CONTINUITY OF TEACHING METHODS FOR SOLVING MATHEMATICAL PROBLEMS IN SCHOOLS AND UNIVERSITY: THE CONTEXT OF THE INTEGRATIVE APPROACH

Abstract

Formulation of the problem. The article has devoted the problem of the continuity of teaching methods for solving mathematical problems (on the example of equations with a parameter) using an integrative approach. The integrative approach in our research combines the integration of learning tools and the integration of learning methods. The purpose of the research is to determine the features of ensuring the continuity of teaching methods for solving mathematical problems at school and university, which takes place with an integrative approach.

Materials and methods. In the study, the analysis of mathematics curricula and educational programs of specialties with a significant mathematical component was carried out, and the search and analysis of relevant problems were followed by the construction of new research problems based on them. A generalization of my own and advanced pedagogical experience regarding the use of ICT in the educational process of schools and universities was also carried out. During work with pupils and students, the educational process was observed.

Results. In the example of a simple logarithmic equation with a parameter, the authors illustrated a complex integrative approach to the implementation of the continuity of teaching methods at schools and universities. This approach was implemented from the point of view of the integration of teaching methods - the method of addition, the technology of enlargement of didactic units, and the method of contrast. And also from the point of view of teaching aids - the use of graphic illustrations, information and communication technologies, schemes, and algorithms of analytical statements. In addition, the integrative approach was also implemented from the content point of view, since integrated images were used during the training - the image of the problem, the image of the problem series, and the image of the solution method.

Conclusions. As a result of the research, the authors came to the following conclusions: a) the idea of the technology of enlargement of didactic units in the form of solving problems in different ways, namely the combination in a specific case of analytical and graphical methods of solving equations with a parameter, contributes to better continuity of mathematics education. This approach ensures the actualization, generalization, and systematization of the abilities of pupils and students to implement knowledge and skills from the two most important content lines of the school mathematics course (the line of equations, inequalities and their systems, and the functional line);  b) the  combination  of  the  process of solving tasks with the process of compiling new consolidated exercises (for example, solving or compiling equations with a parameter using analytical statements or computer mathematics packages) gives practically unlimited opportunities for applying the research method in teaching mathematics at school and university. It also allows talking about the implementation of the didactic principle of continuity, aimed at providing opportunities for students to continue their study of mathematical disciplines at higher levels of education; c) the implementation of continuity of teaching mathematical disciplines involves the integration of related disciplines, the establishment of inter-subject connections. It is ensured by the internal integration of methods, means, components, and content lines of mathematics as an educational subject in schools and universities. Such integration is realized through the construction of integrated images. It is possible only with an in-depth study of specific mathematical problems and under the condition of using a heuristic approach to learning.