Abstract
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.
Highlights
The Relevance of the ProblemThe modern stage of mathematics education requires modern students to be active in acquiring knowledge and be able to use it in life, further education or professional activity (The concept of the development of mathematical education in the Russian Federation, 2013)
To compile a typology of tasks with parameters, including the equation of a circle, we have analyzed a great amount of problems that were used for studying for several years
During the experimental part of the research in 2018– 2019, we carried out the approbation of didactic and methodological materials for the propaedeutic stage of teaching students to solve tasks with parameters, including the equation of a circle
Summary
The Relevance of the ProblemThe modern stage of mathematics education requires modern students to be active in acquiring knowledge and be able to use it in life, further education or professional activity (The concept of the development of mathematical education in the Russian Federation, 2013). The materials have methodological instructions and comments and can be used for organizing students’ self-education
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