Students’ obstacles in solving algebra form problems viewed from mathematical problem-solving ability
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Abstract
Mathematical problem-solving ability is the most effective cognitive instrument in learning mathematics, and enhancing students' mathematical problem-solving ability is the primary objective of education. However, to reach the most effective level of mathematical problem-solving ability, we need to comprehend the reasons behind students' challenges while learning. This research investigates the learning obstacles of the students based on their mathematical problem-solving ability, particularly in algebraic form material. The method used in this research employed qualitative study with a series of Didactical Design Research (DDR) projects to learn the obstacles to the student's mathematical problem-solving ability. Seventy-six eighth-grade students from a public junior high school in Kampar region were given a test to assess their ability to solve mathematical problems. Various research instruments are used, including tests of mathematical problem-solving ability, interview guidelines, and interviews by audio recordings. The data were analyzed using a qualitative approach to determine students' learning obstacles. The findings highlight ontogenic, epistemological, and didactical obstacles students face while understanding the problem, particularly the concept of algebraic form, interpreting the word to the mathematical concept of algebraic form, and designing the algebraic forms.
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Aisyah, N., Susanti, E., Meryansumayeka, M., Siswono, T. Y. E., & Maat, S. M. (2023). Proving geometry theorems: Student prospective teachers’ perseverance and mathematical reasoning. Infinity Journal, 12(2), 377–392. https://doi.org/10.22460/infinity.v12i2.p377-392
Amalina, I. K., & Vidákovich, T. (2023). Development and differences in mathematical problem-solving skills: A cross-sectional study of differences in demographic backgrounds. Heliyon, 9(5), e16366. https://doi.org/10.1016/j.heliyon.2023.e16366
As’ari, A. R., Tohir, M., Valentino, E., & Imron, Z. (2017). Matematika SMP/MTs kelas VII semester 2 [Mathematics for Junior High School/Islamic Junior High School Grade VII Semester 2]. Kementerian Pendidikan dan Kebudayaan.
Asmara, A. S., Waluya, S. B., Suyitno, H., Junaedi, I., & Ardiyanti, Y. (2024). Developing patterns of students' mathematical literacy processes: Insights from cognitive load theory and design-based research. Infinity Journal, 13(1), 197–214. https://doi.org/10.22460/infinity.v13i1.p197-214
Booth, J. L., Barbieri, C., Eyer, F., & Paré-Blagoev, E. J. (2014). Persistent and pernicious errors in algebraic problem solving. The Journal of Problem Solving, 7(1), Article 3. https://doi.org/10.7771/1932-6246.1161
Brousseau, G. (2011). Theory of didactical situations in mathematics. Education didactique, 5(1), 101–104. https://doi.org/10.4000/educationdidactique.1005
Desti, R. M., Pertiwi, C. M., Sumarmo, U., & Hidayat, W. (2020). Improving student’s mathematical creative thinking and habits of mind using a problem-solving approach based on cognitive thinking stage. Journal of Physics: Conference Series, 1657(1), 012042. https://doi.org/10.1088/1742-6596/1657/1/012042
Doorman, M., Drijvers, P., Dekker, T., van den Heuvel-Panhuizen, M., de Lange, J., & Wijers, M. (2007). Problem solving as a challenge for mathematics education in The Netherlands. Zdm, 39(5), 405–418. https://doi.org/10.1007/s11858-007-0043-2
Dostál, J. (2015). Theory of problem solving. Procedia - Social and Behavioral Sciences, 174, 2798–2805. https://doi.org/10.1016/j.sbspro.2015.01.970
Firda, N., Suryadi, D., & Dahlan, J. A. (2023). Kemampuan pemecahan masalah matematis siswa sekolah menengah pertama berdasarkan Polya [Mathematical problem solving ability of junior high school students based on Polya]. Edumatica: Jurnal Pendidikan Matematika, 13(3), 273–284. https://doi.org/10.22437/edumatica.v13i03.29287
Friede, C. R., Irani, T. A., Rhoades, E. B., Fuhrman, N. E., & Gallo, M. (2008). It's in the genes: Exploring relationships between critical thinking and problem solving in undergraduate agriscience students' solutions to problems in mendelian genetics. Journal of Agricultural Education, 49(4), 25–37. https://doi.org/10.5032/jae.2008.04025
Güner, P., & Erbay, H. N. (2021). Prospective mathematics teachers’ thinking styles and problem-solving skills. Thinking Skills and Creativity, 40, 100827. https://doi.org/10.1016/j.tsc.2021.100827
Harisman, Y., Noto, M. S., & Hidayat, W. (2020). Experience student background and their behavior in problem solving. Infinity Journal, 9(1), 59–68. https://doi.org/10.22460/infinity.v9i1.p59-68
Harisman, Y., Noto, M. S., & Hidayat, W. (2021). Investigation of students' behavior in mathematical problem solving. Infinity Journal, 10(2), 235–258. https://doi.org/10.22460/infinity.v10i2.p235-258
Hutajulu, M., Wijaya, T. T., & Hidayat, W. (2019). The effect of mathematical disposition and learning motivation on problem solving: An analysis. Infinity Journal, 8(2), 229–238. https://doi.org/10.22460/infinity.v8i2.p229-238
Jamilah, J., Priskila, P., & Oktaviana, D. (2024). Didactical design to overcome learning obstacles in cuboid volume. Jurnal Elemen, 10(2), 324–340. https://doi.org/10.29408/jel.v10i2.25244
Jatisunda, M. G., Suryadi, D., Prabawanto, S., & Umbara, U. (2025). Pre-service mathematics teacher conducting prospective analysis: A case study on practice didactical design research. Infinity Journal, 14(1), 21–44. https://doi.org/10.22460/infinity.v14i1.p21-44
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, 998586. https://doi.org/10.3389/fpsyg.2022.998586
Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26, 683–710. https://doi.org/10.1007/s13394-013-0097-0
Jupri, A., & Drijvers, P. H. M. (2016). Student difficulties in mathematizing word problems in algebra. Eurasia Journal of Mathematics, Science and Technology Education, 12(9), 2481–2502. https://doi.org/10.12973/eurasia.2016.1299a
Lu, D., & Xie, Y.-N. (2024). The application of educational technology to develop problem-solving skills: A systematic review. Thinking Skills and Creativity, 51, 101454. https://doi.org/10.1016/j.tsc.2023.101454
Novriani, M. R., & Surya, E. (2017). Analysis of student difficulties in mathematics problem solving ability at MTs swasta IRA Medan. International Journal of Sciences: Basic and Applied Research (IJSBAR), 33(3), 63–75.
Pauji, I., Suryadi, D., Setambah, M. A. B. B., & Hendriyanto, A. (2023). Learning obstacle in the introduction to number: A critical study within didactical design research framework. Indonesian Journal of Science and Mathematics Education, 6(3), 430–451. https://doi.org/10.24042/ijsme.v6i3.19792
Pertiwi, C. M., Rohaeti, E. E., & Hidayat, W. (2020). The students' mathematical problem-solving abilities, self-regulated learning, and VBA Microsoft Word in new normal: A development of teaching materials. Infinity Journal, 10(1), 17–30. https://doi.org/10.22460/infinity.v10i1.p17-30
Polya, G. (2014). How to solve it: A new aspect of mathematical method. Princeton university press.
Pramuditya, S. A., Noto, M. S., & Azzumar, F. (2022). Characteristics of students'mathematical problem solving abilities in open-ended-based virtual reality game learning. Infinity Journal, 11(2), 255–272. https://doi.org/10.22460/infinity.v11i2.p255-272
Putri, D. R., & Hidayati, N. (2022). Mathematical problem solving ability of junior high school students on straight line equations. Unnes Journal of Mathematics Education Research, 11(2), 6–11.
Putri, R. I. I., & Riskanita, A. D. (2022). Students' problem-solving ability in solving algebra tasks using the context of Palembang. Journal on Mathematics Education, 13(3), 549–564. https://doi.org/10.22342/jme.v13i3.pp549-564
Rahmi, L., & Yulianti, K. (2022). Learning obstacles yang dihadapi siswa dalam memahami topik relasi dan fungsi [Learning obstacles faced by students in understanding the topic of relations and functions]. JPMI (Jurnal Pembelajaran Matematika Inovatif), 5(4), 929–940. https://doi.org/10.22460/jpmi.v5i4.10917
Riskon, M. (2021). Algebraic thinking ability with creative problem solving integrated 4c model viewed from mathematical disposition. Unnes Journal of Mathematics Education Research, 10(A), 38–53.
Rocha, H., & Babo, A. (2024). Problem-solving and mathematical competence: A look to the relation during the study of Linear Programming. Thinking Skills and Creativity, 51, 101461. https://doi.org/10.1016/j.tsc.2023.101461
Safstrom, A. I., Lithner, J., Palm, T., Palmberg, B., Sidenvall, J., Andersson, C., Bostrom, E., & Granberg, C. (2024). Developing a diagnostic framework for primary and secondary students' reasoning difficulties during mathematical problem solving. Educational Studies in Mathematics, 115(2), 177–196. https://doi.org/10.1007/s10649-023-10278-1
Sari, V. T. A., & Hidayat, W. (2019). The students’ mathematical critical and creative thinking ability in double-loop problem solving learning. Journal of Physics: Conference Series, 1315(1), 012024. https://doi.org/10.1088/1742-6596/1315/1/012024
Septian, A., Widodo, S. A., Afifah, I. N., Nisa, D. Z., Putri, N. P. K., Tyas, M. D., Nisa, R. H., & Andriani, A. (2022). Mathematical problem solving ability in Indonesia. Journal of Instructional Mathematics, 3(1), 16–25. https://doi.org/10.37640/jim.v3i1.1223
Silvia, S., Ratnaningsih, N., & Martiani, A. (2019). Miskonsepsi kemampuan pemecahan masalah matematik berdasarkan langkah polya pada materi aljabar [Misconceptions of mathematical problem solving abilities based on Polya's steps in algebra material]. In Prosiding Seminar Nasional & Call For Papers, (pp. 532–538).
Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. The Journal of Mathematical Behavior, 24(3), 341–350. https://doi.org/10.1016/j.jmathb.2005.09.004
Stacey, K., & Chick, H. (2004). Solving the problem with algebra. In K. Stacey, H. Chick, & M. Kendal (Eds.), The future of the teaching and learning of algebra the 12th ICMI study (pp. 1–20). Springer Netherlands. https://doi.org/10.1007/1-4020-8131-6_1
Supriadi, N., Jamaluddin Z, W., & Suherman, S. (2024). The role of learning anxiety and mathematical reasoning as predictor of promoting learning motivation: The mediating role of mathematical problem solving. Thinking Skills and Creativity, 52, 101497. https://doi.org/10.1016/j.tsc.2024.101497
Suryadi, D. (2019). Penelitian desain didaktis (DDR) dan implementasinya [Didactic design research (DDR) and its implementation]. Gapura Press.
Suryadi, D., Itoh, T., & Isnarto, I. (2023). A prospective mathematics teacher's lesson planning: An in-depth analysis from the anthropological theory of the didactic. Journal on Mathematics Education, 14(4), 723–740. https://doi.org/10.22342/jme.v14i4.pp723-740
Tosho, T. G. (2021). Matematika untuk sekolah menengah pertama kelas VII [Mathematics for junior high school grade VII]. Badan Penelitian dan Pengembangan dan Perbukuan Kementerian Pendidikan dan Kebudayaan.
Unaenah, E., Suryadi, D., & Turmudi, T. (2024). Epistemological learning obstacles on fractions in elementary school. Jurnal Elemen, 10(1), 1–12. https://doi.org/10.29408/jel.v10i1.18306
Utami, H. S., & Puspitasari, N. (2022). Kemampuan pemecahan masalah siswa smp dalam menyelesaikan soal cerita pada materi persamaan kuadrat [Problem solving ability of junior high school students in solving story problems on quadratic equation material]. Jurnal Inovasi Pembelajaran Matematika: PowerMathEdu, 1(1), 57–68. https://doi.org/10.31980/pme.v1i1.1366
van Merriënboer, J. J. G. (2013). Perspectives on problem solving and instruction. Computers & Education, 64, 153–160. https://doi.org/10.1016/j.compedu.2012.11.025
Wicaksono, A., Prabawanto, S., & Suryadi, D. (2024). How students' obstacle in solving mathematical tasks deal with linear equation in one variabel. Al-Jabar: Jurnal Pendidikan Matematika, 15(1), 33–44. https://doi.org/10.24042/ajpm.v15i1.21137
Widodo, S. A., Irfan, M., Trisniawati, T., Hidayat, W., Perbowo, K. S., Noto, M. S., & Prahmana, R. C. I. (2020). Process of algebra problem-solving in formal student. Journal of Physics: Conference Series, 1657(1), 012092. https://doi.org/10.1088/1742-6596/1657/1/012092
Widodo, S. A., Sari, Y. N., Chiphambo, S. M., Fitriani, N., Sulistyowati, F., Murtafiah, W., & Pratama, D. F. (2025). The effect of teaching props on the mathematical problem-solving skills: A meta-analysis study. Infinity Journal, 14(1), 235–258. https://doi.org/10.22460/infinity.v14i1.p235-258
Ying, C. L., Osman, S., Kurniati, D., Masykuri, E. S., Kumar, J. A., & Hanri, C. (2020). Difficulties that students face when learning algebraic problem-solving. Universal Journal of Educational Research, 8(11), 5405–5413. https://doi.org/10.13189/ujer.2020.081143.