Students’ Learning Obstacles in Solving Mathematical Proficiency Tasks: A Hermeneutic Phenomenological Study Focused on Algebra
DOI:
https://doi.org/10.15294/36aygs91Keywords:
Didactical design research, Learning obstacles, mathematical proficiency, linear equation, hermeneutic phenomenologyAbstract
algebra is a fundamental topic in mathematics, particularly emphasized during the junior high school years as an essential subject. In the context of linear equations in one variable, students often struggle with obstacles in basic algebra including variable degrees, variable concepts, coefficients, and constants. However, proficiency in understanding algebraic concepts is significantly lower compared to other areas and skills. As a consequence, this research aimed to explore students' learning obstacles in solving linear equations in one variable in secondary schools based on mathematical proficiency. The research design using the hermeneutic phenomenological approach. This research is a framework of the Didactical Design Research (DDR). DDR is based on two paradigms: the interpretive and the critical paradigms, and it aims to empower students in the context of generating new knowledge as justified true belief. In this study, the researcher delves into the interpretive paradigm. The research subjects involved 46 seventh-grade secondary school students from five different schools across four distinct provinces in Indonesia. The instruments used were test and non-test. The test was done by giving a diagnostic test about linear equation problems, while interviews used the non-test technique. The data collected were analyzed using the Miles and Huberman model, namely data reduction, data presentation, and drawing conclusions. The study findings revealed that students met three types of obstacles in linear equation material, namely ontogenic obstacle, epistemological obstacle and didactical obstacle. However, students faced limited knowledge to solve mathematics problems in one variable, for instance, solving mathematical operations and making modelling problems from real situations deal with linear equations in one variable. Therefore, future research can focus on developing a Didactical Design to reduce this obstacle.
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Al-Mutawah, M. A., Thomas, R., Eid, A., Mahmoud, E. Y., & Fateel, M. J. (2019). Conceptual understanding, procedural knowledge and problem-solving skills in mathematics: High school graduates work analysis and standpoints. International Journal of Education and Practice, 7(3), 258–273.
Algarni, B., & Lortie-Forgues, H. (2023). An evaluation of the impact of flipped-classroom teaching on mathematics proficiency and self-efficacy in Saudi Arabia. British Journal of Educational Technology, 54(1), 414–435. https://doi.org/10.1111/bjet.13250
Altarawneh, A. F., & Marei, S. T. (2021). Mathematical proficiency and preservice classroom teachers’ instructional performance. International Journal of Education and Practice, 9(2), 354–364. https://doi.org/10.18488/journal.61.2021.92.354.364
Arnawa, I. M., Yerizon, & Nita, S. (2019). Errors and misconceptions in learning elementary linear algebra. Journal of Physics: Conference Series, 1321(2). https://doi.org/10.1088/1742-6596/1321/2/022095
Astuti, R., Matematika, P., Muhammadiyah, S., & Lampung, P. (2017). Analisis Learning Obstacles Mahasiswa Dalam Mempelajari Materi Kombinatorial. Jurnal Edumath, 3(1), 56–64.
Bakar, M. T., Suryadi, D., & Darhim, D. (2019). Learning obstacles on linear equations concept in junior high school students: Analysis of intellectual need of DNR-based instructions. Journal of Physics: Conference Series, 1157(3), 32104.
Brousseau, G. U. Y. (2002). Epistemological obstacles, problems, and didactical engineering. Theory of Didactical Situations in Mathematics: Didactique Des Mathématiques, 1970–1990, 79–117.
Casey, S. A. (2015). Examining Student Conceptions Of Covariation: A Focus On The Line Of Best Fit. Journal of Statistics Education, 23(1), 34 pages. https://doi.org/10.1080/10691898.2015.11889722
Corrêa, P. D., & Haslam, D. (2020). Mathematical proficiency as the basis for assessment: A literature review and its potentialities. Mathematics Teaching-Research Journal, 12(4), 3–20.
Edo, S. I., & Tasik, W. F. (2022). Investigation of Students’ Algebraic Conceptual Understanding and the Ability to Solve PISA-Like Mathematics Problems in a Modeling Task. Mathematics Teaching Research Journal, 14(2), 44–60.
Fardian, D., & Dasari, D. (2023). The effects of problem-based learning on mathematical proficiency: A combined bibliometric analysis and meta-analysis review. Journal of Didactic Studies, 1(2), 99–113.
Fardian, D., Herman, T., Suryadi, D., & Prabawanto, S. (2024). Gamifying Mathematics: A hermeneutic phenomenological study focused on Role-Playing Games in Linear Equations. PYTHAGORAS Jurnal Pendidikan Matematika, 19(1).
Fardian, D., Suryadi, D., Prabawanto, S., & Hayuningrat, S. (2024). Research trends on early algebra in the middle school: A combined bibliometric and meta-analysis review. Jurnal Elemen, 10(2), 410–440.
Findell, B., Swafford, J., & Kilpatrick, J. (2001). Adding it up: Helping children learn mathematics. National Academies Press.
Go, M. C. (2023). Enhancing mathematical proficiency assessment: Insights from mathematics teachers. Science International, 35, 773–780.
Hannah, J., Stewart, S., & Thomas, M. (2016). Developing conceptual understanding and definitional clarity in linear algebra through the three worlds of mathematical thinking. Teaching Mathematics and Its Applications: An International Journal of the IMA, 35(4), 216–235.
Hendriyanto, A., Suryadi, D., Sahara, S., Fardian, D., Pauji, I., & Muhaimin, L. H. (2024). From tools to thought partners: Optimizing technology as extended cognition for innovative didactic design. AIP Conference Proceedings, 3220(1).
Islamiyah, W., Suryadi, D., Prabawanto, S., & Gulvara, M. A. (2023). Learning Obtacles for Junior High School Students on The Concept of Quadratic Equations. Jurnal Cendekia : Jurnal Pendidikan Matematika, 7(3), 2313–2326. https://doi.org/10.31004/cendekia.v7i3.2609
Junpeng, P., Marwiang, M., Chiajunthuk, S., Suwannatrai, P., Chanayota, K., Pongboriboon, K., Tang, K. N., & Wilson, M. (2020). Validation of a Digital Tool for Diagnosing Mathematical Proficiency. International Journal of Evaluation and Research in Education, 9(3), 665–674.
Jupri, A., Drijvers, P., & van den Heuvel-Panhuizen, M. (2014). Difficulties in initial algebra learning in Indonesia. Mathematics Education Research Journal, 26(4), 683–710. https://doi.org/10.1007/s13394-013-0097-0
Jupri, A., Usdiyana, D., & Gozali, S. M. (2024). Problem Solving in Geometry Teaching for Pre-service Mathematics Teacher Students from a Computational Thinking Perspective. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(2), 438–449.
Karlsson, N., & Kilborn, W. (2023). Arithmetic and algebraic knowledge in student learning of concepts. International Conference on Education and New Developments Lisbon, Portugal, 1, 3–7.
Khoshaim, H. B. (2020). Mathematics teaching using word-problems: Is it a phobia! International Journal of Instruction, 13(1), 855–868. https://doi.org/10.29333/iji.2020.13155a
Lee, J. Y., Pyon, C. U., & Woo, J. (2023). Digital twin for math education: A study on the utilization of games and gamification for university mathematics education. Electronics, 12(15), 3207.
Li, X. (2010). Cognitive analysis of students’ errors and misconceptions in variables, equations, and functions. Texas A & M University.
Magfiroh, M., Prabawanto, S., & Rosjanuardi, R. (2024). Learning Obstacle of Students in Geometrical Sequence and Series. KnE Social Sciences, 569–577.
Makonye, J. (2015). Understanding of grade 10 learner errors and misconceptions in elementary algebra. Journal of Educational Studies, 2015(Special issue 1), 288–313.
Moustakas, C. (1994). Phenomenological research methods. Thousand Oaks.
Nagle, C., & Moore-Russo, D. (2013). The Concept of Slope: Comparing Teachers’ Concept Images and Instructional Content. Investigations in Mathematics Learning, 6(2), 1–18. https://doi.org/10.1080/24727466.2013.11790330
Nashiru, A., Alhassan, N. I., & Abubakari, Z. S. (2018). Translate Word Problems into Algebraic Expressions: The Case Study of George Polya’s Problem Solving Model. ADRRI Journal of Physical and Natural Sciences, 2(2), 1–25.
Pertiwi, S., Dasari, D., & Sumiaty, E. (2023). High School Students’ontogenic Obstacles in Solving Solid Geometry Problems Viewed From Spatial Ability. Proceedings of the International Conference on Future of Education, 6(1), 1–11.
Pincheira, N., & Alsina, Á. (2021). Teachers’ mathematics knowledge for teaching early algebra: A systematic review from the mkt perspective. Mathematics, 9(20), 2590.
Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning Obstacles in the Making of Lesson Plans by Prospective Mathematics Teacher Students. Education Research International, 2022. https://doi.org/10.1155/2022/2896860
Pratiwi, V., Herman, T., & Suryadi, D. (2019). Algebraic thinking obstacles of elementary school students: A Hermeneutics-phenomenology study. Journal of Physics: Conference Series, 1157(3). https://doi.org/10.1088/1742-6596/1157/3/032115
Puspita, E., & Kustiawan, C. (2024). A Didactical Design Research: Knowledge Acquisition of Mathematics Teacher Prospective Students on Multiple Integral Concepts. Kreano, Jurnal Matematika Kreatif-Inovatif, 15(1), 199–217.
Putri, A. D., Juandi, D., & Turmudi, T. (2024). Realistic mathematics education and mathematical literacy: a meta-analysis conducted on studies in Indonesia. Journal of Education and Learning (EduLearn), 18(4), 1468–1476.
Putri, A. D., Juandi, D., Turmudi, T., Fardian, D., & Rizki, L. M. (2024). Does The Realistic Mathematics Education Approach Enhance Students’ Mathematical Literacy? A Systematic Literature Review. Avalokana Journal of Literature Review, 1(1), 30–37.
Reynders, A., Sciences, N., & Education, F. O. F. (2014). Obstacles That Hamper Learners From Successfully Translating Mathematical Word Problems Into Number Sentences. [Doctoral dissertation] University of the Free State.
Saraswati, S., Putri, R. I. I., & Somakim. (2016). Supporting Students ’ Understanding of Linear. Journal On Mathematics Education, 7(1), 21–32.
Schulz, A. (2023). Assessing student teachers’ procedural fluency and strategic competence in operating and mathematizing with natural and rational numbers. Journal of Mathematics Teacher Education, 1–28.
Siregar, R. N., Suryadi, D., Prabawanto, S., & Mujib, A. (2022). Cognitive Flexibility of Students In Solving Mathematical Problems: A phenomenology study. Kreano, Jurnal Matematika Kreatif-Inovatif, 13(2), 355–369.
Suherman, E., Turmudi, S. D., Herman, T., Suhendra, P. S., & Nurjanah, R. A. (2001). Strategi Pembelajaran Matematika Kontemporer. Bandung: JICA–Universitas Pendidikan Indonesia.
Sulastri, L., & Arhasy, E. A. R. (2017). Kajian learning obstacle materi persamaan dan pertidaksamaan linear satu variabel pada pembelajaran matematika di sekolah menengah pertama. JP3M (Jurnal Penelitian Pendidikan Dan Pengajaran Matematika), 3(2), 151–159.
Suryadi, D. (2019a). Landasan filosofis penelitian desain didaktis (DDR). Pusat Pengembangan DDR Indonesia.
Suryadi, D. (2019b). Penelitian desain didaktis (DDR) dan implementasinya. Bandung: Gapura Press. Cet. Ke, 1.
Suryadi, D. (2023). Jalan Epistemik Menghasilkan Pengetahuan melalui Didactical Design Research (DDR). Seminar Nasional Pendidikan, Lombok, Indonesia.
Suryadi, D., & Itoh, T. (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.
Swan, M. (2014). Designing tasks and lessons that develop conceptual understanding, strategic competence and critical awareness. Tarefas Matemáticas: Livro de Atas Do Encontro de Investigação Em Educação Matemática, 9–28.
Thorpe, J. A. (2018). Algebra: What should we teach and how should we teach it? In Research issues in the learning and teaching of algebra (pp. 11–24). Routledge.
Utami, N. S., & Prabawanto, S. (2023). Student obstacles in learning early algebra: A systematic literature review. AIP Conference Proceedings, 2734(1).
Utami, N. S., Prabawanto, S., & Priatna, N. (2022). A didactical design for introducing the concepts in algebraic forms using the theory of praxeology. Beta: Jurnal Tadris Matematika, 15(1), 53–71. https://doi.org/10.20414/betajtm.v15i1.508
Utami, N. S., Prabawanto, S., & Suryadi, D. (2023). How Students Generate Patterns in Learning Algebra? A Focus on Functional Thinking in Secondary School Students. European Journal of Educational Research, 12(2), 913–925. https://doi.org/10.12973/eu-jer.12.2.913
Vilianti, Y. C., Pratama, F. W., & Mampouw, H. L. (2018). Description of The Ability of Social Arithedical Stories by Study Problems by Students VIII SMP Reviewed from The Polya Stage. International Journal of Active Learning, 3(1), 23–32.
Yansa, H., Retnawati, H., & Janna, M. (2021). Misconceptions of basic algebra on linear equation in one variable material. Journal of Physics: Conference Series, 1882(1). https://doi.org/10.1088/1742-6596/1882/1/012091
Yunus, Z., Razak, N. A., & Khairani, A. Z. (2012). Application of Mathematics Proficiency Model. Learning Science and Mathematics, 7.
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