STUDENT STRATEGIES AND ERRORS IN SOLVING MATHEMATICAL REPRESENTATION PROBLEMS ON A QUADRATIC FUNCTION MATERIAL

Hesty Marwani Siregar(1), Nurjanah Nurjanah(2*), Turmudi Turmudi(3), Darhim Darhim(4), Elah Nurlaelah(5),

(1) Universitas Pendidikan Indonesia
(2) Universitas Pendidikan Indonesia
(3) Universitas Pendidikan Indonesia
(4) Universitas Pendidikan Indonesia
(5) Universitas Pendidikan Indonesia
(*) Corresponding Author


Abstract


Students often experience difficulties in using multiple mathematical representations when solving quadratic function problems, particularly in connecting visual, symbolic, and verbal forms. While previous studies have mainly focused on identifying students’ errors, the strategies underlying these errors remain insufficiently explored. This study aims to identify the students’ strategies when solving mathematical representation problems on quadratic functions material. Using a descriptive qualitative approach, written responses from 127 students at two public high schools in Pekanbaru were analyzed and supported by interviews with six selected students to clarify their reasoning. The findings show that students predominantly relied on procedural strategies, such as point substitution or mechanical formula use, with limited conceptual understanding. Although most students attempted the visual task, many produced inaccurate graphs. The symbolic and verbal indicators showed very high non-response rates, indicating difficulties in translating contextual information into algebraic form and expressing mathematical reasoning. These results highlight the need for instructional approaches that integrate multiple representations and strengthen conceptual connections.

Keywords


Errors; mathematical representation; quadratic function; strategies

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References


Azizah, N. N., Susiswo, & Sisworo. (2021). Analytical Thinking Process of Students in Solving Mathematical Problems of Quadratic Functions. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 10(1), 328–338. https://doi.org/10.24127/ajpm.v10i1.3440

Fitrianna, A. Y., Dinia, S., Mayasari, M., & Nurhafifah, A. Y. (2018). Mathematical Representation Ability of Senior High School Students: An Evaluation from Students’ Mathematical Disposition. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 3(1), 46–56. https://doi.org/10.23917/jramathedu.v3i1.5872

Goldin, G. A. (2002). Representation in Mathematical Learning and Problem Solving. In L.D English (Ed). International Research in Mathemtical Education IRME (pp. 197–218). Lawrence Erbaum Associates.

Hariyani, M., Suherman, Andriani, M., & Herawati. (2023). The Importance of Mathematical Representation Ability for Elementary School Students: A Literature Review and Its Implications. Syekh Nurjati International Conference on Elementary Education (SICEE), 1, 38–46. https://doi.org/10.24235/sicee.v1i0.14579

Hatisaru, V. (2020). Exploring Evidence of Mathematical Tasks and Representations in the Drawings of Middle School Students. International Electronic Journal of Mathematics Education, 15(3), 1–21. https://doi.org/10.29333/iejme/8482

Hidayanti, D. R., & Hidayati, K. (2025). Identification Of Students’ Errors In Solving Mathematical Literacy Problems On Quadratic Function Material. International Journal of Progressive Sciences and Technologies (IJPSAT), 51(1), 216–222. https://doi.org/10.52155/ijpsat.v51.1.7271

Hilsania, S. A., & Masrukan. (2023). Mathematical Representation Ability of Students on Linear Program Material in Terms of Learning Interests in Problem-Based Learning. Journal of Medives : Journal of Mathematics Education IKIP Veteran Semarang, 7(2), 190–202. https://doi.org/10.31331/medivesveteran.v7i2.2553

Husain, D. S., Darhim, & Kusnandi. (2022). Kemampuan Representasi Matematis Ditinjau dari Adversity Quotient dan Self-Efficacy. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(4), 3684–3694. https://doi.org/10.24127/ajpm.v11i4.5903

Johnson, E. L. (2018). A New Look at the Representations for Mathematical Concepts: Expanding on Lesh’s Model of Representations of Mathematical Concepts. Forum on Public Policy Online, 2018(1), 1–11.

Korstjensa, I., & Moserb, A. (2018). Series: Practical guidance to qualitative research. Part 4: Trustworthiness and publishing. European Journal of General Practice, 24(1), 120–124. https://doi.org/10.1080/13814788.2017.1375092

Listiawati, E., & Juniati, D. (2021). An APOS Analysis of Student’s Understanding of Quadratic Function Graph. Journal of Physics: Conference Series, 1–9. https://doi.org/10.1088/1742-6596/1747/1/012028

Mainali, B. (2021). Representation in Teaching and Learning Mathematics. International Journal of Education in Mathematics, Science, and Technology (IJEMST), 9(1), 1–21. https://doi.org/10.46328/ijemst.1111

Nasrun, Prahmana, R. C. I., & Akib, I. (2023). The Students’ Representative Processes in Solving Mathematical Word Problems. Knowledge, 3(1), 70–79. https://doi.org/10.3390/knowledge3010006

NCTM. (2000). Principles and Standards for School Mathematics. National Council of Teachers of Mathematics.

Novitasari, P., Usodo, B., & Fitriana, L. (2021). Visual, Symbolic, and Verbal Mathematics Representation Abilities in Junior High School’s Students. The 2nd Annual Engineering and Vocational Education (AEVEC), 1–8. https://doi.org/10.1088/1742-6596/1808/1/012046

Pramesti, C. A., Shoffa, S., & Soemantri, S. (2024). Analysis of Class X MAN Surabaya Students’ Mistakes in Solving Function Questions Quadratics Based on Learning Styles and Newman Procedures. JOELI: Journal of Educational and Learning Innovation, 1(2), 147–160. https://doi.org/10.72204/3e8ha171

Prayitno, S., Lu’luilmaknunn, U., Sridana, N., & Subarinah, S. (2021). Analyzing the Ability of Mathematics Students as Prospective Mathematics Teachers on Multiple Mathematical Representation. Proceedings of the 2nd Annual Conference on Education and Social Science (ACCESS 2020), 309–313. https://doi.org/10.2991/assehr.k.210525.096

Rahmah, K., In’am, A., & Laila, A. R. N. (2022). Analysis of Mathematic Representation Ability by Using YouTube Media as a Mathematics Learning Source. Jurnal Silogisme: Kajian Ilmu Matematika Dan Pembelajarannya, 7(2), 77–83. https://doi.org/10.24269/silogisme.v7i2.5505

Safitri, R. F., Qohar, A., & Sisworo. (2025). Students’ Errors in Translating Mathematical Representations from Symbolic to Graphical Form in Quadratic Functions. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 14(2), 496–508. https://doi.org/https://doi.org/10.24127/ajpm.v14i2.10822

Shinariko, L. J., Hartono, Y., Yusup, M., Hiltrimartin, C., & Araiku, J. (2021). Mathematical Representation Ability on Quadratic Function Through Proof Based Learning. 4th Sriwijaya University Learning and Education International Conference, 653–659. https://doi.org/10.2991/assehr.k.201230.177

Stahl, N. A., & King, J. R. (2020). Expanding Approaches for Research: Understanding and Using Trustworthiness in Qualitative Research. Journal of Developmental Education, 44(1), 26–28.

Suominen, A. L. (2018). Abstract Algebra and Secondary School Mathematics Connections as Discussed by Mathematicians and Mathematics Educators. In N. Wasserman (Ed.), Connecting Abstract Algebra to Secondary Mathematics, for Secondary Mathematics Teachers (pp. 149–173). Springer. https://doi.org/10.1007/978-3-319-99214-3_8

Utomo, D. P., & Syarifah, D. L. (2021). Examining mathematical representation to solve problems in trends in mathematics and science study: Voices from Indonesian secondary school students. International Journal of Education in Mathematics, Science and Technology, 9(3), 540–556. https://doi.org/10.46328/IJEMST.1685

Wardah, S., Utomo, D. P., & Putri, O. R. U. (2021). An Analysis of Errors on Mathematical Symbol as a Metaphor in Linear Programming. Jurnal Didaktik Matematika, 8(1), 45–58. https://doi.org/10.24815/jdm.v8i1.18304

Yuhasriati, Y., Johar, R., Khairunnisak, C., Rohaizati, U., Jupri, A., & Zubaidah, T. (2022). Students Mathematical Representation Ability in Learning Algebraic Expression using Realistic Mathematics Education. Jurnal Didaktik Matematika, 9(1), 151–169. https://doi.org/10.24815/jdm.v9i1.25434




DOI: http://dx.doi.org/10.24127/ajpm.v15i1.14891

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