DOI: 
http://dx.doi.org/10.15293/1813-4718.2401.01
UDC: 
372.016:51+13
Dulatova Zainep Asanalievna
Кандидат физико-математических наук, Cand. Sci. (Physics and Mathematics), Chair of the Department of Mathematics and Method of Teaching Mathematics, Irkutsk State University, dulatova@yandex.ru, Irkutsk
Kovyrshina Anna Ivanovna
Кандидат физико-математических наук, Cand. Sci. (Physico-mathemat.), Assoc. Prof. of the Department of Mathematics and Method of Teaching Mathematics, Irkutsk State University, annkow@mail.ru, Irkutsk
Lapshina Elena Sergeevna
Кандидат физико-математических наук, Cand. Sci. (Physical and mathematical), Assoc. Prof. of the Department of mathematics and method of teaching mathematics, Irkutsk State University, esl7828@gmail.com, Irkutsk
Shtykov Nikolay Nikolaevich
Кандидат физико-математических наук, Cand. Sci. (Physico-mathemat.), Assoc. Prof. of the Department of Mathematics and Method of Teaching Mathematics, Irkutsk State University, tukubik8@gmail.com, Irkutsk

Development of Synthesis as a General Logical Method of Cognition in the Process of Teaching Mathematics of Students and Future Teachers

Abstract: 
General logical cognitive actions form the basis of almost all cognitive methods. This determines the necessity of their purposeful formation in the process of subject teaching. A special role in the development of cognitive methods belongs to mathematics, in the process of teaching which these actions manifest themselves in the most explicit form. In the article we consider the formation of synthesis as a basic general logical method. The purpose of our study is to develop approaches to the organization of subject-based teaching aimed at the formation and development of synthetic thinking of school students and teacher education students. The methodology of the research is the theory of funding of logical constructions, developed on the basis of the concept of funding in education (V. D. Shadrikov, E. I. Smirnov). The results of the study. Examples demonstrating the main types of synthesis in mathematics learning are considered. These types include: synthesis as a leading action in the construction a mathematical model and synthesis as a representation of a logically justified solution to a problem. The problems of synthesis implementation by students in the process of solving mathematical problems are analyzed. The specificity of educational tasks that contribute to the formation of synthetic thinking is studied. The role of combinatorial tasks as tasks with prevailing logical component in the formation of synthetic thinking of students is described. In conclusion, on the basis of the theory of funding, the typification of types of synthesis in school mathematical education is proposed.
Keywords: 
methods of cognition; general logical cognitive actions; synthesis; analysis
Please register
References: 

1. Dulatova, Z. A., Kovyrshina, A. I., Lapshina, E. S., Shtykov, N. N., 2021. Organization of training of future teachers, aimed at forming their culture of translatuon of universal learning activities, no. 5, pp. 48–57. DOI: 10.15293/1813-4718.2105.05 (In Russ., abstract in Eng.)
2. Engels, F., 1953. Dialectics of nature. Moscow: State Publishing House of Political Literature, 328 p. (In Russ.)
3. Korolev, M. Yu., 2009. Teaching students a simulation method. Science and School, no. 6, pp. 38–41. (In Russ., abstract in Eng.)
4. Shtoff, V. A., 1966. Modeling and philosophy. Leningrad: Nauka Publ., 303 p. (In Russ.)
5. Arnold, V. I., 2017. Why do we study mathematics? What mathematicians themselves think about this. Kvant, no. 7, pp. 4–8. (In Russ.)
6. Gilev, A. A., 2010. Systematization of cognitive Operations. Vestnik of the Samara State Technical University, no. 3, pp. 27–31. (In Russ., abstract in Eng.)
7. Boltyansky, V. G., Savin, A. P., 2002. Conversations about mathematics. Book 1. Discrete objects. Moscow: FIMA Publ., MССМE Publ., 368 p. (In Russ.)
8. Johnson-Laird, P. N., 2001. Mental models and deduction. Trends in Cognitive Sciences, no. 5 (10), pp. 434–442. DOI: https://doi.org/10.15293/1813-4718.2401.0010.1016/S1364-6613(00)01751-4
9. Stolyar, A. A., 1965. Logical problems in teaching mathematics. Minsk: Higher School Publ., 254 p. (In Russ.)
10. Tyumeneva, Yu., Uglanova, I., Solopov, R., Obukhov, А., 2020. The development of a deductive reasoning test: the construct structure and factors affecting the test item difficulty. Psychological Studies, no. 13 (69). DOI: https://doi.org/
10.15293/1813-4718.2401.0010.54359/ps.v13i69.208 (In Russ., abstract in Eng.)
11. Solso, R. L., 1996. Cognitive psychology. Moscow: Trivola Publ., 600 p. (In Russ.)
12. Kintsch, W., van Dijk, T. A., 1978. Toward a model of text comprehension and production. Psychological Review, no. 85 (5), pp. 363–394. DOI: https://doi.org/10.15293/1813-4718.2401.0010.1037/0033-295X.85.5.363
13. Dulatova, Z. A., Kovyrshina, A. I., Lapshina, E. S., Shtykov, N. N., 2019. The conception of foundation in the formation, development and assessment of logical universal learning activities. Proceedings of the 6th International School-Seminar. Mongolia, Khanh: Irkutsk State University Publ., pp. 39–42. (In Russ., abstract in Eng.)
14. Piaget, J., 2008. The language and thought of the child. Moscow: Rimis Publ., 416 p. (In Russ.)
15. Uglanova, I. L., Pogozhina, I. N., 2021. What the New Measure of Thinking in School Students Has to Offer to Contemporary Education. Educational Studies Moscow, no. 4, pp. 8–34. DOI: 10.17323/1814-9545-2021-4-8-34 (In Russ., abstract in Eng.)