SETTING AND SOLVING RESEARCH PROBLEMS IN TEACHING MATHEMATICAL DISCIPLINES
ПОСТАНОВКА ТА РОЗВ’ЯЗАННЯ ДОСЛІДНИЦЬКИХ ЗАДАЧ ПРИ ВИКЛАДАННІ МАТЕМАТИЧНИХ ДИСЦИПЛІН
DOI:
https://doi.org/10.31110/fmo2025.v40i3-06Keywords:
research activity, learning process, continued fraction, Farey sequence, Stern-Brocot tree, irreducible over the field polynomial, reciprocal polynomial, axiomatic theoryAbstract
Formulation of the problem. Research tasks are a necessary component of the educational process, and their use contributes to the development of critical and creative thinking, and the formation of the ability to act in a non-standard situation. Along with the need for thorough pedagogical research on the theoretical foundations of the implementation of research-based learning technology, a number of practical issues arise related to the preparation of teachers for the organization of research activities in the educational process. The purpose of this article is to review the available research on the research approach to teaching, to describe my own experience of setting research tasks in teaching mathematics and organizing their solution by students, to analyze the possibilities of finding sources of research tasks and creating them independently.
Materials and methods. Methods used: analysis of the application of individual components of the theory of research problem solving, analysis of existing studies on the impact of research results on increasing student motivation. The study used textbooks on higher mathematics, algebra and number theory, and the basics of mathematics for higher education institutions, as well as scientific publications and their discussions..
Results. The article demonstrates the possibilities of organizing students' research activities in teaching mathematical courses, using the theory of solving research problems, analyzes some possibilities of creating research problems, and considers methods of solving the proposed research problems (the method of focal object, accumulation of educational material, brainstorming).
Conclusions. Mathematical courses are a favorable basis for ensuring research activities of university students. The article emphasizes the inclusion of research tasks into the learning process on a regular basis. University professors should improve their own experience in organizing students' research activities, as well as the experience of professors from foreign universities who have been working on the implementation of research-based learning for some time. It is clear that the transition to this technology will be long and will require gradual changes in the curricula of the specialties. Research will also be needed on methods of increasing student motivation to ensure the effectiveness of research activities.
Downloads
References
Ammar, M., Al-Thani, Noora J., & Ahmad, Z. (2024). Role of pedagogical approaches in fostering innovation among K-12 students in STEM education. Social Sciences & Humanities Open, 9, 1-13. https://pdf.sciencedirectassets.com/320567/1-s2.0-S2590291123X00035/1-s2.0-S2590291124000366/main.pdf
Artemenko, A. O., & Styeganceva, P. G. (2021). Formuvannya u studentiv navichok doslidnickoyi diyalnosti na konkretnomu prikladi [The formation of the students’ research activity skills with the specific example]. Visnik Zaporizkogo nacionalnogo universitetu. Pedagogichni nauki – Proceedings of Zaporizhzhia National University. Pedagogical sciences, 2, 35-38. https://doi.org/10.26661/2522-4360-2020-2-05 (in Ukrainian).
Babak, A., & Vorozhbit-Gorbatyuk, V. (2021). Pedagogichnij universitet yak prostir rozvitku kreativnogo mislennya zdobuvacha vishoyi osviti [The pedagogical university as the space for the development of the creative thinking of the students]. Graal nauki – Grail of science, 11, 489-491. https://doi.org/10.36074/grail-of-science.24.12.2021.088 (in Ukrainian).
Bulvinska, O. (2019). Suchasni metodi navchannya i vikladannya na osnovi doslidzhennya: zarubizhnij dosvid [Modern methods of research-based teaching: foreign experience]. Osvitologichnij diskurs – Educological discourse, 1-2 (24-25), 83–103. http://doi:10.28925/2312-5829.2019.1-2.83103 (in Ukrainian).
Dobronravova, I. S. (1990). Sinergetika: stanovlenie nelinejnogo myshleniya [Sinergetics: formation of non-linear thinking]. Lybid. http://www.philsci.univ.kiev.ua/biblio/Dobr-sinerg/index.html (in Russian).
Freeman, S., Eddy, SL., McDonough, M., Smith, MK., Okoroafor, N., Jordt, H., & Wenderoth, MP. (2014). Active learning increases student performance in science, engineering, and mathematics. Proceedings of the national academy of sciences of the United States of America, 111 (23), 8410-8415. https://doi.org/10.1073/pnas.1319030111
Gilbert, D. (1948). Osnovaniya geometrii [Basics of geometry]. OGIZ. https://web.archive.org/web/20110728164722/http://ilib.mccme.ru/djvu/geometry/osn_geom.htm (in Russian).
Grib’yuk, O. O., & Yunchik, V. L. (2016). Vikoristannya teoriyi rozv’yazuvannya doslidnickih zadach u konteksti proektno-doslidnickoyi diyalnosti v procesi navchannya matematiki [Using theory of solving problems in context of research in learning mathematics]. Suchasni informacijni tehnologiyi ta innovacijni metodiki navchannya u pidgotovci fahivciv: metodologiya, teoriya, dosvid, problem – Modern information technologies and innovation methodologies of education in professional training methodology theory experience problems, 44, 153-163. https://vspu.net/sit/index.php/sit/article/view/3100/2530 (in Ukrainian).
Harkki, T., Vartiainen, H., Scitamaz-Hakkarainen, P., & Hakkarainen, K. (2021). Co-teaching in non-linear projects : A contextulised mofel of co-teaching to support educational change. Teaching and Teacher Education, 97, 1-14. https://www.sciencedirect.com/science/article/pii/S0742051X20313792
Hrybiuk, O. (2022). Experience in Implementing Computer-Oriented Methodological Systems of Natural Science and Mathematics Research Learning in Ukrainian Educational Institutions. In J. Machado, F. Soares, J. Trojanowska, & S. Yildirim (Eds.) Innovations in Mechatronics Engineering (pp. 55-68). Lecture Notes in Mechanical Engineering. Springer, Cham. https://www.researchgate.net/publication/352462787_Experience_in_Implementing_Computer-Oriented_Methodological_Systems_of_Natural_Science_and_Mathematics_Research_Learning_in_Ukrainian_Educational_Institutions
Kozak, L. V. (2016). Rozvitok universitetskoyi osviti: navchannya na osnovi doslidzhennya [Development of university education: studying based on research]. Osvitologichnij diskurs - Educological discourse, 2(14), 38–52. https://doi.org/10.28925/2312-5829.2016.2.3852 (in Ukrainian).
Kremen, V. G. (2005). K obshestvu znanij – cherez sovershenstvovanie sistemy obrazovaniya [To the knowledge society via improvement of the education system]. U L. G. Melnik (Red.), Socialno-ekonomicheskie problemy informacionnogo obshestva – Social and economic problems of information society. (s. 34 – 48). ITD Universitetskaya kniga. http://essuir.sumdu.edu.ua/handle/123456789/44614 (in Russian).
Lisitsyina, E. S., Faure, E. V., Shvyidkiy, V. V., & Scherba, A. I. (2006). Nekotoryie svoystva mnogochlenov i ih ispolzovanie v zadachah svyazi [Some properties of polynomials and their use in connection problems]. Cherkasskiy gosudarstvennyiy tehnologicheskiy universitet. Vestnik ChGTU – Cherkasy State Technological University. Bulletin ChGTU, (4), 134-140. (in Russian).
Markov, L. N., & Razmyislovich, G. P. (1999). Vyisshaya matematika (Chast 1) [Higher mathematics] (Part 1). Amalfeya. (in Russian).
Nor Farida, H., Khairiyah, M. Y., Mohammad Zamry, J., & Helmi, S. A. (2012). Motivation in Problem-based Learning Implementation. Procedia - Social and Behavioral Sciences, 56, 233 – 242. https://pdf.sciencedirectassets.com/277811/1-s2.0-S1877042812X00272/1-s2.0-S1877042812041122/main.pdf
Proshkin, V., Astafieva, M., & Radchenko, S. (2018). Formation of critical thinking of future mathematics teachers by means of geometry. Educological discourse, 1-2 (20-21), 100–115. https://doi.org/10.28925/2312-5829.2018.1-2.1416 (in Ukrainian).
Proshkin, V.V., & Proshkina, I.O. (2016). Navchannya, zasnovane na doslidzhennyah: vid ideyi do realizaciyi [Study based on the investigation]. Visnik luganskogo nacionalnogo universitetu imeni tarasa shevchenka. Pedagogichni nauki – Bulletin of Lugansk National University named after Taras Shevchenko. Pedagogical sciences, 1 (298), 94-100. http://nbuv.gov.ua/UJRN/vlup_2016_1(1)__13 (in Ukrainian).
Rvachev, V.L., & Sheiko, T.I. (1995). R-function is a boundary value problem in mechanics. Appl. Mech. Rev., 48(4), 151-188. https://doi.org/10.1115/1.3005099
Stegancev, E.V., & Grechneva, M.A. (2019). Zavisimost mezhdu kriviznoj i krucheniem sfericheskoj i konicheskoj krivyh [The relation between the curvature and the torsion of the spherical curve and the conic curve]. Vestnik Hersonskogo nacionalnogo tehnicheskogo universiteta – Bulletin of Herson national technical university, 2(69), 294 – 298. https://kntu.net.ua/ukr/IInformacijni-resursi/Elektronna-biblioteka-HNTU/Periodichni-vidannya-HNTU/Visnik-Hersons-kogo-nacional-nogo-tehnichnogo-universitetu/Arhiv-nomeriv/2019/Visnik-2-69 (in Russian).
Van-der-Varden, B. L. (1976). Algebra [Algebra]. Mir. https://violity.com/en/116676062-van-der-varden-b-l-algebra-1976 (in Russian).
Velichko, I.G., & Stegantseva, P.G. (2010). Example of a function of two variables that cannot be an RR-function. Ukr. Mat. Zh., 62(2), 270–274. https://umj.imath.kiev.ua/index.php/umj/article/view/2863
Vorozhbit-Gorbatyuk, V. V., Zozulya, K. V., & Sobchenko, T. M. (2021). Naukovij gurtok v realizaciyi ideyi navchannya cherez doslidzhennya zdobuvachiv pershogo bakalavrskogo rivnya vishoyi osviti (z dosvidu HNPU imeni G. S. Skovorodi) [Science group for the realization of the idea of the study as the research of the students of the first bachelor level (from the HNPU named after G.S. Scovoroda)]. Teoriya ta metodika navchannya ta vihovannya – The theory and methodic of the study and education, 50, 19-29. https://doi.org/10.34142/23128046.2021.50.02 (in Ukrainian).
Downloads
Published
Issue
Section
Categories
How to Cite
License
Copyright (c) 2025 Eugene Stegantsev, Аlena Chernienko
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
- Authors grant the journal a right of the first publication of the work under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License (CC BY-NC-SA 4.0)that allows others freely to use (read, copy and print) submissions, search content and link to published articles, disseminate their full text and use them for any legitimate non-commercial purposes (i.e. educational or scientific) with the mandatory reference to the article’s authors and initial publication in this journal.
- Original published articles cannot be used by users (exept authors) for commercial purposes or distributed by third-party intermediary organizations for a fee.
