CRITICAL AND MATHEMATICAL THINKING IN THE STRUCTURE OF MATHEMATICAL COMPETENCE OF FUTURE MATHEMATICS TEACHERS
DOI:
https://doi.org/10.31110/fmo2024.v39i5-06Keywords:
mathematical competence, critical thinking, mathematical thinking, mathematical problems, future mathematics teachersAbstract
Formulation of the problem. The impact of globalization on the complexity of social structures underscores the importance of developing critical thinking in the professional training of future mathematics teachers. A key component of their mathematical competence is mathematical thinking, which encompasses not only knowledge and skills but also the ability to analyze and solve complex problems. Despite the lack of a single definition, the contemporary scientific and pedagogical community acknowledges the existence and significance of mathematical thinking. Various approaches to defining mathematical thinking reveal its specific characteristics, particularly its association with abstract objects of study.
Critical thinking, as an integral part of mathematical competence, facilitates purposeful intellectual activity, helping to delineate problems, analyze information, and find optimal solutions. Identifying and substantiating the complementarity of critical and mathematical thinking in solving mathematical problems is crucial for developing effective educational approaches in training future mathematics teachers.
Materials and Methods. The study employs theoretical methods such as systematic analysis of research by domestic and foreign scholars, as well as systematization and generalization of practical experience.
Results. The authors provide a characterization of critical and mathematical thinking within the cognitive activity structure during the formation of mathematical competence in future mathematics teachers. The main differences between these types of thinking are identified: abstraction and formalization in mathematical thinking, and systematic and contextual approaches in critical thinking. The study describes the specifics of various aspects of mathematical and critical thinking in solving mathematical problems and formulates a series of questions that further elucidate the unique characteristics of both types of thinking.
Conclusions. Critical and mathematical thinking mutually support and enhance each other, with their complementarity creating a synergistic effect that ensures more comprehensive and effective problem-solving in mathematics. Considering these factors in the refinement of existing and the development of new educational technologies will promote the growth of mathematical competence among future mathematics teachers..
Downloads
References
APEC –Tsukuba (Organising Committee) (2006). First announcement. International Conference on Innovative Teaching of Mathematics through Lesson Study. CRICED, University of Tsukuba.
Blitzer, R. (2003). Thinking mathematically. New Jersey: Prentice Hall.
Halil, C. Ç., & Furkan, Ö. (2020). Mathematical Thinking as a Predictor of Critical Thinking Dispositions of Pre-service Mathematics Teachers. International Journal of Progressive Education, 16 (4), 81 – 98. https://doi.org/10.29329/ijpe.2020.268.6.
Henderson, P. B., Hichtner, L., Fritz, S. J., Marion, B., Scharff, C., Hamer, J., & Riedesel, C. (2002). Materials development in support of mathematical thinking. ACM SIGCSE Bulletin, 35(2), 185–190. https://doi.org/10.1145/782941.783001.
Mason, J., Burton, L., & Stacey, K. (2010). Thinking mathematically (Second edition). Harlow England: Pearson Education Limited.
Stacey, K. (2005). The place of problem solving in contemporary mathematics curriculum documents. Journal of Mathematical Behavior, 24, 341 – 350.
Marchenko, V.S. (2017). Pidhotovka maibutnikh uchyteliv fizyko-matematychnykh spetsialnostei do rozvytku matematychnoho myslennia uchniv osnovnoi shkoly [Preparation of future teachers of physical and mathematical specialties for the development of mathematical thinking of primary school students]. dys. ... kand. ped. nauk : 13.00.04. Odesa.
Sliepkan, Z. I. (2000). Metodyka navchannia matematyky [Methods of teaching mathematics]: Pidruch. dlia stud. mat. spetsialnostei ped. navch. zakladiv. K.: Zodiak-EKO.
Chkana, Ya., & Martynenko, O. (2023). Krytychne myslennia yak vazhlyva skladova matematychnoi kompetentnosti maibutnikh uchyteliv matematyky[Critical thinking as an important component of mathematical competence of future teachers of mathematics]. Osvita. Innovatyka. Praktyka – Education. Innovation. Practice, 11(5), 102-107. https://doi.org/10.31110/2616-650X-vol11i5-015.
Downloads
Published
Issue
Section
Categories
How to Cite
License
Copyright (c) 2024 Ярослав Чкана, Олена Мартиненко
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.
