Methodical aspects of the formation of new competencies in students for the development of tasks for students within the framework of a modular approach

Introduction. The article highlights the methodical aspects of preparing a future teacher of mathematics for the development of assignments for students, presents various methods of involving students in the activity of developing assignments at the stage of formalization of a real situation, reveals the features of building an educational module aimed at formation of students' competencies in developing tasks for the formalization stage when solving tasks. The article reveals the stages of formations of actions that are part of the modeling, and drawing up adequate exercises on their basis.

Materials and Methods. The study is based on a systematic approach that allows us to consider the learning process as a system aimed at the methodological preparation of students for the design of tasks for the formation of schoolchildren's ability to model; the activity approach provides a phased formation of the actions that are part of the modeling; a modular approach that ensures the construction of an educational module for the formation of new competencies in the design of tasks in future mathematics teachers, aimed at the formation of modeling actions in schoolchildren; a competence-based approach, on the basis of which the methodical foundations of the formation of new competencies in students are identified.

Results. It was found that the process of methodical preparation of future teachers for the development of assignments for students should be built taking into account the specifics of future professional activities; the structure of practical lessons within the educational module should be built in accordance with the activity approach, which ensures the gradual formation of the actions that are part of the modeling. The organization of students' work on the analysis of the structure and content of tasks presented in the works of domestic and international studies, will allow students to be included in the work on identifying the composition of actions necessary to solve practice-oriented tasks, on the selection of situations, for the formalization of which mathematical knowledge and skills are needed to model, for constructing the plot of practice-oriented tasks. The methods of organizing the activities of students at motivational and content stages are highlighted, examples of constructed tasks are given.

Discussion and Conclusions. The article discusses the stages of identifying the actions that are part of the formalization in the process of analyzing real situations, formulates methods for including students in the activity of drawing up the conditions of the problem and formulating various questions for schoolchildren, allowing them to be included in the compilation of a meaningful and mathematical model of the situation presented in task. The conclusion formulated in the article is that in the process of forming new competencies in future mathematics teachers, it is necessary to organize their activities for the selection of a set of actions that make up the modeling and to drawing up a plot and questions for a practice-oriented task based on the selected actions.

1. Bobrovskaya A.V. Teaching the method of mathematical modeling by means of the course of geometry of the Pedagogical Institute: the dissertation of the candidate of pedagogical sciences: 13.00.02. St. Petersburg, 1996. 232 p. (In Russ.)

2. Bozhenkova L.I. Methodology for the formation of universal educational actions in teaching geometry: a methodological guide. 4th edition, electronic. Moscow, Laboratoriya znanij Publ., 2020. 208 p. (In Russ.)

3. Bychkov A.V. Analysis of applied problems in modern textbooks on algebra and geometry from the standpoint of the requirements of the Federal State Educational Standard. Razvitie obrazovaniya, 2019, no. 4(6), pp. 59-63. (In Russ.)

4. Glazkov YU.A., Egupova M.V. Geometry simulator: grade 7. To the textbook of L.S. Atanasyan and others. "Geometry. 7-9 grades". GEF (to the new textbook). Moscow, «Ekzamen» Publ., 2019, 80 p. (In Russ.)

5. Glazkov YU.A., Egupova M.V. Geometry simulator: grade 8. To the textbook of L.S. Atanasyan and others. "Geometry. 7-9 grades". GEF (to the new textbook). Moscow, «Ekzamen» Publ., 2019, 80 p. (In Russ.)

6. Dorofeev A.S., Sosinskaya S.S. Models of a training course in the development of distance learning systems. Prikladnaya informatika, 2007, no. 3(9), pp. 25-37. (In Russ.)

7. Egupova M.V., Moshura YU.V. On the plots of problems for the practical applications of mathematics in test papers for schoolchildren. Aktual'nye problemy obucheniya matematike i informatike v shkole i vuze: materialy V Mezhdunarodnoj zaochnoj nauchnoj konferencii, g. Moskva, 18-22 dekabrya 2019 g. / pod red. M.V. Egupovoj, L.I. Bozhenkovoj: [elektronnoe izdanie setevogo rasprostraneniya]. Moscow, MPGU Publ., 2020. Pp. 102-110. (In Russ.)

8. Ivashchenko N.A. Advantages of modular developmental technology. Teoretiko-metodologicheskie aspekty prepodavaniya matematiki v sovremennyh usloviyah: materialy III Mezhdunarodnoj zaochnoj nauchno-prakticheskoj konferencii (1–7 iyunya 2020 g., g. Lugansk). Lugansk, Knita Publ., 2020. Pp. 247-254. (In Russ.)

9. Kasprzhak A.G. Why Our Students Failed PISA Test. Direktor shkoly, 2005, no. 4, pp. 4-13. (In Russ.)

10. Kovaleva G.S., Krasnyanskaya K.A. International assessment of educational achievements of students (Program for International Student Assessment - PISA). Examples of assignments in mathematics. Moscow, Centr ocenki kachestva obrazovaniya ISMO RAO Publ., 2006. 41 p. (In Russ.)

11. Korotkih D.E., SHabanov A.G., Mazurin A.E. Pedagogical modeling as a method of scientific knowledge. Innovacii v obrazovanii, 2019, no. 12. (In Russ.)

12. International program for assessing educational achievements of students (2018). Centr ocenki kachestva obrazovaniya Instituta strategii razvitiya obrazovaniya Rossijskoj akademii obrazovaniya: [sajt]. Available at: http://www.centeroko.ru/pisa18/pisa2018_pub.html (accessed: 15.10.2020). (In Russ.)

13. Methods of developing teaching mathematics: a textbook for universities / V.А. Dalinger [et al.]; under total. ed. V.A. Dalinger. 2nd edition, revised and enlarged. Omsk, 2020. (In Russ.)

14. Modernization of teacher education in the context of the global educational agenda: pedagogy and psychology of potential opportunities: collective monograph / Fedorov A.A. [et al.]. Nizhny Novgorod, 2015. 296 p. (In Russ.)

15. Modular training. Kompetentnostno-orientirovannaya strategiya professional'noj podgotovki pedagoga: kollektivnaya monografiya / pod red. L.E. SHaposhnikova, V.V. Nikolinoj, O.A. Safonovoj. Nizhny Novgorod, NGPU Publ., 2011. Pp. 128-141. (In Russ.)

16. Organization of project activities at school in the light of the requirements of the Federal State Educational Standard: a methodological guide. Moscow, Vlados Publ., 2018. 121 p. (In Russ.)

17. Perevoshchikova E. N. Technology of constructing diagnostic tasks in a test form. Izvestiya PGU Povolzhskij region, 2014, no. 2(30), pp. 205-218. (In Russ.)

18. Perevoshchikova E.N. Rating plan as a mechanism for assessing the degree of competence formation. Vestnik Mininskogo universiteta, 2018, vol. 6, no. 2(23), doi: https://doi.org/10.26795/2307-1281-2018-6-2-9. (In Russ.)

19. Personalized model of education / E.I. Kazakova, D.S. Ermakov, P.N. Kirillov, N.I. Koryakina, S.A. Yankevich. Moscow, ANO «Platforma novoj shkoly» Publ., 2019. 36 p. (In Russ.)

20. Polikarpov S.A. Mathematical education in Russia. New principles of training teachers of mathematics. Problemy sovremennogo matematicheskogo obrazovaniya: Materialy Rossijsko-Amerikanskogo simpoziuma 18-20 noyabrya 2016 g. / pod red. A.P. Karpa i S.A. Polikarpova. Moscow, MPGU Publ., 2017. Pp. 74-92. Available at: http://mpgu.su/wp-content/uploads/2017/05/Problemyi_Sovr_Matem_Obr_Sbornik.pdf (accessed: 15.10.2020). (In Russ.)

21. Approximate basic educational program. Direction of training (specialty) 44.03.05 Pedagogical education. Higher education level. Bachelor's degree. Registered in the state register of VET. Available at: http://xn--n1aabc.xn--p1ai/projects (accessed: 15.10.2020). (In Russ.)

22. Problems of modern mathematical education: materials of the Russian-American Symposium on November 18-20, 2016 / ed. A.P. Karp and S.A. Polikarpov. Moscow, Moscow State Pedagogical University Publ., 2017.148 p. (In Russ.)

23. Professional standard of the Pedagogue 2020, approved by the Government of the Russian Federation. Available at: https://rusjurist.ru/kadry/professionalnye_standarty/profstandart-pedagoga-utverzhdennyj-pravitelstvom-rf/ (accessed: 03.09.2020). (In Russ.)

24. Development of an educational module in a personalized model of education: a methodological guide / ed. D.S. Ermakov. Moscow, 2019. 56 p. (In Russ.)

25. Roslova L.O., Krasnyanskaya K.A., Kvitko E.S. Conceptual foundations for the formation and assessment of mathematical literacy. Otechestvennaya i zarubezhnaya pedagogika, 2019, vol. 1, no. 4(61), pp. 58-79. (In Russ.)

26. Theory and technology of teaching mathematics in secondary school: a textbook for students of mathematical specialties of pedagogical universities / ed. T.A. Ivanova. 2nd edition, revised and enlarged. Nizhny Novgorod, NGPU Publ., 2009. 355 p. (In Russ.)

27. Tereshin N.A. Applied orientation of the school mathematics course: a book for the teacher. Moscow, Prosveshchenie Publ., 1990. 96 p. (In Russ.)

28. Federal State Educational Standard of Higher Education - Bachelor's Degree in the field of training 03.44.05 Pedagogical education (with two training profiles), approved by order of the Ministry of Education and Science of the Russian Federation dated 02.22.2018. No. 125. Available at: https://rulaws.ru/acts/Prikaz-Minobrnauki-Rossii-ot-22.02.2018-N-125/ (accessed: 15.10.2020). (In Russ.)

29. SHapiro I.M. Using tasks with practical content in teaching mathematics. Moscow, Prosveshchenie Publ., 1990. 96 p. (In Russ.)

30. SHaulova Z.V., Nedyurmagomedov G.G. Formation of educational skills of primary school students. Vysshee obrazovanie segodnya, 2018, no. 10, pp. 26-30. (In Russ.)

31. Blum W. Anwendungsorientierter Mathematikunterricht – Trends und Perspektiven. Kadunz G. et al. (eds.) Trends und Perspektiven: Schriftenreihe Didaktik der Mathematik. Vol. 23. Hoelder-Pichler-Tempsky. Wien, 1996. Pp. 15-38.

32. Dunn Peter K., Marshman Margaret F. Teaching mathematical modelling: a framework to support teachers’ choice of resources. Teaching Mathematics and its Applications: An International Journal of the IMA, 2020, vol. 39, no. 2, pp. 127-144, doi: https://doi.org/10.1093/teamat/hrz008.

33. Grover S. The 5th ‘C’ of 21st Century Skills? Try Computational Thinking (Not Coding). 2018. Available at: https://www.edsurge.com/news/2018-02-25-the-5th-c-of-21stcentury-skills-try-computational-thinking-not-coding (accessed: 23.10.2020).

34. Niss M. Mathematical Competencies and the learning of mathematics: The Danish KOM Project. Gagatsis A., Papastavridis S. (eds.) 3rd Mediterranean Conference on Mathematical Education - Athens, Hellas 3-4-5 January 2003. Athen, Hellenic Mathematical Society, 2003. Pp. 116-124.

35. Niss M., Blum W. The Learning and Teaching of Mathematical Modelling (1st ed.). Routledge. London, 2020. DOI: https://doi.org/10.4324/9781315189314.

36. Niss M., Blum W., Galbraith P. Introduction. Blum W., Galbraith P., Henn H.-W., Niss M. (eds.) Modelling and Applications in Mathematics Education (The 14th ICMI Study). New York, Springer, 2007. Pp. 3-32.

37. Niss M., Højgaard T. (eds.) Competencies and mathematical learning: Ideas and inspiration for the development of mathematics teaching and learning in Denmark. Report No. 485. 2011. Available at: https://pure.au.dk/portal/files/41669781/thj11_mn_kom_in_english.pdf (accessed: 27.10.2020).

38. Niss M., Jensen T.H. Kompetencer og matematiklæring: Ideer og inspiration til udvikling af matematikundervisning i Danmark. Uddannelsesstyrelsens temahæfteserie nr. 18-2002. Copenhagen: Undervisningsministeriet, 2002. Available at: http://static.uvm.dk/Publikationer/2002/kom/hel.pdf (accessed: 23.10.2020).

39. Niss M.A., Højgaard T. Mathematical competencies revisited. Educational Studies in Mathematics, 2019, vol. 102(1), pp. 9-28, doi: https://doi.org/10.1007/s10649-019-09903-9.

40. Perevoshchikova E.N., Samoilova G.S., Lapin N.I., Elizarova E.U., Panova I.V. The methodology for developing professional competencies of bachelors in the program «Pedagogical Education». Revista ESPACIOS, 2019, vol. 40(33), p. 26.

41. PISA 2012 Assessment and Analytical Framework. OECD Publishing, 2013. DOI: http://dx.doi.org/10.1787/9789264190511-en.

42. PISA 2015 Assessment and Analytical Framework: Science, Reading, Mathematic, Financial Literacy and Collaborative Problem Solving. OECD Publishing, Paris, 2017. DOI: http://dx.doi.org/10.1787/9789264281820-en.

43. PISA 2018 Assessment and Analytical Framework: Reading, Mathematics and Science. OECD Publishing, 2018. DOI: https://doi.org/10.1787/b25efab8-en.

44. PISA 2018 Results (Volume I). What Students Know and Can Do. Available at: https://www.oecd.org/pisa/publications/pisa-2018-results-volume-i-5f07c754-en.htm (accessed: 23.10.2020).

45. PISA 2021 Mathematics framework (DRAFT). Available at: https://www.oecd.org/pisa/sitedocument/PISA-2021-mathematics-framework.pdf (accessed: 15.10.2020).