Key Problems of Complex Topics in Mathematics as the Basis of Teaching Methods in the Conditions of Self-Education

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

Solving math problems through the principles of scientific creativity

© 2020 by the authors. Ongoing changes in mental and personal characteristics of the modern child initiate the updating of means and forms of education. And they, in their turn, update methodological techniques and approaches to the use of methods during the math class. The source of updating methodological techniques may be the principles used when solving scientific problems. Scientific creativity traditionally systematizes knowledge and skills for their use to a wide range of sciences. Therefore, the principles of scientific creativity have a lot in common with different subjects, showing the student the unity of approaches in working with knowledge. In this regard, the article is aimed at substantiating the principles of scientific creativity as effective methodological techniques for finding solutions to math problems and, on their basis, developing recommendations for conducting classes that prepare for final certification at school in mathematics. The leading research methods in this case are: observation of the methodological work of teachers of mathematics, conversations with teachers, analysis of guidance papers and questionnaires of teachers, statistical processing of research results. In 2018-2019 the experiment in which 19 mathematics teachers took part was conducted. Based on its results the authors of the article succeeded in: highlighting the principles of finding solutions to math problems based on the approaches used in scientific creativity; developing and implementing on the basis of these principles recommendations for conducting classes that prepare for final certification at school in mathematics. The effectiveness of using the principles of finding solutions to math problems was assessed. It allowed the authors to conclude that students have an increase in the speed of finding solutions to math problems by an average of 11%. Practical use of the proposed principles makes it possible to organize training for schoolchildren in solving math problems in traditional forms of teaching, but taking into account the particularities of the development of the modern schoolchild. Methodological recommendations developed by the authors can be used to teach students how to find solutions to math problems during classes that prepare for final certification at school in mathematics