About relevance of fundamentalisation of mathematical training of students of the pedagogical directions during the digital era

Introduction. The era of post-industrial society of knowledge differs from the previous socio-economic period in many important aspects: total digitalisation, automation and robotisation, and furthermore, cross-disciplinary integration of various scientific fields, among which mathematics is of particular relevance. Over the last decades, the language, tools and methods of the digital era have emerged as the basic universal research tools in physics, biology, chemistry, and engineering, organisation of production and in many other theoretical and applied spheres of activity. Against the background of progressively advanced mathematisation, which covers larger functional intellectual space, it is extremely important to provide the fundamental, advancing nature of mathematical training of students, including in the first place the students of the pedagogical directions. The graduates of pedagogical higher education institutions will have not only to convey certain academic educational information, but to coordinate educational trajectories according to a training maxim in their lifetime that is hardly possible without understanding of basic mathematics.

The aim of the present publication is to discuss methodological, culturological and didactic aspects of mathematical training of students of the pedagogical directions.

Methodology and research methods. In the course of the work, the authors used the provisions and requirements of the new Federal State Educational Standards (FSES). The psychological and pedagogical framework of the research is based on the concepts of developing learning and upbringing, vocational and pedagogical orientation of training of future teachers and the idea of lifelong education. The analytical review and synthesis of the content of philosophical, mathematical, pedagogical, methodological literature and normative documents was conducted. The state of mathematical components of pedagogical education and its ways of fundamentalisation were considered according to the theory of training, comparative, culturological and system-based types of analysis.

Results and scientific novelty. The authors note the imbalance between the fundamental mathematical preparation, which is relevant for a modern person, and the competency-based approach, which currently dominates in education and constraints to students’ holistic understanding of mathematical area of knowledge, even within the boundaries of a particular discipline. The situation is exacerbated by an avalanche distribution of information technologies. One of the negative consequences of this situation is replacement of meaningful learning of mathematics with “coaching” of school students and university students for formal test performance. To address these challenges, culturological educational models, which form common cultural ideas of modern mathematics according to the principle of a cultural conformity, have to be the predominant in education, but not competency-based attitudes focused on narrow specialisation. Mathematical modelling, discrete mathematics and computation processes are identified as the most significant components of a new stage of universal mathematical culture evolution. As a result of a digital era, general-education concepts have already become the key concepts of various sections of mathematics, therefore, it is necessary to start a general introduction to the study of these concepts at the stages of school education.

It is highlighted that fundamentalisation of mathematical preparation plays the leading role in the development of logical and professional innovative thinking of students through the understanding of multifunctional structures and schemes (as means and knowledge methods) similar to mathematical structures and schemes. It is appropriately useful to include special courses into a variable part of the master’s programmes (according to education directions), implying students’ research activities: “Mathematical Modelling in Professional Education”, “Bases of Modern Mathematical Culture”, “Discrete Mathematics”, “Mathematical Bases of the System Analysis”, etc.

The authors are convinced that the introduction of the concept of mathematical preparation, based on the culturological and system-based approaches, will help to resolve an apparent contradiction between, on the one hand, the necessary integration and fundamentalisation of knowledge acquired by students, and, on the other hand, the disciplinary dissociations of educational material, shortcomings of competency-based training and formal use of information technologies.

Practical significance. The materials of the publication can be useful for future and practicing teachers of mathematics, computer science and related academic disciplines. Moreover, the present publication can be used by education professionals interested in improving the education quality.

1. Abdurazakov M. M., Gadjiev D. D., Tsvetkova O. N., Tokmazov G. V. Factors influencing the content and character of the professional activity of a modern teacher in the information and educational environment. Informatika i obrazovanie = Informatics and Education. 2018; 9: 42-51. DOI: 10.32517/0234-0453-2018-33-9-42-51 (In Russ.)

2. Glushkov V. M. Kibernetika. Voprosy teorii i praktiki = Cybernetics. Questions of the theory and practice. Moscow: Publishing House Nauka; 1986. 888 p. (In Russ.)

3. Yershov A. P. Izbrannye trudy = Chosen works. Novosibirsk: Publishing House Nauka, Sibirskaja izdatel’skaja firma; 1994. 413 p. (In Russ.)

4. Ruzavin G. I. Matematizacija nauchnogo znanija = Matematisation of scientific knowledge. Moscow: Publishing House Mysl’; 1984. 207 p. (In Russ.)

5. Perminov E. A. O of methodology of realisation of the discrete line in the content of profile training in mathematics at school. Vestnik Cheljabinskogo gosudarstvennogo pedagogicheskogo universiteta = Herald of Chelyabinsk State Pedagogical University. 2012; 6: 69-79. (In Russ.)

6. Kuznetsov A. A., Monakhov V. M., Abdurazakov M. M. Modern and future professional activity of the teacher of Informatics. Informatika i obrazovanie = Informatics and Education. 2016; 5 (274): 3-12. (In Russ.)

7. Kalinina A. How to prepare the country for the fourth industrial revolution. Gazeta RBK = RBC Daily Newspaper [Internet]. 2017 Jan 16 [cited 2019 Feb 20]. Available from: https://www.rbc.ru/newspaper/2017/01/16/5878d2389a 79470077130332 (In Russ.)

8. Sadovnichiy V. A. Traditions and present. Vysshee obrazovanie v Rossii = Higher Education in Russia. 2003; 1: 11-18. (In Russ.)

9. Usol’tsev A. P. Inflation of the competency-based approach in the Russian pedagogical science and practical teaching. Obrazovanie i nauka = The Education and Science Journal [Internet]. 2017 [cited 2019 Feb 20]; (1): 9-25. Available from: https://doi.org/10.17853/1994-5639-2017-1-9-25 (In Russ.)

10. Klekovkin G. A. Training problems in the conditions of open information space. Obrazovanie i nauka = The Education and Science Journal [Internet]. 2014 [cited 2019 Feb 20]; 7 (116): 4-23. Available from: https://doi.org/10.17853/1994-5639-2014-7-4-23 (In Russ.)

11. Geyn A. G. Zemlja informatika = Zemlya of the information scientist. A grant for teachers. Ekaterinburg: Ural State University; Publishing House of the Teacher’s Club; 1997. 206 p. (In Russ.)

12. Borisenkov V. P. Quality of education and problems of preparation of pedagogical shots. Obrazovanie i nauka = The Education and Science Journal [Internet]. 2015 [cited 2019 Feb 20]; 3 (122): 4-18. Available from: https://doi.org/10.17853/1994-5639-2015-3-4-28 (In Russ.)

13. Perminov E. A. About methodological aspects of realisation of culturological approach in mathematical education. Pedagogika = Pedagogics. 2011; 9: 49-55. (In Russ.)

14. Perminov E. A. Metodicheskaja sistema obuchenija diskretnoj matematike studen-tov pedagogicheskih napravlenij v aspekte integracii obrazovanija = The methodical system of training in discrete mathematics of students of the pedagogical directions in aspect of integration of education. Ekaterinburg: Russian State Vocational Pedagogical University; 2013. 286 p. (In Russ.)

15. Egorchenko I. V. Fundamentalisation of mathematical education: Aspects of feature of interpretations of the direction of realisation. In: Gumanitarizacija srednego i vysshego matema-ticheskogo obrazovanija: sostojanie, perspektivy: materialy Vserossijskoj nauchnoj konferencii = Humanitarisation of Secondary and Higher Mathematical Education: State, Prospects. Materials of the All-Russian Scientific Conference; 2005; Saransk. Saransk: Mordovia State Pedagogical Institute; 2005. p. 7-10. (In Russ.)

16. Kudryavtsev L. D. Sovremennaja matematika i ee prepodavanie = Modern mathematics and its teaching. Moscow: Publishing House Nauka; 1985. 176 p. (In Russ.)

17. Perminov E. A., Anakhov S. V., Grishin A. S., Savitskiy E. S. On the research of the methodology of mathematisation of pedagogical science. International Journal of Environmental & Science Education. 2016; 11 (16): 9339-9347.

18. Fedorov V. A. Professional pedagogical education in the changing social and economic conditions: Scientific ensuring development. Obrazovanie i nauka = The Education and Science Journal. 2008; 9 (57): 127-134. (In Russ.)

19. Kholodnaya M. A. Psihologija intellekta. Paradoksy issledovanija = Psychology of intelligence. Paradoxes of research. 2nd edition. St.-Petersburg: Publishing House Piter; 2002. 272 p. (In Russ.)

20. Slastenin V. A., Isaev I. F., Shiyanov E. N. Pedagogika = Pedagogy. Ed. by V. A. Slastenin. Moscow: Publishing House Akademija; 2002. 576 p. (In Russ.)

21. Zeer E. F., Zavodchikov D. P. Identification of universal competences of graduates by the employer. Vysshee obrazovanie v Rossii = Higher Education in Russia. 2007; 11: 46-56. (In Russ.)

22. Abdurazakov M. M., Mukhidinov M. G. Model of training of future teacher of informatics for professional activity. Pedagogika = Pedagogy. 2016; 5: 71-79. (In Russ.)

23. Abdurazakov M. M. Teacher-students in interaction-related educational environment: Culture of knowledge, cognition and information communication. Pedagogika = Pedagogy. 2018; 9: 39-46. (In Russ.)

24. Abdurazakov M. M., Aziyev R. A-S., Muhidinov M. G. The principles of constructing a methodical system for teaching computer science in general educational school. Espacios. 2017; 38 (40): 2. Available from: https://www.revistaespacios.com/a17v38n40/a17v38n40p02.pdf

25. Zhukov V. N. About some reasons of the crisis phenomena in modern education. Vestnik vysshej shkoly = Higher School Herald. 2010; 10: 27-30. (In Russ.)

26. Vechtomov E. M. Osnovnye matematicheskie struktury = Main mathematical structures. Kirov: Publishing House Raduga-PRESS; 2013. p. 292. (In Russ.)

27. Mitin N. A. New models of mathematical psychology and information processes [Internet]. 2015 [cited 2019 Feb 20]. Available from: http://spkurdyumov.narod.ru/Mitin12.htm. (In Russ.)

28. Perminov E. A. Matematicheskoe modelirovanie v professional’nom obrazovanii = Mathematical modeling in professional education Ekaterinburg: Russian State Vocational Pedagogical University; 2015. 116 p. (In Russ.)

29. Perminov E. A. Metodicheskaja sistema obuchenija diskretnoj matematike studentov pedagogicheskih napravlenij = The methodological system of training in discrete mathematics of students of the pedagogical directions. Ekaterinburg: Russian State Vocational Pedagogical University; 2015. 256 p. (In Russ.)

30. Zagvyazinsky V. I. How to break in the present? Obrazovanie i nauka = The Education and Science Journal [Internet]. 2012 [cited 2019 Feb 20]; 7 (96): 91-97. Available from: https://doi.org/10.17853/1994-5639-2012-7-91-97 (In Russ.)

31. Iskrin N. S., Chichkanova T. A. Management of education. Obrazovanie i nauka = The Education and Science Journal [Internet]. 2015 [cited 2019 Feb 20]; 1 (120): 7-21. Available from: https://doi.org/10.17853/1994-5639-2015-1-7-21 (In Russ).

32. Testov V. A. Obnovlenie soderzhanija obuchenija matematike: istoricheskie i me-todologicheskie aspekty = Updating of content of training in mathematics: Historical and methodological aspects. Vologda: Vologda State Pedagogical University; 2012. 176 p. (In Russ.)