MATHEMATICAL MODELING AS A LENS OF THE REAL WORLD
DOI:
https://doi.org/10.31110/2413-1571-2023-038-4-008Keywords:
modelling, applied problem, practical problem, model problem, the cycle of mathematical modelling, the competencies of the mathematical modellingAbstract
Formulation of the problem.Mathematical modeling today is not just a trend, but an urgent need for education. However, the introduction of this method into the school course of Mathematics as a method of scientific research and the basis for the development, for acquiring mathematical knowledge and skills is quite limited.
Materials and Methods. The analysis of the courseware on the research problem; the systematization and generalization of different approaches to determine the content of mathematical modelling; the analysis and systematization of domestic and foreign experience in using the method of mathematical modelling.
Results. A part of our research on the content of mathematical modelling in education abroad (based on publications in English-language sources) and in Ukraine in this paper is presented. Various definition statements of mathematical modelling are considered, the terms that scientists use when studying this concept are outlined. The attention is focused on the importance of the analysis of mathematical modelling as an activity and the structure as well. The cycle schemes of mathematical modelling, which are most often used in the scientific and methodological papers, are introduced. Based on the analysis of the structures of the competence in mathematical modelling that are described in the studies of various authors groups of subcompetences have been identified. They are important for the formation of skills to solve the corresponding model problems.
Conclusions. Disclosing the content of the mathematical modelling concept will help the teacher focus on the specific individual actions that students should master in order to successfully complete the entire cycle of mathematical modelling. The condition of strong interest of teachers of Mathematics and the availability of relevant knowledge and skills in the actual use of mathematical modelling in the school course of Mathematics and in the corresponding University courses are important.
Downloads
References
Bakhrushyn, V. Ye. (2004). Matematychne modeliuvannia [Mathematical modeling]. ZIDMU (in Ukrainian)
Prus, A.V., & Shvets, V.O. (2007). Teoriia ta praktyka prykladnoi spriamovanosti shkilnoho kursu stereometrii [Theory and practice of the applied orientation of the school course of stereometry]. ZhDU im.I.Franka. (in Ukrainian)
Semenova, I. Yu. (2014). Matematychni modeli MSS [Mathematical models of MSS]. Kyiv (in Ukrainian)
Stanzhytskyi, O. M., Taran, Ye. Yu., & Hordynskyi, L. D. (2006). Osnovy matematychnoho modeliuvannia [Fundamentals of mathematical modeling]. Kyivskyi universytet (in Ukrainian)
Shvets, V. O. (2009). Matematychne modeliuvannia yak zmistova liniia shkilnoho kursu matematyky [Mathematical modeling as a content line of the school mathematics course]. Dydaktyka matematyky: problemy i doslidzhennia – Didactics of mathematics: problems and research, (32), 16-23.
Blum, W. (1996). Anwendungsbezüge im Mathematik-unterricht – Trends und Perspektiven. Trends und Perspektiven. Schriftenreihe Didaktik der Mathematik, (23), 15 – 38 (in German).
Blum, W., & Borromeo Ferri, R. (2009). Mathematical Modeling: Can It Be Taught And Learnt? Journal of Mathematical Modeling and Application, 1(1), 45-58.
Blum, W., & Leiß, D. (2006). How do students and teachers deal with modeling problems? In C. Haines, P. Galbraith, W. Blum and S.Khan (Eds.), Mathematical Modeling (ICTMA12): Education, Engineering and Economics (pp 222 – 231). Chichester: Horwood Publishing.
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do? In S. J. Cho (Ed.), The Proceedings of the 12th International Congress on Mathematical Education (pp. 73–96). Cham: Springer International Publishing.
Borromeo Ferri, R. (2010). On the influence of mathematical thinking styles on learners’ modelling behavior. Journal für Mathematik-Didaktik, 31(1), 86–95.
Burkhardt, H., & Muller. E. R. (2006). Applications and Modelling for Mathematics. In W. Blum, P. Galbraith, H.-W. Henn, & M. Niss (Eds.), Modelling and Applications in Mathematics Education. New ICMI Studies Series no. 10, New York: Springer. To appear.
Greefrath, G., & Vorhölter, K. (2016). Teaching and Learning Mathematical Modelling, ICME-13 Topical Surveys, DOI 10.1007/978-3-319-45004-9_1.
Hankeln, Corinna (2020). Mathematical modeling in Germany and France: a comparison of students’ modeling processes. Journal of Educational Studies in Mathematics, (103), 209–229.
Kutluca, T., & Kaya, D. (2023). Mathematical modelling: A retrospective overview. Journal of Computer and Education Research, 11 (21), 240-274. https://doi.org/10.18009/jcer.1242785.
Kaiser, G. (1995). Realitätsbezüge im Mathematikunterricht – Ein Überblick über die aktuelle und historische Diskussion. In G. Graumann, et al. (Eds.): Materialen für einen realitätsbezogenen Mathematikunterricht (pp 64 – 84). Bad Salzdetfurth: Franzbecker.
Maaß, K. (2006). What are modelling competencies? ZDM, 38(2), 113–142.
Niss, M., Blum, W., & Galbraith, P. (2007). Introduction. In W. Blum, P.L. Galbraith, H.-W. Henn & M. Niss (Eds.), Modelling and applications in mathematics education. The 14th ICMI Study (pp. 3–32). New York: Springer.
Pollak, H. O. (1969). How can we teach applications of mathematics? Educational Studies in Mathematics 2(2/3), 393-404.
Downloads
Published
How to Cite
License
Copyright (c) 2023 Алла Прус
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.
