Functional Thinking of Prospective Math Teachers in Solving Non-Linear Number Pattern Problems

Authors

  • Musratul Azizi Universitas Islam Negeri Mataram
  • Al Kusaeri Universitas Islam Negeri Mataram
  • M. Syawahid Universitas Islam Negeri Mataram

DOI:

https://doi.org/10.51700/mutaaliyah.v5i1.895

Keywords:

functional thinking, generalization, pattern

Abstract

This article aims to understand the functional thinking of prospective mathematics teachers in solving non-linear number pattern problems. The functional thinking process consists of the entry, attack, and review stages in solving mathematical problems. The method used in this study is a qualitative approach with a case study type, and data collection is carried out using task-based interview techniques. This study involved 18 participants from students of the Mathematics Education study program at the State Islamic University of Mataram, from 18 participants 2 participants were selected as subjects because they had the correct answers. The results of this study indicate that both prospective mathematics teachers use different representations to express their ideas and functional thinking in solving non-linear number pattern problems. They start the generalization process with the relating action, where they connect the number of towers with the number of known matchsticks. The contribution of this study provides new insights into how prospective mathematics teachers think functionally which can be the basis for developing learning strategies, more effective learning processes and preparing prospective teachers as professionals.

Downloads

Download data is not yet available.

References

Badawi, A., Agoestanto, A., Matematika, J., & Semarang, U. N. (2016). Analisis Kemampuan Berpikir Aljabar Dalam Matematika Pada Siswa SMP Kelas VIII. Unnes Journal of Mathematics Education, 5(3).

Blanton, M. L., & Kaput, J. J. (2011). Functional Thinking as a Route Into Algebra in the Elementary Grades. https://doi.org/10.1007/BF02655895.J.J.

Debrenti, E. (2015). Visual Representations In Mathematics Teaching: An Experiment With Students. Acta Didactica Napocensia, 8(1).

Development, T., Induction, M., Scheme, P., Instruction, D., & Campbell, S. (2001). The Development of Mathematical Induction as a Proof Scheme: A Model for DNR-Based Guershon Harel University of California , San Diego Running Head: Mathematical Induction. 185–212.

Ellis, A. B. (2007). A taxonomy for categorizing generalizations: Generalizing actions and reflection generalizations. In Journal of the Learning Sciences (Vol. 16, Issue 2). https://doi.org/10.1080/10508400701193705

Faseha, H., Evendi, E., & Nugraha, Y. (2021). Analisis kesalahan siswa dalam memecahkan masalah perbandingan berdasarkan langkah polya. Journal Of Math Tadris (jMt), 01(01), 40–54.

Kaput, J. J., Carraher, D. W., & Blanton, M. L. (2008). Algebra In The Early Grades.

Kutbi, M., Putra, E. D., Et, A., & Marsidi. (2022). Identifikasi Proses Berpikir Siswa Dalam Memecahkan Masalah Matematika Ditinjau Dari Perbedaan Gender. 2(1), 185–205.

Markworth, K. A. (2010). Growing and Growing: Promoting Functional Thinking With Geometric Growing Patterns.

Mason, J., Burton, L., & Stacey, K. (2010). Thinking Mathematically.

Pang, J., & Sunwoo, J. (2022a). An analysis of teacher knowledge for teaching functional thinking to elementary school students. Asian Journal for Mathematics Education, 1(3), 306–322. https://doi.org/10.1177/27527263221125112

Pang, J., & Sunwoo, J. (2022b). An analysis of teacher knowledge for teaching functional thinking to elementary school students. Asian Journal for Mathematics Education, 1(3), 306–322. https://doi.org/10.1177/27527263221125112

Pinto, E., & Cañadas, M. C. (2017). Functional thinking and generalisation in third year of primary school To cite this version: HAL Id: Hal-01914666. 471–479.

Rahmah, N. H., & Masduki, M. (2023). PRE-SERVICE MATHEMATICS TEACHERS’ ALGEBRAIC THINKING IN SOLVING MATHEMATICS PROBLEMS BASED ON ADVERSITY QUOTIENT. Prima: Jurnal Pendidikan Matematika, 7(2), 172. https://doi.org/10.31000/prima.v7i2.8714

Siregar, A. P., Juniati, D., & Sulaiman, R. (2017). Profil Berpikir Fungsional Siswa SMP Dalam Menyelesaikan Masalah Matematika Ditinjau Dari Perbedaan Jenis Kelamin. 2(2), 144–152.

Suryowati, E. (2021). Proses berpikir fungsional siswa SMP dalam menyelesaikan soal matematika. AKSIOMA: Jurnal Matematika Dan Pendidikan Matematika, 12(1), 109–119.

Syawahid, M. (2022). Elementary students’ functional thinking in solving context-based linear pattern problems. Beta: Jurnal Tadris Matematika, 15(1), 37–52. https://doi.org/10.20414/betajtm.v15i1.497

Taranova, T. N., Misherina, I. V., Pashina, S. A., Bukreeva, I. V., Lysenko, N. A., & Nedopovs, I. I. (2023). Development of expert thinking of future teachers. SHS Web of Conferences, 164, 00131. https://doi.org/10.1051/shsconf/202316400131

Tarida, L., Budiarto, M. T., & Lukito, A. (2024). State of the art of functional thinking, scaffolding, problem solving and self efficacy (a systematic mapping study). 020017. https://doi.org/10.1063/5.0194597

Wijayanti, E. W. (2020). PROSES BERPIKIR SISWA SMP DALAM MENYELESAIKAN MASALAH MATEMATIKA MATERI FUNGSI DITINJAU DARI PERBEDAAN JENIS KELAMIN. 9(3), 504–508.

Wilkie, K. J., & Clarke, D. (2014). Developing Students ’ Functional Thinking in Algebra through Different Visualisations of a Growing Pattern ’ s Structure. 2008, 637–644.

Published

2025-02-22

How to Cite

Azizi, Musratul, Al Kusaeri, and M. Syawahid. “Functional Thinking of Prospective Math Teachers in Solving Non-Linear Number Pattern Problems”. Jurnal al Muta’aliyah: Pendidikan Guru Madrasah Ibtidaiyah 5, no. 1 (February 22, 2025): 15-27. Accessed December 21, 2025. https://journal.staidk.ac.id/index.php/almutaliyah/article/view/895.

Issue

Section

Articles (Peer Reviewed)