Ways of thinking siswa dalam menyelesaikan masalah pola bilangan non rutin: Suatu penelitian fenomenologi hermeneutik

Aiyub Aiyub(1),

(1) Universitas Islam Negeri Ar-Raniry Banda Aceh


This study was conducted with the aim of investigating and exploring students' ways of thinking (WoT) in solving non-routine number pattern problems. This study used a qualitative method with a hermeneutic phenomenological approach with grade 8 students at a junior high school in Banda Aceh. To achieve the research objectives, data collection was carried out using a written test instrument with a number pattern on a 4-digit palindrome, structured documentation, and clinical interviews. The results of the study show that students' WoT in solving non-routine number pattern problems is that there are four approaches used in solving non-routine problems, namely: first, determining the special case; second, determining the pattern; third, using a mathematical model; and fourth, using a similar problem. The subject of critical reflection uses the three WoTs above except for using similar problems. The subject of explicit reflection uses the three approaches above except for using a mathematical model. While Subjects who cannot solve the problem only use the strategy of identifying special cases. Another finding is that the subject of critical reflection tends to use different strategies from those given by the teacher, is unique, and gives reasons for algebraic forms. In contrast, explicit reflection subjects tend to be less flexible in using strategies and tend to use inductive or arithmetic reasons. To support students in their ability to pattern and think algebraically, teachers must accustom students to solving non-routine mathematical problems in various contexts of learning by using number patterns.


Ways of thinking; solution to problem; number patterns; palindrome

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Aiyub, A. (2023). Proses berpikir matematis dan berpikir kritis siswa dalam menyelesaikan masalah matematis non rutin berdasarkan kerangka teori situasi didaktis. Disertasi (S3). Universitas Pendidikan Indonesia.

Aiyub, A., Suryadi, D., Fatimah, S., & Kusnandi, K. (2022). Investigation of the critical thinking process in solving non-routine mathematical problems. European Online Journal of Natural and Social Sciences, 11(4), 1212–1233.

Brady, C., Lesh, R., & Sevis, S. (2015). Extending the reach of the models and modelling perspective: A course-sized research site. In G. A. Stillman et al. (Eds.), Mathematical Modelling in Education Research and Practice (pp. 55–66). Dordrecht: Springer International Publishing. https://doi.org/10.1007/978-3-319-18272-8_4

Brousseau, G. (2002). Theory of didactical situations in mathematics. In R. S. and V. W. Nicola Balacheff, Mantin Cooper (Ed.), Kluwer Academic Publishers (Edited and). Kluwer Academic Publishers. https://doi.org/10.1007/0-306-47211-2

Creswell, J. W. (2007). Qualitative inquiry & research design: Choosing among five approaches (Second Eds). Sage Publication, Inc.

Eatough, V., & Smith, J. (2017). Interpretative phenomenological analysis. In: Willig, C. and Stainton-Rogers, W. (eds.) Handbook of qualitative psychology. Sage Publication Ltd.

English, L. D. (2016). STEM education K-12: Perspectives on integration. International Journal of STEM Education, 3(1), 1–8. https://doi.org/10.1186/s40594-016-0036-1

English, L. D. (2023). Ways of thinking in STEM-based problem solving. ZDM - Mathematics Education. https://doi.org/10.1007/s11858-023-01474-7

Harel, G. (2008). What is mathematics? A pedagogical answer to a philosophical question. In B. Gold & R. A. Simons (Eds.), Proof and Other Dilemmas: Mathematics and Philosophy. United States of America: The Mathematical Association of America, Inc. https://doi.org/10.5948/upo9781614445050.018

Harel, G., & Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. In A. Schoenfeld, J. Kaput, & E. Dubinsky (Eds.), Research in collegiate mathematics education III (pp. 234-283). Providence, RI: American Mathematical Society. https://doi.org/10.1090/cbmath/007/07

Herman, T. (2000). Strategi pemecahan masalah (problem solving) dalam pembelajaran matematika. In Makalah. Tidak Diterbitkan. http://file.upi.edu/Direktori

Lee, K., Ng, S. F., Bull, R., Lee Pe, M., & Ho, R. H. M. (2011). Are patterns important? An investigation of the relationships between proficiencies in patterns, computation, executive functioning, and algebraic word problems. Journal of Educational Psychology, 103(2), 269–281. https://doi.org/10.1037/a0023068

Lesh, R., Riggs, C., English, L., & Sevis, S. (2013). Problem solving in the primary school (K-2) Let us know how access to this document benefits you. The Mathematics Enthusiast, 10(1–2), 35–60.

Maass, K., Geiger, V., Romero Ariza, M., & Goos, M. (2019). The role of mathematics in interdisciplinary STEM education. ZDM Mathematics Education, 51(6), 869–884. https://doi.org/10.1007/s11858-019-01100-5

Muthukaruppan, S., Eswari, A., & Rajendran, L. (2013). Mathematical modelling of a biofilm: The Adomian decomposition method. Natural Science, 05(04), 456–462. https://doi.org/10.4236/ns.2013.54059

NCTM. (2000). Principles standards and for school mathematics. Reston, VA: The National Council of Teachers of Mathematics, Inc.

Polya, G. (1985). How to solve it. In Princeton University Press (Second Edi).

Ricoeur, P. (1986). Lectures on ideology and utopia. New York: Columbia University Press. https://archive.org/details/pdfy-oRPzWEh3nXrYxehT/page/n13/mode/2up

Suryadi, D. (2019a). Landasan filosofis penelitian desain didaktis (DDR) [philosophical foundations of didactic design research (DDR)]. Bandung: Gapura Press.

Suryadi, D. (2019b). Penelitian desain didaktical (DDR) dan implementasinya. Bandung: Gapura Press.

Tall, D. (2008). The transition to formal thinking in mathematics. Mathematics Education Research Journal, 20(2), 5–24. https://doi.org/10.1007/BF03217474

Uyangör, S. M. (2019). Investigation of the mathematical thinking processes of students in mathematics education supported with graph theory. Universal Journal of Educational Research, 7(1), 1–9. https://doi.org/10.13189/ujer.2019.070101

DOI: https://doi.org/10.34007/jdm.v4i2.1851


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Journal of Didactic Mathematics

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