Mathematical Olympiad issues to identify students' reasoning ability using Polya's model

  • Mohammad Tohir Mathematics Education, Universitas Ibrahimy, Situbondo, East Java 68374, Indonesia https://orcid.org/0000-0001-8342-0972
  • Muhasshanah Muhasshanah Information Technology, Universitas Ibrahimy, Situbondo, East Java 68374, Indonesia
  • Riyan Hidayat Institut Penyelidikan Matematik & Department of Science and Technical Education, Universiti Putra Malaysia, Selangor 43400, Malaysia
  • Erik Valentino Mathematics Education, STKIP Bina Insan Mandiri, East Java 60229, Indonesia
  • Tommy Tanu Wijaya Mathematics Education, Beijing Normal University, Beijing 100875, China
Keywords: Mathematical Olympiad, Polya’s Model, Problem-Solving, Reasoning Ability

Abstract

This research aims to describe the level of mathematical reasoning ability of students in solving mathematical Olympiad problems based on problem-solving of the Polya model. This study employed descriptive analysis with a qualitative approach. Data were collected by using observation, documentation, and interviews. The study subjects were 27 junior high school students participating in the National Science Competition in Indonesia. Meanwhile, the Miles and Huberman analysis model was used as the data analysis. The results of this study indicated that: (1) the level of students’ mathematical reasoning-ability based on the problem-solving of Polya models in the category of "sufficiently competent" (high-group students), in the category of "less competent" (medium-group students), and in the category of "incompetent" (low-group students); (2) the most complex and rarely performed stages by students in Polya’s model were at the "devising a plan" and "looking back" stages; and (3) the Polya's model used in solving mathematical Olympiad test items was more suitable for those considered as routine-questions, and it was not suitable for non-routine questions. This study also showed that, on average, the students had difficulty finding initial ideas to start working on the test items.

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References

Alfin, J., & Fuad, A. (2019). Development of Group Science Learning (GSL) model to improve the skills of collaborative problem solving, science process, and self-confidence of primary schools teacher candidates. International Journal of Instruction, 12(1), 147–164. https://doi.org/10.29333/iji.2019.12110a

Alford, J., & Head, B. W. (2017). Wicked and less wicked problems: A typology and a contingency framework. Policy and Society, 36(3), 397–413. https://doi.org/10.1080/14494035.2017.1361634

Arnellis, A., Jamaan, E. Z., & Amalita, N. (2018). Efforts to improve mathematics teacher competency through training program on design olympiad mathematics problems based on higher order thinking skills in the Junior High School. IOP Conference Series: Materials Science and Engineering, 335(1), 1-5. https://doi.org/10.1088/1757-899X/335/1/012118

Ayal, C. S., Kusuma, Y. S., Sabandar, J., & Dahlan, J. A. (2016). The enhancement of mathematical reasoning ability of Junior High School students by applying mind mapping strategy. Journal of Education and Practice, 7(25), 50–58. https://eric.ed.gov/?id=EJ1115860

Cropley, A. J., & Urban, K. K. (2000). Programs and strategies for nurturing creativity. International Handbook of Giftedness and Talent. https://doi.org/10.1016/b978-008043796-5/50034-6

Grossoehme, D. H. (2014). Overview of qualitative research. Journal of Health Care Chaplaincy, 20(3), 109–122. https://doi.org/10.1080/08854726.2014.925660

Hughes, E. M., Riccomini, P. J., & Lee, J.-Y. (2020). Investigating written expressions of mathematical reasoning for students with learning disabilities. The Journal of Mathematical Behavior, 58(1), 100775. https://doi.org/10.1016/j.jmathb.2020.100775

Hulaikah, M., & Degeng, I. (2020). The effect of experiential learning and adversity quotient on problem-solving ability. International Journal of Instruction, 13(1), 869–884. https://doi.org/10.29333/iji.2020.13156a

Kadir, K. (2018). Proses berpikir kreatif dalam pemecahan masalah geometri ditinjau dari tingkat kemampuan geometri siswa kelas VIII MTs Madani Alauddin [Creative thinking process in solving geometry problems judging from the geometry ability level of class VIII Students at MTs Madani Alauddin]. Pascasarjana. S1 thesis, Pascasarjana. http://eprints.unm.ac.id/7893/

Lailiyah, S., Kusaeri, K., Retnowati, E., & Erman, E. (2022). A Ruppert’s framework: How do prospective teachers develop analogical reasoning in solving algebraic problems? JRAMathEdu (Journal of Research and Advances in Mathematics Education), 7(3). https://doi.org/10.23917/jramathedu.v7i3.17527

Lambert, V. A., & Lambert, C. E. (2012). Qualitative descriptive research: An acceptable design. Pacific Rim International Journal of Nursing Research, 16(4), 255–256. https://he02.tci-thaijo.org/index.php/PRIJNR/article/view/5805

Maswar, M. (2019). Strategi pembelajaran Matematika Menyenangkan Siswa (MMS) berbasis metode permainan mathemagic, teka-teki dan cerita matematis. Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 1(1), 28–43. https://doi.org/10.35316/alifmatika.2019.v1i1.28-43

McGee, E. O. (2015). Robust and fragile mathematical identities: A framework for exploring racialized experiences and high achievement among black college students. Journal for Research in Mathematics Education, 46(5), 599–625. https://doi.org/10.5951/jresematheduc.46.5.0599

Miles, M. B., & Huberman, A. M. (1994). Qualitative data analysis: An expanded sourcebook. Sage.

Munawwarah, M., Laili, N., & Tohir, M. (2020). Keterampilan berpikir kritis mahasiswa dalam memecahkan masalah matematika berdasarkan keterampilan abad 21 [Students' critical thinking skills in solving mathematical problems based on 21st century skills]. Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 2(1), 37–58. https://doi.org/10.35316/alifmatika.2020.v2i1.37-58

Murni, A., Sabandar, J., Kusumah, Y. S., & Kartasamita, B. G. (2013). The Enhancement of junior high school students’ abilities in mathematical problem solving using soft skill-based metacognitive learning. Indonesian Mathematical Society Journal on Mathematics Education, 4(2), 194–203. https://doi.org/10.22342/jme.4.2.554.194-203

Muttaqin, H., Susanto, S., Hobri, H., & Tohir, M. (2021). Students’ creative thinking skills in solving mathematics Higher Order Thinking Skills (HOTS) problems based on online trading arithmetic. Journal of Physics: Conference Series, 1832(1), 12036. https://doi.org/10.1088/1742-6596/1832/1/012036

Nadrah, W. H., Ab Halim, F., sern Lai, C., & Abdullah, S. S. Z. S. (2020). Mathematical thinking styles among engineering students: Perceptions versus assessment test. Journal of Technical Education and Training, 12(1), 245–253. https://publisher.uthm.edu.my/ojs/index.php/JTET/article/view/3232

Napitupulu, E. E., Suryadi, D., & Kusumah, Y. S. (2016). Cultivating upper secondary students’ mathematical reasoning-ability and attitude towards mathematics through problem-based learning. Journal on Mathematics Education, 7(2), 117–128. https://doi.org/10.22342/jme.7.2.3542.117-128

NCTM. (2009). Focus in high school mathematics: Reasoning and sense making. National Council of Teachers of Mathematics.

Pathuddin, P., Linawati, L., Mubarik, M., Fadlun, F., & Anggraini, A. (2022). High logical-mathematical intelligence learner’s problem-solving performance on integer operation problem. AIP Conference Proceedings, 2577(1). https://doi.org/10.1063/5.0096068

Runco, M. A., Acar, S., & Cayirdag, N. (2017). A closer look at the creativity gap and why students are less creative at school than outside of school. Thinking Skills and Creativity, 24, 242–249. https://doi.org/10.1016/j.tsc.2017.04.003

Sari, A. P., Ikhsan, M., & Saminan, S. (2017). Creative Thinking Process of Students in Solving Mathematical Problems Based on Wallas Model. Beta Tadris Mathematics Journal, 10(1), 18–32. http://www.jurnalbeta.ac.id/index.php/betaJTM/article/view/102

Su, J., Ye, J., Nie, L., Cao, Y., & Chen, Y. (2023). Optimizing spaced repetition schedule by capturing the dynamics of memory. IEEE Transactions on Knowledge and Data Engineering. https://doi.org/10.1109/TKDE.2023.3251721

Sulistiawati, D. S., & Fatimah, S. (2016). Peningkatan kemampuan penalaran matematis menggunakan desain didaktis berdasarkan kesulitan belajar pada materi luas dan volume [Improving mathematical reasoning ability using didactical design based on learning difficulty in area and volume material]. JPPM, 9(1), 175–188. https://adoc.pub/peningkatan-kemampuan-penalaran-matematis-menggunakan-desain.html

Sumartini, T. S. (2015). Peningkatan kemampuan penalaran matematis siswa melalui pembelajaran berbasis masalah [Increasing students' mathematical reasoning ability through problem based learning]. Mosharafa: Jurnal Pendidikan Matematika, 4(1), 1–10. https://www.neliti.com/publications/226594/peningkatan-kemampuan-penalaran-matematis-siswa-melalui-pembelajaran-berbasis-ma

Surajiyo, S. A., & Andiani, S. (2007). Dasar-dasar logika. Cetakan Ke-2 [Basics of logic. 2nd Printing]. Jakarta.

Surya, E., & Putri, F. A. (2017). Improving mathematical problem-solving ability and self-confidence of high school students through contextual learning model. Journal on Mathematics Education, 8(1), 85–94. https://doi.org/10.22342/jme.8.1.3324.85-94

Tambunan, H. (2019). The effectiveness of the problem-solving strategy and the scientific approach to students’ mathematical capabilities in High Order Thinking skills. International Electronic Journal of Mathematics Education, 14(2), 293–302. https://doi.org/10.29333/iejme/5715

Tohir, M. (2017). Pengembangan bahan ajar olimpiade matematika berdasarkan model pemecahan masalah untuk meningkatkan kemampuan penalaran matematis siswa [Development of mathematics olympiad teaching materials based on problem solving models to improve students' mathematical reasoning abilities]. In Tesis. Magister Pendidikan Matematika Universitas Jember. Program Pascasarjana Universitas Jember. https://doi.org/10.13140/RG.2.2.31121.79200

Tohir, M., Maswar, M., Atikurrahman, M., Saiful, S., & Rizki Pradita, D. A. (2020). Prospective teachers’ expectations of students’ mathematical thinking processes in solving problems. European Journal of Educational Research, 9(4), 1735–1748. https://doi.org/10.12973/EU-JER.9.4.1735

Tohir, M., Susanto, Hobri, Suharto, & Dafik. (2018). Students’ creative thinking skills in solving mathematics olympiad problems based on problem-solving Polya and Krulik-Rudnick model. Advanced Science Letters, 24(11), 8361–8364. https://doi.org/10.1166/asl.2018.12563

Ursulasari, Y. (2019). The effectiveness of learning cycle with lesson study for learning community to build students creative thinking skills on algebraic form. Journal of Physics: Conference Series, 1265(1), 1-9. https://doi.org/10.1088/1742-6596/1265/1/012007

Widjajanti, K., Nusantara, T., As’ari, A. R., Irawati, S., Haris, Z. A., Akbar, D. N., & Lusbiantoro, R. (2019). Delaying Scaffolding Using GeoGebra: Improving the Ability of Vocational Students to Draw Conclusions. TEM Journal, 8(1), 305-310. https://doi.org/10.18421/TEM81-42

Yee, S. P., & Bostic, J. D. (2014). Developing a contextualization of students’ mathematical problem-solving. The Journal of Mathematical Behavior, 36, 1–19. https://doi.org/10.1016/j.jmathb.2014.08.002

Published
2023-12-31
How to Cite
Tohir, M., Muhasshanah, M., Hidayat, R., Valentino, E., & Wijaya, T. T. (2023). Mathematical Olympiad issues to identify students’ reasoning ability using Polya’s model. Alifmatika: Jurnal Pendidikan Dan Pembelajaran Matematika, 5(2), 264-281. https://doi.org/10.35316/alifmatika.2023.v5i2.264-281
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