employee
Vladivostok, Vladivostok, Russian Federation
The present study is devoted to a comprehensive analysis of the relationship between students' individual cognitive preferences in presenting mathematical problem conditions and their academic performance. The relevance of the work is due to the contradiction between the traditional system of mathematical education, focused on symbolic representations, and modern scientific data that emphasize the critical role of a multimodal approach and cognitive flexibility in the learning process. The research focuses on the problem of effective study of geometry, which places unique demands on thinking, assuming a synthesis of visual-imaginative intuition and a strict formal-logical apparatus. The theoretical basis of the work is the theory of semiotic representative registers by Raymond Duval, the concept of cognitive styles by Maria Kholodnaya, as well as the dual coding model by Alan Paivio. The empirical part of the study includes conducting a survey among university students aimed at identifying dominant preferences in the perception of educational information: figurative, symbolic, or mixed types. The data obtained are subjected to statistical analysis using the Mann-Whitney criterion to compare academic performance in algebra and geometry between the selected groups. The results show that the group of students who consciously prefer a mixed format of information presentation demonstrate statistically significantly higher academic performance in geometry compared to the group strictly focused on symbolic representations. At the same time, there are no similar differences in academic performance in algebra between the groups. Besides, the group of students who consciously prefer a mixed format of information presentation demonstrate statistically significantly higher academic performance in geometry compared to the group strictly focused on symbolic representations. At the same time, there are no similar differences in academic performance in algebra between the groups. This suggests that cognitive flexibility, expressed in the ability to freely switch between different semiotic registers, is a key competence predictor.
cognitive styles, imaginative thinking, sign-symbolic thinking, representation of mathematical problems, academic performance, multimodal learning, geometry, algebra.
1. Paivio A. Mental representations: A dual coding approach. Oxford University Press; 1986. URL: https://doi.org/10.1093/acprof:oso/9780195066661.001.0001
2. Riding R., Cheema I. Cognitive styles – An overview and integration. Educational Psychology. 1991; (3–4): 193–215. URL: https://doi.org/10.1080/0144341910110301
3. Kieran C. (Ed.). Teaching and learning algebraic thinking with 5- to 12-year-olds: The global evolution of an emerging field of research and practice. Springer International Publishing. 2018. URL: https://doi.org/10.1007/978-3-319-68351-5
4. Radford L. The emergence of symbolic algebraic thinking in primary school. In C. Kieran (Ed.). Teaching and learning algebraic thinking with 5- to 12-year-olds (p. 3–25). Springer. 2018. URL: https://doi.org/10.1007/978-3-319-68351-5_1
5. Hegarty M., Kozhevnikov M. Types of visual-spatial representations and mathematical problem solv-ing. Journal of Educational Psychology. 1999; 91 (4): 684–689. URL: https://doi.org/10.1037/0022-0663.91.4.684
6. Duval R. Understanding the mathematical way of thinking – The registers of semiotic representations. Springer International Publishing; 2017. URL: https://doi.org/10.1007/978-3-319-56910-9
7. Khatin-Zadeh O., Farsani D., Breda A. How can transforming representation of mathematical entities help us employ more cognitive resources? Frontiers in Psychology. 2023; (14): 1091678. URL: https://doi.org/10.3389/fpsyg.2023.1091678
8. Khatin-Zadeh O., Farsani D., Yazdani-Fazlabadi B. Transforming dis-embodied mathematical repre-sentations into embodied representations, and vice versa: A two-way mechanism for understanding mathematics. Cogent Education. 2022; 9 (1): 2154041. https://doi.org/10.1080/2331186X.2022.2154041
9. Khatin-Zadeh O., Farsani D. The role of motion simulation hinge in enhancing inhibition and working memory during mental simulation of motion events. Cogent Education. 2024; 11 (1): 2419700. URL: https://doi.org/10.1080/2331186X.2024.2419700
10. Bal A.P. Skills of using and transforming multiple representations of the prospective teachers. Proce-dia – Social and Behavioral Sciences. 2015; (197): 582–588. URL: https://doi.org/10.1016/j.sbspro.2015.07.197
11. Yao X. Representation transformations in transition from empirical to structural generalization. The Journal of Mathematical Behavior. 2022; (66): 100964. URL: https://doi.org/10.1016/j.jmathb.2022.100964
12. Kuzu O. Preservice mathematics teachers' representation transformation competence levels in the pro-cess of solving limit problems. Acta Didactica Napocensia. 2020; 13 (2): 306–355. URL: https://doi.org/10.24193/adn.13.2.20
13. Sokolowski A. The effects of using representations in elementary mathematics: Meta-analysis of re-search. IAFOR Journal of Education. 2018; 6 (3): 129–152. URL: https://doi.org/10.22492/ije.6.3.08
14. Clark-Wilson A. Transforming mathematics teaching with digital technologies: A community of prac-tice perspective. In Mathematics education in the digital era. 2017; (9): 63–82. URL: https://doi.org/10.1007/978-3-319-33808-8_4
15. Rahmawati D. Translation between mathematical representation: How students unpack source repre-sentation? Jurnal Matematika dan Pembelajaran. 2019; 7 (1): 50–64.
16. Psychological and pedagogical foundations of teaching mathematics at school: for a mathematics teacher about pedagogical psychology / L.M. Friedman. - Moscow: Prosveshchenie, 1983. - 160 p.: ill.
17. Davydov V.V. Developmental training program (Elkonin-Davydov system): I–VI classes: Mathemat-ics. Moscow; 1996.
18. Methodology of teaching mathematics. Formation of techniques of mathematical thinking: a textbook for universities / ed. N.F. Talyzina. 2nd ed., Revised and add. Moscow: Yurayt; 2025. 193 p.
19. Holodnaya M.A. On the pole-splitting effect of cognitive styles: twenty years later. Bulletin of St. Petersburg University. Psychology. 2025; 15 (1): 35–50. URL: https://doi.org/10.21638/spbu16.2025.102
20. Ekintsev V.I. Self-disclosure of non-verbal communication components in the process of internal dialogue when solving visual problems. In the book Self-disclosure of abilities as internal dialogue: cog-nitive, metacognitive and existential human resources. Vladivostok: Publishing House of VVSU; 2021.P. 59-68.
