Abstract:

This article substantiates the possibility of solving physical problems which boiled down to differential equations in the study of physics through the organization of a computational experiment. The methodological basis of the study is the work of the authors, who have been devoted to the mathematical competence of physics teachers. The idea of introducing relevant tasks into the physics course, mainly in advanced study, is to replace the differential equation with the simplest difference equation, and then study it using digital technologies. At the same time, it is obviously possible to have a catastrophic accumulation of error when moving away from the initial conditions. Therefore, we propose a technology for preparing a corresponding computational experiment by a teacher. It includes a stage of theoretical research, a stage of model parameter selection, and a stage of problem formulation.

The possibility of setting relevant problems at the level of a school physics course is substantiated. The illustration of the study of some types of the problems that come down to first-order differential equations and linear differential equations of higher orders is given. It is shown that the implementation of activities for organizing the described computational experiments involves special teacher training in the context of postgraduate continuing education. The necessity of updating teachers' skills to solve equations with separable variables (Separable Differential Equations), linear differential equations with constant coefficients and a special right-hand side, to compose recurrence relations, and to master mathematical packages is substantiated. Approaches to the study of relevant topics in physics teacher training courses are proposed to form the readiness to conduct computational experiments for physical problems boiled down to classical differential equations.

The results obtained in this work will allow us to adjust, if necessary, the programs on the theory and methods of teaching physics in pedagogical and classical universities, as well as the programs of in-service training courses for physics teachers in the system of continuous postgraduate pedagogical education. Possible further research on this topic is also related to the introduction of modified in-service teacher training courses in physics that include this topic, as well as consideration of a wider range of models that allow research at the level of school mathematics and physics courses.

Keywords: mathematical competence of physics teacher; postgraduate teacher education, mathematical modeling, differential equations, difference equations, computational experiment.

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