ANALISIS KESALAHAN MULTIDIMENSIONAL SISWA DALAM PEMECAHAN MASALAH ALJABAR: TINJAUAN DARI PERSPEKTIF REPRESENTASI SEMIOTIK
DOI:
https://doi.org/10.36277/defermat.v9i1.2494Keywords:
algebra problem solving, semiotic representation, error analysis, student ability levels, representational flexibilityAbstract
This study aims to uncover the multidimensional error patterns of students in solving algebra problems from the perspective of semiotic representation at various ability levels. This study used a qualitative approach involving 30 seventh-grade junior high school students. The research subjects were selected by purposive sampling, then six students were determined representing the high, medium, and low ability categories. Data were obtained through written tests and interviews, then analyzed based on Nolting's error classification, which includes misread direction error, careless error, concept error, application error, test procedure error, and transformation error. The results showed that students at all ability levels experienced difficulties in converting between representations (transformation error), especially from verbal to symbolic (algebraic expression) and symbolic to geometric expression. High-ability students were able to reason symbolically but failed to connect it to the visual context (graphical expression), while medium-ability students tended to use trial and error strategies that resulted in application errors. Students in the low-ability group showed concept errors and fundamental representation errors (transformation errors). In general, transformation errors were the most dominant type of error, followed by concept errors and application errors. These findings indicate that algebra learning needs to be designed by integrating various semiotic representations so that students' conceptual understanding can develop more deeply.
References
Adu‐Gyamfi, K., Stiff, L. V., & Bossé, M. J. (2012). Lost in Translation: Examining Translation Errors Associated With Mathematical Representations. School Science and Mathematics, 112(3), 159–170. https://doi.org/10.1111/j.1949-8594.2011.00129.x
Azzahra, N., & Herman, T. (2022). STUDENTS’ LEARNING OBSTACLES IN SOCIAL ARITHMETIC. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 11(1), 187. https://doi.org/10.24127/ajpm.v11i1.4621
Bossé, M. J., Adu-Gyamfi, K., & Chandler, K. (2014). Students’ Differentiated Translation Processes.
Castro, E., Cañadas, M. C., Molina, M., & Rodríguez-Domingo, S. (2022). Difficulties in semantically congruent translation of verbally and symbolically represented algebraic statements. Educational Studies in Mathematics, 109(3), 593–609. https://doi.org/10.1007/s10649-021-10088-3
Cooper, T. (2008). Generalising the pattern rule for visual growth patterns: Actions that support 8 year olds’ thinking. Educational Studies in Mathematics. https://doi.org/10.1007/S10649-007-9092-2
Dahiana, W. O., & Halija, W. (2024). Representasi Semiotik dalam Pemecahan Masalah Aljabar. Penerbit Adab.
Dahiana, W. O., Herman, T., Nurlaelah, E., & Pereira, J. (2023). Student Semiotic Representation Skills in Solving Mathematics Problems. Jurnal Didaktik Matematika, 10(1), 34–47. https://doi.org/10.24815/jdm.v10i1.30770
Damayanti, D. (2024). ANALISIS KESALAHAN REPRESENTASI MATEMATIS SISWA PADA MATERI SISTEM PERSAMAAN LINEAR DUA VARIABEL BERDASARKAN TEORI NOLTING. CENDEKIA: Jurnal Ilmu Pengetahuan, 4(4), 432–439. https://doi.org/10.51878/cendekia.v4i4.3365
Duval, R. (2006). A Cognitive Analysis of Problems of Comprehension in a Learning of Mathematics. Educational Studies in Mathematics, 61, 103–131. https://doi.org/10.1007/s10649-006-0400-z
Eric, C.-S., & Hala, G. (2022). Supporting Understanding Using Representations. Mathematics Teacher: Learning and Teaching PK-12, 115(6), 394–403. https://doi.org/10.5951/MTLT.2021.0155
Ferretti, F., Gambini, A., & Spagnolo, C. (2024). Management of semiotic representations in mathematics: Quantifications and new characterizations. European Journal of Science and Mathematics Education, 12(1), 11–20. https://doi.org/10.30935/scimath/13827
Fonger, N. L., Ellis, A. B., & Dogan, M. F. (2020). A quadratic growth learning trajectory. The Journal of Mathematical Behavior, 59, 100795. https://doi.org/10.1016/j.jmathb.2020.100795
Fumador, E., & Agyei, D. (2018). Students’ Errors and Misconceptions in Algebra: Exploring the Impact of Remedy Using Diagnostic Conflict and Conventional Teaching Approaches. 6, 1–15.
Gaona, J., Rodrigo Hernández, Felipe Guevara, & Víctor Bravo. (2022). Influence of a Function’s Coefficients and Feedback of the Mathematical Work When Reading a Graph in an Online Assessment System. International Journal of Emerging Technologies in Learning (IJET), 17(20), 77–98. https://doi.org/10.3991/ijet.v17i20.32641
Hadiyanti, Y. R., & Manurung, M. M. H. (2025). A Qualitative Analysis of Students’ Errors in Fraction Word Problems Based on Polya’s Stages of Problem Solving: Evidence from Papua, Indonesia. Edumatica : Jurnal Pendidikan Matematika, 15(2). https://doi.org/10.22437/edumatica.v15i2.43746
Hannula, M. S., Di Martino, P., Pantziara, M., Zhang, Q., Morselli, F., Heyd-Metzuyanim, E., Lutovac, S., Kaasila, R., Middleton, J. A., Jansen, A., & Goldin, G. A. (2016). Attitudes, Beliefs, Motivation and Identity in Mathematics Education: An Overview of the Field and Future Directions. Springer International Publishing. https://doi.org/10.1007/978-3-319-32811-9
Hart, K. M., Brown, M. L., Hart, K. M., & Booth, L. R. (1984). Ratio: Children’s Strategies and Errors A Report of the Strategies and Errors in Secondary Mathematics Project.
Hong, Y., Li, Q., Gong, R., Ciao, D., Huang, S., & Zhu, S.-C. (2021). SMART: A Situation Model for Algebra Story Problems via Attributed Grammar. Proceedings of the AAAI Conference on Artificial Intelligence, 35(14), 13009–13017. https://doi.org/10.1609/aaai.v35i14.17538
Klein, P., Burkard, N., Hahn, L., Dahlkemper, M. N., Eberle, K., Jaeger, T., Kuhn, J., & Herrlich, M. (2021). Coordinating vector field equations and diagrams with a serious game in introductory physics. European Journal of Physics, 42(4), 045801. https://doi.org/10.1088/1361-6404/abef5c
Kouropatov, A., & Dreyfus, T. (2014). Learning the integral concept by constructing knowledge about accumulation. ZDM, 46, 533–548. https://doi.org/10.1007/s11858-014-0571-5
Kuo, E., Hull, M. M., Elby, A., & Gupta, A. (2019). Mathematical Sensemaking as Seeking Coherence between Calculations and Concepts: Instruction and Assessments for Introductory Physics. ArXiv: Physics Education. https://www.semanticscholar.org/paper/4bc4b2869f1ab4ba38c2ba72d2c087f98d73df61
Leikin, R. (2009). Development of teachers’ conceptions through learning and teaching: Meaning and potential of multiple-solution tasks. Canadian Journal of Science Mathematics and Technology Education, 9, 203.
Lesh, R., & Harel, G. (2003). Problem Solving, Modeling, and Local Conceptual Development.
Li, Y., & Schoenfeld, A. H. (2019). Problematizing teaching and learning mathematics as “given” in STEM education. International Journal of STEM Education, 6(1), 44, s40594-019-0197–0199. https://doi.org/10.1186/s40594-019-0197-9
Maries, A., Lin, S.-Y., & Singh, C. (2016). The impact of students’ epistemological framing on a task requiring representational consistency. 212–215. https://doi.org/10.1119/perc.2016.pr.048
Mathaba, P. N., Bayaga, A., Tîrnovan, D., & Bossé, M. J. (2024). Error analysis in algebra learning: Exploring misconceptions and cognitive levels. Journal on Mathematics Education, 15(2), 575–592. https://doi.org/10.22342/jme.v15i2.pp575-592
Mellone, M., Verschaffel, L., & Dooren, W. V. (2014). MAKING SENSE OF WORD PROBLEMS: THE EFFECT OF REWORDING AND DYADIC INTERACTION.
Mercan Erdoğan, S., Çeti̇N, H., & Ari, K. (2021). Development of Multiple Representation Translating Measurement Tool and Examination of 9th Grade Students’ Multiple Representations Translate Skills in Algebra. Acta Didactica Napocensia, 14(2), 160–180. https://doi.org/10.24193/adn.14.2.12
Miles, M. B., Huberman, A. M., & Saldaña, J. (2014). Qualitative data analysis: A methods sourcebook (Edition 3). Sage.
Muharani, A., Kurniadi, E., & Araiku, J. (2025). Kemampuan Representasi Matematis Siswa dalam Pembelajaran Pemodelan Matematika pada Materi Aplikasi Program Linear. 09(01).
Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49. https://doi.org/10.1007/BF03217544
Ng, S. F., & Lee, K. (2009). The Model Method: Singapore Children’s Tool for Representing and Solving Algebraic Word Problems. Journal for Research in Mathematics Education, 40(3), 282–313. https://doi.org/10.5951/jresematheduc.40.3.0282
Nolting, P. D. (2002). Winning at Math. Academic Success Press Inc.
Nolting, P. D. (with Internet Archive). (2014). Winning at math: Your guide to learning mathematics through successful study skills. Bradenton, FL : Academic Success Press, Inc. http://archive.org/details/winningatmathyou0000nolt_o8k1
Oudman, S., van de Pol, J., & van Gog, T. (2022). Effects of self-scoring their math problem solutions on primary school students’ monitoring and regulation. Metacognition and Learning, 17(1), 213–239. https://doi.org/10.1007/s11409-021-09281-9
Putri, A. A., Priatna, N., & Kusnandi, K. (2023). Analysis of Student Errors in Solving Mathematics Problems Based on Newman Procedure and Providing Scaffolding. Numerical: Jurnal Matematika Dan Pendidikan Matematika, 7(2), 321–332. https://doi.org/10.25217/numerical.v7i2.3993
Putri, A., & Basir, M. A. (2025). Identifikasi Kesalahan Siswa dalam Menyelesaikan Soal Numerasi: Tinjauan melalui Kerangka Teori Nolting.
Qurohman, M. T., Wijayanto, Z., & Suwarto, S. (2025). Investigating Critical Thinking Indicators in the Context of Algebra Problem Solving: A Study in Indonesia.
Radford, L. (2000). SIGNS AND MEANINGS IN STUDENTS’ EMERGENT ALGEBRAIC THINKING: A SEMIOTIC ANALYSIS.
Reinhard, A., Felleson, A., Turner, P. C., & Green, M. (2022). Assessing the impact of metacognitive postreflection exercises on problem-solving skillfulness. Physical Review Physics Education Research, 18(1), 010109. https://doi.org/10.1103/PhysRevPhysEducRes.18.010109
Soesanto, R. H. (2021). A Review Of Student Error Analysis In Linear Algebra Course Based On Kastolan Stage Model. De Fermat : Jurnal Pendidikan Matematika, 4(1), 1–12. Retrieved from https://jurnal.pmat.uniba-bpn.ac.id/index.php/DEFERMAT/article/view/147
Sanjosé, V., Gómez-Ferragud, C. B., & Solaz-Portolés, J. J. (2024). Online processing while monitoring worked-out examples with embedded errors: Defining university student profiles. European Journal of Psychology of Education, 39(1), 297–317. https://doi.org/10.1007/s10212-023-00685-6
Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2). https://findanexpert.unimelb.edu.au/scholarlywork/1355979-finding-and-using-patterns-in-linear-generalising-problems
Susanti, Y. T. (2018). Profil Berpikir Kreatif Menurut Wallas dalam Menyelesaikan Soal Materi Balok Ditinjau dari Tipe Kepribadian Florence Littauer Siswa Kelas VIII G.
Ziatdinov, R., & Valles, J. R. (2022). Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics. Mathematics, 10(3), 398. https://doi.org/10.3390/math10030398
