Key Problems of Complex Topics in Mathematics as the Basis of Teaching Methods in the Conditions of Self-Education
Natalia A. Zelenina 1 * , Nadezhda V. Telegina 2, Gennadi B. Pronchev 3, Roza I. Yagudina 4, Farid M. Galimov 5, Elena V. Slepneva 6
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1 Vyatka State University, Kirov, RUSSIA
2 Kazan (Volga region) Federal University, Kazan, RUSSIA
3 Lomonosov Moscow State University, Moscow, RUSSIA
4 I.M. Sechenov First Moscow State Medical University (Sechenov University), Moscow, RUSSIA
5 Kazan National Research Technical University named after A. N. Tupolev – KAI, Kazan, RUSSIA
6 Kazan National Research Technological University, Kazan, RUSSIA
* Corresponding Author


Ensuring a high quality of teaching mathematics to students is inextricably linked with teaching how to solve creative mathematical problems. These problems traditionally include tasks of high educational, developmental and diagnostic value. Teaching how to solve such problems allows training graduates with the highest level of the subject knowledge. The problem under study is relevant due to the need to form students’ ability to solve problems with parameters in order to achieve high results in mathematics, intellectual and personal growth. The problem has a new meaning during temporary distance learning, emphasizing the need to create educational and methodological materials that allow students to organize self-education on complex topics in mathematics. The purpose of this research is to develop and describe a teaching methodology for solving problems with parameters based on the allocation of basic (key) problems. The authors have developed a methodology for constructing a system of tasks based on systematizing the theoretical and task material, highlighting students’ basic knowledge and skills, describing the intra- and inter-subject connections of the topic “Equation of a circle in tasks with parameters”. This methodology includes a typology of problems with parameters containing the equation of a circle, a substantiated description of the system of basic (key) problems, the role and content of the propaedeutic stage of teaching. The materials have passed multi-stage approbation and shown their consistency in achieving high results in mathematics. They can help teachers to prepare lessons and extracurricular activities, authors to provide teaching aids for students and teachers, and serve as the basis for a special course for students of pedagogical universities.


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Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2021 - Volume 17 Issue 10, Article No: em2020

Publication date: 24 Aug 2021

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