Methodological aspects of teaching schoolchildren to solve mathematical problems of increased complexity
DOI: 10.23951/1609-624X-2023-2-16-25
Various solutions to mathematical problems can cause certain difficulties for schoolchildren. The use of a scheme allowing to organize and systematize the search for a solution to a problem makes it possible to ensure the interaction of participants in the educational process, aimed at creative initiative, mathematical intuition, activity, and independence in reasoning. The result is the ability of the student to solve various problems individually. The goal is to substantiate a step-by-step scheme for solving the problem for its application in the process of teaching mathematics to schoolchildren. The system and activity approach compose the research base. The work used such methods as generalization, systematization, classification, analysis of domestic and foreign studies. Russian and foreign researchers in their works divide the activity of schoolchildren in solving problems into separate stages, which contributes to the formation of the main methods of action aimed at obtaining educational results. The proposed schemes differ in content, as well as in the number of allocated stages.. Generalization and systematization of the studied experience made it possible to modify them taking into account the needs of the participants in the educational process. During training, the task of increased complexity is solved not only by the student, but also by the teacher. The above scheme summarizes their activities, makes it possible not only to analyze the problem, but also to characterize the methodological and methodological aspects of the solution. Accordingly, it includes the following stages: analytical, schematic, methodological, descriptive, verification, research, methodical. At the analytical and schematic stages, the actual search for a solution to the problem is carried out, its main content is represented using mathematical models and various schemes. At the methodological stage, the task is characterized from the point of view of the methods used and the mental operations used. The descriptive and verification stages are directed by recording the problem solution and his validate that includes logical, computing and other mistakes. During the research phase, an analysis of the conditions of the problem is carried out, the existence of its solution is determined when they change. The methodological stage enables the teacher to generalize and systematize issues related to learning to solve a problem. The scheme considered in this paper systematizes and structures the activities of both the teacher and students in solving problems for the gradual formation of the ability to search for it.
Keywords: teaching mathematics to schoolchildren, difficult problem, mathematic problem solution stages, student development
References:
1. Kontseptsiya razvitiya matematicheskogo obrazovaniya v Rossiyskoy Federatsii [Russian Federation mathematical education development conception] (in Russian). URL: https://docs.cntd.ru/document/499067348 (accessed 15 September 2022).
2. Grinshpon Ya. S., Podstrigich A. G. Osobennosti obucheniya shkol’nikov resheniyu zadach povyshennoy slozhnosti po matematike [Special features of teaching high-school students skills for solving mathematics problems of higher complexity]. Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta – Tomsk State Pedagogical University Bulletin, 2015, vol. 8 (161), pp. 48–52 (in Russian).
3. Nakhman A. D. Zadachnyy podkhod kak tekhnologicheskya osnova protsessa obucheniya matematike [Task approach as a technological basis of the process of teaching of mathematics]. Mezhdunarodnyy zhurnal eksperimental’nogo obrazovaniya, 2018, no. 2, pp. 34–39 (in Russian).
4. Dalinger V. A., Pustovit E. A. Rol’ i mesto zadach v formirovanii uchebno-issledovatel’skoy kompetentnosti uchashchikhsya shkoly [Problem role and place for schoolchildren educational and research competence forming]. Vestnik Krasnoyarskogo gosudarstvennogo pedagogicheskogo universiteta imeni V. P. Astaf’yeva – The bulletin of KSPU named after V. P. Astafyev, 2012, no. 2, pp. 51–55 (in Russian).
5. Klekovkin G. A., Maksutin A. A. Zadachnyy podkhod v obuchenii matematike [Problem approach for mathematics learning]. Moscow, Samara, SF SEI HPE MSPU Publ., 2009. 184 p. (in Russian).
6. Jäder J., Sidenvall J., Sumpter L. Students’ Mathematical Reasoning and Beliefs in Non-routine Task Solving. Int. J. of Sci. and Math. Educ., 2017, no. 15, pp. 759–776. https://doi.org/10.1007/s10763-016-9712-3
7. Polya G. Kak reshat’ zadachu. Perevod s angliyskogo V. G. Zvonarevoy i D. N. Bella [How to solve it. Translated from English by V. G. Zvonareva i D. N Bell]. Moscow, Gosudarstvennoye uchebno-pedagogicheskoye izdatel’stvo Ministerstva prosveshcheniya RSFSR Publ., 1961. 208 p. (in Russian).
8. Acuña A. M. Polya and GeoGebra: A dynamic approach to problem solving. European Journal of Science and Mathematics Education, 2014, no. 2 (2A), pp. 231–235. https://doi.org/10.30935/scimath/9649
9. Kostyuchenko R. Yu. Metodika obucheniya uchashchikhsya resheniyu matematicheskikh zadach: soderzhaniye etapov resheniya [Methodology of teaching students of solving mathematical problems: solution steps and their content]. Vestnik Sibirskogo instituta biznesa i informatsionnykh tekhnologiy – Herald of Siberian Institute of Business and Information Technologies, 2018, no. 4 (28), pp. 117–123 (in Russian).
10. Vasil’yeva G. N. Metodicheskiye aspekty deyatel’nostnogo podkhoda pri obuchenii matematike v sredney shkole [Methodical aspects of activity approach by mathematics training at school]. Perm, PSPU Publ., 2009. 136 p. (in Russian).
11. Jiang Y., GongT., Saldivia L. E. et al. Using process data to understand problem-solving strategies and processes for drag-anddrop items in a large-scale mathematics assessment. Large-scale Assess Educ., 2021, vol. 9, no. 2. https://doi.org/10.1186/s40536-021-00095-4
12. Fridman L. M., Turetskiy E. N. Kak nauchit’sya reshat’ zadachi [How problem solving study]. Moscow, Prosveshcheniye Publ., 1989. 196 p. (in Russian).
13. Popov N. I., Yakovleva E. V. Ispol’zovaniye metoda skhematizatsii pri obuchenii studentov i shkol’nikov matematike [Use of the schematization method in teaching students and pupils in math]. Vestnik Syktyvkarskogo universiteta. Seria 1. Matematika. Mekhanika. Informatika – Siktivkar University Bulletin. Series 1. Mathematics. Mechanics. Computer science, 2020, no. 4 (37), pp. 74–87 (in Russian). DOI: 10.34130/1992-2752_2020_4_74
14. Jacinto H., Carreira S. Knowledge for teaching mathematical problem-solving with technology: An exploratory study of a mathematics teacher’s proficiency. European Journal of Science and Mathematics Education, 2023, no. 11 (1), pp. 105–122. https://doi.org/10.30935/scimath/12464
15. Polya G. Matematicheskoye otkrytiye. Resheniye zadach: osnovnyye ponyatiya, izucheniye i prepodavaniye. Perevod s angliyskogo V. S. Bermana, pod red. I. M. Yagloma [Mathematical discovery. On understanding, learning and teaching problem solving. Translate form English by V. S. Berman; edited by I. M. Yaglom]. Moscow, Nauka Publ., 1970. 452 p. (in Russian).
16. Testov V. A. O nekotorykh vidakh metapredmetnykh resul’tatov obucheniya matematike [Some types of metasubject results when teaching mathematics]. Obrazovaniye i nauka – Education and Science, 2016, no. 1 (130), pp. 4–20. DOI: 10.17853/1994-5639-2016-1-4-20 (in Russian).
17. Bernikova I. K. Skhemy kak sredstva organizatsii myshleniya v protsesse obucheniya matematike [Schemes as thinking organization tools for mathematics learning]. Vestnik Omskogo universiteta – Omsk University Bulletin, 2015, no. 1, pp. 23–27 (in Russian).
18. Kol’yagin Yu. M. Zadachi v obuchenii matematike. Chast’ 2. Obucheniye matematike cherez zadachi i obucheniye resheniyu zadach [Problem for mathematics training. Part 2. Mathematics training by way of problems and problems solution training]. Moscow, Prosveshcheniye Publ., 1977. 144 p. (in Russian).
19. Ivanova T. A., Ul’yanova I. V. Metodika raboty s zadachey na uroke matematiki v kontekste FGOS OOO novogo pokoleniya [Methods of working with problems in the math lessons in the context of the new generation FSES]. Podgotovka budushchego uchitelya k proyektirovaniyu sovremennogo uroka. Pod red. N. V. Kuznetsovoy, E. V. Beloglazovoy [Future mathematics teachers preparing for modern lesson designing. Edited by N. V. Kuznecova, E. V. Beloglazova]. Saransk, 2016. Pp. 207–225 (in Russian).
20. Aksyonov A. A., Nikolaev V. A. Metodicheskiye priyomy ob’’yasneniya v protsesse obucheniya logicheskomu poisku resheniya shkol’nykh matematicheskikh zadach [Methodological methods of explanation in the process of learning logical search for solving school mathematics problem]. Uchyonyye zapiski Orlovskogo gosudarstvennogo universiteta – Scientifics notes of Orel State University, 2021, no. 2 (91), pp. 135–139 (in Russian).
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Issue: 2, 2023
Series of issue: Issue 2
Rubric: GENERAL AND INCLUSIVE EDUCATION
Pages: 16 — 25
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