Learning obstacles in the generalization process: In case number pattern topic

Authors

  • Nyla Farhatul Maula Department of Mathematics Education, Faculty of Mathematics and Sciences Education, Universitas Pendidikan Indonesia, Indonesia
  • Didi Suryadi Department of Mathematics Education, Faculty of Mathematics and Sciences Education, Universitas Pendidikan Indonesia, Indonesia
  • Al Jupri Department of Mathematics Education, Faculty of Mathematics and Sciences Education, Universitas Pendidikan Indonesia, Indonesia

DOI:

https://doi.org/10.22219/raden.v4i2.36342

Keywords:

learning obstacles, generalization, number pattern

Abstract

Generalization plays an important role in mathematics because it is considered inherent in mathematical thinking in general. Where number pattern is a topic that is closely related to generalization. Problems are still found in generalizing number patterns so this can cause learning obstacles. This research aims to identify learning obstacles for Junior high school students in the generalization process with a focus on number pattern topics. This research is qualitative research with a case study method. The research subjects consisted of 30 grade 8 students in Jakarta who had studied number pattern. Subjects were given three test tasks, the results of which were used to figure out learning obstacles in the generalization process experienced by students and then continued with interviews with ten subjects. The findings show that learning obstacles in the pattern generalization process occur primarily at the expression and symbolic stages. Most students bypassed the generalization method, relying instead on formulas or manual calculations. Based on these results, it is recommended that educators implement didactic designs that offer targeted interventions during the expression and symbolic stages, such as using more interactive and symbolic reasoning activities to strengthen students' understanding and generalization skills in number patterns.

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References

Abakah, F., & Brijlall, D. (2024). Investigating algebraic generalization strategies of Ghanaian high school learners. Learning and Individual Differences, 111, 102077.

Barbosa, A., & Vale, I. (2015). Visualization in pattern generalization: Potential and challenges. Journal of the European Teacher Education Network, 10(3), 57–70.

Beaton, M. (2014). Learning to perceive what we do not yet understand: Letting the world guide us. In: Cappuccio, M., Froese, T. (eds) Enactive Cognition at the Edge of Sense-Making. New Directions in Philosophy and Cognitive Science. Palgrave Macmillan, London.

Brief, B. (2003). Algebraic skills & strategies for elementary teacher & students. Educational Resources Information Center.

Brousseau, G. (2002). Theory of didactical situation in mathematics. New York: Kluwer Academic Publishers.

Dindyal, J. (2007). High school students’ use of patterns and generalisations. Proceedings of the 30th Annual Conferences of the Mathematics Education Research Group of Australasia, 1(July), 236–245.

Disnawati, H., & Nahak, S. (2019). Pengembangan lembar kerja siswa berbasis etnomatematika tenun timor pada materi pola bilangan. Jurnal Elemen, 5(1), 64–79.

Dreyfus, T. (1991). Advanced mathematical thinking processes. In D. Tall (Ed.), Advanced Mathematical Thinking (25-41). Boston: Kluwer Academic Publisher

Fadiana, M., Amin, S. A & Lukito, A. (2018). Profil generalisasi berdasarkan perspektif semiotik siswa operasional konkret dan operasional formal. Jurnal Ilmiah Pendidikan Matematika, 3(2), 99-106

Fauzi, A. H. N., & Masduki, M. (2022). Student’s anomaly reasoning in solving number pattern in terms of gender. Jurnal Didaktik Matematika, 9(2), 328–342.

Firdaus, A. M., Murtafiah, W., Lukitasari, M., Lestari, N. D. S., Ernawati, T., & Widodo, S. A. (2023). Generalization of patterns drawing of high-performance students based on action, process, object, and schema theory. European Journal of Educational Research, 12(1), 421-433.

Guner, P., Uygun, T., & Ersoy, E. (2013). 7th and 8th grade students' generalization strategies of patterns. International Journal of Global Education, 2(4), 37-54

Hariyomurti, B., Prabawanto, S., & Jupri, A. (2020). Learning obstacle siswa dalam pembelajaran barisan dan deret aritmetika. JURING (Journal for Research in Mathematics Learning), 3(3), 283.

Jackson, G.B. Seeing what is not seen. Phenom Cogn Sci 17, 503–519 (2018).

Jelahu, R. A., Loka Son, A., Bete, H., García-García, J., Sudirman, S., & Alghadari, F. (2023). Profile of middle school students’ mathematical literacy ability in solving number pattern problems. International Journal of Science Education and Cultural Studies, 2(1), 1–14.

Jurow, A. S. (2004). Generalizing in interaction: Middle school mathematics students making mathematical generalizations in a population-modeling project. Mind, Culture, and Activity, 11, 279–30

Kusumaningtyas, S. I., Junianti, D. & Lukito, A. (2017). Pemecahan masalah generalisasi pola siswa kelas VII SMP ditinjau dari gaya kognitif field independendt dan field dependent. Kreano Jurnal Matematika KreatifInovatif, 8(1), 76-84.

Lannin, J. K. (2005). Generalization and justification: The challenge of introducing algebraic reasoning through patterning activities. Mathematical Thinking and Learning, 7(3), 231-258.

Marzano, J. (1988). Dimensions of thinking: A framework for curriculum and instruction. Virginia: Association for Supervision and Curriculum Development.

Mulligan, J., & Mitchelmore, M. (2009). Awareness of pattern and structure in early mathematical development. Mathematics Education Research Journal, 21(2), 33–49.

Orton, A. (Ed.). (2005). Pattern in the teaching and learning of mathematics (2nd ed.). London: Continuum.

Radford, L. (2001). Factual, contextual and symbolic generalizations in algebra. Pme Conference, 4(January 2001), 81–89.

Somasundram, P., Akmar, S. N., & Eu, L. K. (2019). Pattern generalisation by year five pupils. International Electronic Journal of Mathematics Education, 14(2), 353-362.

Spangenberg, E. D., & Pithmajor, A. K. (2020). Grade 9 mathematics learners’ strategies in solving number-pattern problems. Eurasia Journal of Mathematics, Science and Technology Education, 16(7).

Stacey, K. (1989). Finding and using patterns in linear generalising problems. Educational Studies in Mathematics, 20(2), 147–164., https://doi.org/10.1007/BF00579460

Suryadi, D. (2018). Ontologi dan epistemologi dalam penelitian desain didaktis (DDR). makalah bahan diskusi di lingkungan departemen pendidikan matematika, Universitas Pendidikan Indonesia, Bandung.

Tillema, E.S., & Gatza, A. (2017). The processes and products of students' generalizing activity. International Group for the Psychology of Mathematics Education.

Warren, E. (2005). Patterns supporting the development of early algebraic thinking. Building Connections: Research, Theory and Practice, 2, 759–766.

Wijns, N., Torbeyns, J., De Smedt, B., & Verschaffel, L. (2019). Young children’s patterning competencies and mathematical development: A review. In K. M. Robinson, H. P. Osana, & D. Kotsopoulos (Eds.), Mathematical learning and cognition in early childhood: Integrating interdisciplinary research into practice (139–161). Cham: Springer

Wilkie, K. J. (2024). Secondary students' algebraic thinking and their engagement with quadratic patterns: The role of problem-solving and problem-posing tasks. Global Journal of Mathematical Analysis, 18(2), 104-120.

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Published

2024-10-28 — Updated on 2024-10-28

How to Cite

Maula, N. F., Suryadi, D., & Jupri, A. (2024). Learning obstacles in the generalization process: In case number pattern topic. Research and Development in Education (RaDEn), 4(2), 964–976. https://doi.org/10.22219/raden.v4i2.36342

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