., Subanji., Susiswo., & Susanto., H. (2023). Cognitive map: diagnosing and exploring students’ misconceptions in algebra. Mathematics Teaching Research Journal, 15(5), 49-75. https://files.eric.ed.gov/fulltext/EJ1412238.pdf
Irawati, Zubainur, C. M., & Ali, R. M. (2018). Cognitive conflict strategy to minimize students’ misconception on the topic of addition of algebraic expression. Journal of Physics: Conference Series, 1088. https://doi.org/10.1088/1742-6596/1088/1/012084
Jitendra, A. K., Dougherty, B., Sanchez, V., & Suchilt, L. (2022). Using multiple representations to foster multiplicative reasoning in students with mathematics learning disabilities. Teaching Exceptional Children, 0(0). https://doi.org/10.1177/00400599221115627
Jupri, A., Usdiyana, D., & Sispiyati, R. (2020). Peran representasi matematis dalam pembelajaran perkalian bentuk aljabar melalui pendekatan matematika realistik. Jurnal Elemen, 6(1), 89–98. https://doi.org/10.29408/jel.v6i1.1716
Kaput, J. J. (1998). Representations, inscriptions, descriptions and learning: a kaleidoscope of windows. Journal of Mathematical Behavior, 17(2), 265–281. https://doi.org/10.1016/S0364-0213(99)80062-7
Meltzer, D. E. (2002). The relationship between mathematics preparation and conceptual learning gains in physics: A possible “hidden variable” in diagnostic pretest scores. American Journal of Physics, 70(12), 1259–1268. https://doi.org/10.1119/1.1514215
Munusamy, T., Hayati, M., Yatim, M., & Suhaimi, S. (2025). Challenges in teaching and learning mathematics among remedial students. International journal of academic research in business and social sciences, 15(3), 1496–1504. https://doi.org/10.46886/IJARBSS/v15-i3/16642
Mutodi, P., Mosimege, M., & Maphutha, K. (2023). Learners’ misconceptions and errors when solving inequalities. Mathematics Education Journal, 7(2), 136–158. https://doi.org/10.22219/mej.v7i2.27675
Nansiana, M. N., Usodo, B., & Fitriana, L. (2024). Analysis of epistemological obstacles experienced by Indonesian junior high school students in solving mathematical literacy problems from the perspective of algebraic thinking skills. Jurnal Pendidikan Progresif, 14(02), 1334–1354. https://doi.org/10.23960/jpp.v14.i2.202495
Ndemo, O., & Ndemo, Z. (2018). Secondary school students’ errors and misconceptions learning algebra. Journal of Education and Learning (EduLearn), 12(4), 690–701.https://doi.org/10.11591/edulearn.v12i4.9556
Otero, N., Druga, S., & Lan, A. (2025). A benchmark for math misconceptions: bridging gaps in middle school algebra with al-supported instruction. Discover Education, 4(277), 1-31. https://doi.org/10.1007/s44217-025-00742-w
Powell, S.R., & Fuchs, L. S. (2015). Intensive intervention in mathematics. Learning Disabilities Research and Practice, 30(4), 182–192. https://doi.org/10.1111/ldrp.12087
Prediger, S., Roesken-Winter, B., & Leuders, T. (2019). Which research can support PD facilitators? Strategies for content‑related PD research in the Three‑Tetrahedron Model. Journal of Mathematics Teacher Education, 22: 407–425. https://doi.org/10.1007/s10857-019-09434-3
Prosser, S. K., & Bismarck, S. F. (2023). Concrete-representational-abstractive (CRA) instructional approach in an Algebra I inclusion class: knowledge retention versus students’ perception. Education Sciences, 13(10), 1061. https://doi.org/10.3390/educsci13101061
Rau, M. A. (2017). Conditions for the effectiveness of multiple visual representations in enhancing STEM learning. Educational Psychology Review, 29(4), 717–761. https://doi.org/10.1007/s10648-016-9365-3
Rau, M. A., & Matthews, P. G. (2017). How to make ‘more’ better? Principles for effective use of multiple representations to enhance students’ learning about fractions. ZDM Mathematics Education, 49(4), 531–544. https://doi.org/10.1007/s11858-017-0846-8
Reinhold, F., Hofer, S., Berkowitz, M., Strohmaier, A., Scheuerer, S., Loch, F., Heuser, B. V., & Reiss, K. (2020). The role of spatial, verbal, numerical, and general reasoning abilities in complex word problem solving for young female and male adults. Mathematics Education Research Journal, 32(2), 189–211. https://doi.org/10.1007/s13394-020-00331-0
Riccomini, P. J., Smith, G. W., & Fries, K. M. (2015). The language of mathematics: the importance of teaching and learning mathematical vocabulary. Reading & Writing Quarterly, 31(3), 235–252. https://doi.org/10.1080/10573569.2015.1030995
Rittle-Johnson, B., Schneider, M., & Star, J. R. (2015). Not a one-way street: Bidirectional relations between procedural and conceptual knowledge of mathematics. Educational Psychology Review, 27(4), 587–597. https://doi.org/10.1007/s10648-015-9302-x
Stemele, B. P., & Asvat, Z. J. (2024). Exploring learner errors and misconceptions in algebraic expressions with grade 9 learners through the use of algebra tiles. Research in Mathematics, Science and Technology Education, 28(1), 153-170. https://doi.org/10.1080/18117295.2024.2334989
Tsamir, P., & Almog, N. (2001). Students’ strategies and difficulties: the case of algebraic inequalities. International Journal of Mathematical Education in Science and Technology, 32(4), 513–524. https://doi.org/10.1080/00207390110038277
Üce, M., & Ceyhan, İ. (2019). Misconception in chemistry education and practices to eliminate them : literature analysis. Journal of Education and Training Studies, 7(3), 202–208. https://doi.org/10.11114/jets.v7i3.3990
Ünal, Z. E., Ala, A. M., Kartal, G., Özel, S., & Geary, D. C. (2023). Visual and symbolic representations as components of algebraic reasoning. Journal of Numerical Cognition, 9(2), 327–345. https://doi.org/10.5964/jnc.11151
Winarso, W., Toheri, T., & Udin, T. (2023). Addressing the challenge of mathematical misconceptions: development of interactive multimedia based on cognitive conflict strategy. Journal of Education Technology, 7(3), 513–522. https://doi.org/10.23887/jet.v7i3.63037
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
View My Stats