Problem Solving on Arithmetic Sequences and Series Material Based on the Level of Mathematical Ability
DOI:
10.29303/jm.v8i3.12981Published:
2026-10-01Downloads
Abstract
Background: Problem solving is an essential skill in mathematics learning. Students’ ability to solve problems varies according to their level of mathematical ability, which needs to be profiled to improve the effectiveness of the learning process.
Aims: This study aims to describe the problem-solving profile of students on arithmetic sequences and series material based on their level of mathematical ability at SMA Negeri 1 Banawa Tengah.
Methods: This research used a qualitative approach with a descriptive case study design. The subjects consisted of three students selected using purposive sampling, representing one student each from the high, medium, and low mathematical ability categories, determined based on mathematics report card scores processed according to Arikunto’s (2013) criteria. Data were collected through written tasks and student interviews, and analysed using the Miles, Huberman, and Saldana (2014) model comprising data condensation, data presentation, and conclusion drawing.
Results: The problem-solving profile of students with high mathematical ability (NF) and students with medium mathematical ability (AW) in solving problems fulfilled all four problem-solving indicators based on Polya’s stages: understanding the problem, devising a plan, carrying out the plan, and looking back. The problem-solving profile of students with low mathematical ability (FD) only fulfilled three of the four indicators, consisting of understanding the problem, devising a plan, and carrying out the plan.
Conclusion: Students with high and medium mathematical ability fulfilled all four of Polya’s problem-solving stages, while students with low ability could only fulfil three stages, being unable to review their answers at the looking back stage.
Keywords:
Arithmetic Sequences and Series Mathematical Ability Problem SolvingReferences
Arikunto, S. (2013). Prosedur suatu pendekatan praktik. Rineka Cipta.
Bell, E. T., & Polya, G. (1973). How to solve it: A new aspect of mathematical method. Princeton University Press. https://doi.org/10.2307/2306109
Fitriana, I. N., & Mampouw, H. L. (2019). Skema kognitif siswa dalam menyelesaikan soal peluang ditinjau dari pendekatan Polya. Mosharafa: Jurnal Pendidikan Matematika, 8(3), 353–364. https://doi.org/10.31980/mosharafa.v8i3.510
Irianti, N. P. (2020). Analisis kemampuan penalaran siswa dalam memecahkan masalah matematika berdasarkan langkah-langkah Polya. MUST: Journal of Mathematics Education, Science and Technology, 5(1), 80. https://doi.org/10.30651/must.v5i1.3622
Kamila, N. S., & Adirakasiwi, A. G. (2021). Analisis kesalahan siswa dalam menyelesaikan masalah matematika dengan menggunakan prosedur Polya. Jurnal Pembelajaran Matematika Inovatif, 4(4), 749–754. https://doi.org/10.22460/jpmi.v4i4.749-754
Kemendikbud. (2014). Peraturan Menteri Pendidikan dan Kebudayaan Republik Indonesia Nomor 59 Tahun 2014. Kementerian Pendidikan dan Kebudayaan.
Kouvela, E., Hernandez-Martinez, P., & Croft, T. (2017). “This is what you need to be learning”: An analysis of messages received by first-year mathematics students during their transition to university. Mathematics Education Research Journal, 30(2), 165–183. https://doi.org/10.1007/s13394-017-0226-2
Kurniasih, I., & Sani, B. (2014). Implementasi kurikulum 2013: Konsep dan penerapan. Kementerian Pendidikan dan Kebudayaan.
Maulidya, A. (2018). Berpikir dan problem solving. Ihya Al-Arabiyah: Jurnal Pendidikan Bahasa dan Sastra Arab, 4(1), 11–29. http://jurnal.uinsu.ac.id/index.php/ihya/article/view/1381
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook (3rd ed., T. R. Rohidi, Trans.). Sage Publications.
Netriwati, N. (2016). Analisis kemampuan mahasiswa dalam pemecahan masalah matematis menurut teori Polya. Al-Jabar: Jurnal Pendidikan Matematika, 7(2), 181–190. https://doi.org/10.24042/ajpm.v7i2.32
Permendikbud. (2013). Peraturan Menteri Pendidikan dan Kebudayaan Nomor 69 Tahun 2013 tentang kerangka dasar dan struktur kurikulum SMA/MA. Kementerian Pendidikan dan Kebudayaan.
Pohan, N., & Siregar, E. Y. (2021). Analisis kemampuan pemecahan masalah matematis siswa pada materi bangun ruang di kelas VIII SMP Negeri 5 Sipirok. Jurnal MathEdu (Mathematics Education Journal), 4(1), 60–65. http://journal.ipts.ac.id/index.php/MathEdu/article/view/1971
Van Galen, F., & Van Eerde, D. (2013). Solving problems with the percentage bar. Journal on Mathematics Education, 4(1), 1–8.
Veldhuis, M., & van den Heuvel-Panhuizen, M. (2020). Supporting primary school teachers’ classroom assessment in mathematics education: Effects on student achievement. Mathematics Education Research Journal, 32(3), 449–471. https://doi.org/10.1007/s13394-019-00270-5
License
Copyright (c) 2026 Rahmamina Minarahma
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
