Analysis of Seventh-Grade Students’ Performance in National Mathematics Competitions by Topic and Task Type: A Comparison of Specialized and Regular Classes
Abstract
Mathematics competitions are increasingly attracting the researchers’ attention in the field of mathematics education, as they offer numerous benefits to students — from deepening and broadening their knowledge to developing problem-solving skills. Given that seventh-grade students in the Republic of Serbia have, for many years had, the opportunity to attend specialized classes for mathematically gifted students (SM classes), the question arises whether grouping these students in homogeneous classes affects their performance in national mathematics competitions. The aim of this paper is to make a detailed comparison of the performance of students from SM and regular classes in the national competitions and to analyze the tasks in which the two groups statistically significant differences. The analysis of students’ performance in 50 competition tasks showed that SM students achieved statistically significantly better results in 23 tasks,while the students from the regular class only performed better in one task. Greatest differences in favor of SM students were observed in number theory, followed by geometry and combinatorics, with the smallest differences in algebra tasks. SM students were significantly more successful in solving proof-based tasks than their peers from regular classes. A detailed analysis of tasks content suggests that the differences in performance may be due to the broader and deeper mathematical education that SM students have, as well as their superior ability to synthesize various mathematical concepts and statements in the problem-solving process. The results of this study can serve as a guide for both teachers and students in preparing for mathematics competitions.
References
De Losada, M. F., & Taylor, P. J. (2022). Perspectives on mathematics competitions and their relationship with mathematics education. ZDM Mathematics Education, 54, 941–959. https://doi.org/10.1007/s11858-022-01404-z
Facciaroni, L., Gambini, A., & Mazza, L. (2023). The difficulties in geometry: A quantitative analysis based on results of mathematics competitions in Italy. European Journal of Science and Mathematics Education, 11(2), 259–270. https://doi.org/10.30935/scimath/12590
Karp, A. (2009). Teaching the Mathematically Gifted: An Attempt at a Historical Analysis. In R. Leikin, A. Berman & B. Koichu (Eds.), Creativity in Mathematics and the Education of Gifted Students (pp. 11–29). Sense Publishers. https://doi.org/10.1163/9789087909352_003
Keldibekova, A. O. (2020). About the subject content of Mathematical Olympiads for schoolchildren. Perspektivy nauki i obrazovania – Perspectives of Science and Education, 46(4), 269–282. https://doi.org/10.32744/pse.2020.4.18
Kenderov, P. (2022). Mathematical competitions: an integral part of the educational process. ZDM – Mathematics Education, 54, 983996. https://doi.org/10.1007 /s11858-022-01348-4
Kim, M. (2016). A Meta-Analysis of the Effects of Enrichment Programs on Gifted Students. Gifted Child Quarterly, 60(2), 102–116. https://doi.org/10.1177/ 0016986216630607
Kulik, J. A., & Kulik, C. C. (1987). Effects of ability grouping on student achievement. Equity & Excellence in Education, 23(1–2), 22–30. https://doi.org/10.1080/ 1066568870230105
Laamena, C. M., Nusantara, T., Irawan, E. B., & Muksar, M. (2018). How do the Undergraduate Students Use an Example in Mathematical Proof Construction: A Study based on Argumentation and Proving Activity. International Electronic Journal of Mathematics Education, 13(3), 185–198. https://doi.org/10.12973/iejme/3836
Leikin, R. (2007). Habits of mind associated with advanced mathematical thinking and solution spaces of mathematical tasks. In D. Pitta, P. Phillippou & G. Phillippou (Eds.), Proceedings of the Fifth Congress of the European Society for Research in Mathematics Education (pp. 2330–2339).
Liljedahl, P. (2019). Conditions for supporting problem-solving: Vertical non-permanent surfaces. In P. Liljedahl & M. Santos-Trigo (Eds.), Mathematical problem solving (pp. 289–310). Springer.
Mićić, V., & Kadelburg, Z. (2022). 75 godina rada Društva matematičara Srbije. Nastava matematike, LXVII(3-4), 39–68.
Neihart, M. (2007). The socioaffective impact of acceleration and ability grouping: Recommendations for best practice. Gifted Child Quarterly, 51(4), 330–341. https://doi.org/10.1177/0016986207306319
Nieto-Said, J. H., & Sánchez-Lamoneda, R. (2022). The curriculum for mathematical competitions. ZDM - Mathematics Education, 54(5), 1043–1057. https://doi.org/10.1007/s11858-022-01389-9
Guidelines on the Curriculum for Seventh and Eighth Grade Students of Primary Education Gifted in Mathematics [Pravilnik o nastavnom planu i programu za učenike sedmog i osmog razreda osnovnog obrazovanja i vaspitanja obdarene za matematiku] (2019). Prosvetni glasnik, Službeni glasnik Republike Srbije, br. 12/2019.
Rochayati, M. Y., & Rochayani, M. Y. (2024). The Effect of Enrichment Program on the Achievement of Vocational High School Gifted Students in Mathematics Competitions. Jurnal Ilmu Pendidikan (JIP) STKIP Kusuma Negara, 15(2), 127–137.
Sal'kov, N. A., Vyshnyepolskiy, V. I., Aristov, V. M., & Kulikov V. P. (2017). Academic Olympics on descriptive geometry as a catalyst of heuristic thinking. Geometry & Graphics, 2, 93–101. https://doi.org/10.12737/article_5953f3767b1e80.12067677
Špijunović, K., & Maričić, S. (2013). Pupils’ Performance in the District Mathematics Competition as the Indicator of Efficiency of Primary Mathematics Education. In H. Butenko & B. Kozuh (Eds.), Contemporary School and Education (pp. 133–146). Ministry of Education and Science, Youth and Sport of Ukraine, Horlivka Institute for Foreign Languages of the State Higher Educational Establishment „Donbas State Pedagogical University” A. F. M. Krakow University, Faculty of Education University of Primorska.
Sriraman, B. (2003). Mathematical Giftedness, Problem Solving, and the Ability to Formulate Generalizations: The Problem-Solving Experiences of Four Gifted Students. The Journal of Secondary Gifted Education, 14(3), 151–165. https://doi.org/10.4219/jsge-2003-425
Steenbergen-Hu, S., Makel, M. C., & Olszewski-Kubilius, P. (2016). What one hundred years of research says about the effects of ability grouping and acceleration on K–12 students’ academic achievement: Findings of two second-order meta-analyses. Review of Educational Research, 86(4), 849–899. https://doi.org/10.3102/0034654316675417
Swiatek, M. A., & Lupkowski-Shoplik, A. (2005). An Evaluation of the Elementary Student Talent Search by Families and Schools. Gifted Child Quarterly, 49(3), 247–259. https://doi.org/10.1177/001698620504900306
Vulović, N., Maričić, S., & Ranđelović, B. (2024). Analiza uspešnosti rešavanja geometrijskih zadataka na okružnim takmičenjima učenika četvrtog razreda osnovne škole. Zbornik Instituta za pedagoška istraživanja, 56(2), 259279. https://doi.org/10.2298/ZIPI2402259V
Vulović, N., Milenković, A., & Milikić, M. (2024). Razlike u postignućima učenika 7. i 8. razreda koji nastavu pohađaju u osnovnim školama i pri gimnazijama na državnim takmičenjima iz matematike. Zbornik radova Pedagoškog fakulteta, Užice, 27(26), 221244. https://doi.org/10.5937/ZRPFU2426221V
Vulović, N., Mihajlović, A., & Milinković, J. (2023). Polne razlike na matematičkim takmičenjima u Republici Srbiji. Inovacije u nastavi, XXXVI(3), 119135. DOI: 10.5937/inovacije2303119V