SUMMARY
The author examines methodological principles of simulation relating to the theory of knowledge. Special attention is paid to the concept of analogy as well as to its importance for simulation, synthesis and abstraction, isomorphism and homomorphism. The article considers some peculiarities of modeling and highlights the versatility of simulation as a research method. The article also outlines the need for experimental research as well as for the research method for teaching mathematics to school students. Research objectives are considered as a kind of learning tasks for problem situations solving, requiring the experimentation with dynamic models of mathematical objects. The author examines the use of special mathematical software and mathematical methods for teaching mathematics as well as for the experiments in mathematics, including computer modeling application. The classification of educational software for the development of students’ creative potential is proposed. The paper considers method system of research training in mathematics as a computer-oriented training system. The author focuses on the possibilities of using systematic research techniques and teaching methods, variative didactic constructs for teaching mathematics. The level model of research training and the classification of research objectives are studied. We offer the possibility of adjustment to the user of the computer-oriented system of education. The relationship between the model, on the one hand, and material and non-material types of the prototype, on the other hand, is analysed. The features of new information and communication technologies application are discussed. The author clarifies the definition of the model. Attention is also paid to the model stages which facilitate the content of the simulation algorithm reveal. The article considers the possibility of using computer mathematics systems in computer studies while teaching mathematics in the classroom and in extracurricular time. In the study we formulate the objectives on the generalization of properties, types, tasks, and functions as a universal method of knowledge (parametricity, consistency, information, imagery, abstraction, simplification). The paper clarifies the definition of a model and specifies the properties of the model as an epistemological tool.