THE METHOD OF MATHEMATICAL AND DIDACTIC MODELING IN THE PREPARATION OF FUTURE TEACHERS ON THE EXAMPLE OF THE LAW OF NEWTON'S UNIVERSAL GRAVITATION

Mathematical and didactic modelling (MDM) is an innovative technique that is used in the training of future teachers of mathematics and computer science at the Kazan Federal University. The MDM acronym combines the approaches of mathematical and computer modelling of real processes, the principles of didactic engineering and problem-based approach. Also, an attempt is made to link MDM with the concept of A.N. Meltzoff (Science. 2009. v. 325. p. 284 -288) (and other authors), named as "New science of learning". Students are encouraged to develop MDM projects that have two objectives. On the one hand, they should develop a mathematical and information model of the proposed process using computer programs ("GeoGebra", "maple"), on the other hand, a methodology for teaching the project of this model to their future students at the school. At the same time, it is important that MDM is an integral, interconnected educational complex that takes into account interdisciplinary communication and psychological motivational factors. For example, the themes of students' project work on creating a model of two-body motion under the influence of gravity force include the development of two types of models: 1) the body motion thrown at an angle to the horizon; 2) the orbits of objects in the solar system. Then, students together with schoolchildren, using "GeoGebra", develop various modifications of the model. Students (future teachers) develop the didactic component of MDM - modelling interaction with their school students. The end result - a computer model is obtained individually, depending on the students' imagination. For example, for the first type of model - a model of a cannon on the background of an ancient castle, shooting at a target. These are game models. In the second case, astronomical objects are studied, where the strategy of "importance" is present. The experience shows that the use of different interpretations (models) based on a single physical and mathematical law strengthens the mastering of this law. The method of learning based on the use of MDM creates motivation for independent research activities of students and develops mathematical, computer and methodological competencies.