Figurative and symbolic thinking in teaching mathematics: diagnostics of preferences and pedagogical implications

• Чернявская Валентина Станиславовна

  Valentina S. Chernyavskaya. Vladivostok State University. Vladivostok. Russia

• Екинцев Владислав Иванович

  Vladislav I. Ekintsev. Vladivostok State University. Vladivostok. Russia

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.
Keywords: cognitive styles, imaginative thinking, sign-symbolic thinking, representation of mathematical problems, academic performance, multimodal learning, geometry, algebra.