MATHEMATICAL MODELING IN THE CONTENT OF STUDENTS-ECOLOGISTS’ TRAINING OF MATHEMATICS

Abstract

According to modern studies in the field of didactics, the content of education, such as mathemati-cal, should be represented by two components of knowledge: information and methodological. The purpose of current research is to identify the potential of mathematical modeling, as a general scientific method of cognition in the process of forming both components of the educational content for students of environmental training directions. Materials and methods . The basis of the research, devoted to the study of the place and role of mathematical modeling in the training of future ecologists was the analysis of literature and the comprehension of experience of teaching mathematics for students of environmental training direc-tions in other Russian universities. Most of the presented models in the publications form knowledge, subjectively new only for the students. The paper is considering in detail the process of constructing by students new scientific knowledge on the basis of mathematical modeling, using methods of multivariate statistical analysis. Results. The information component of the mathematical education content, which includes training in mathematical modeling for students-ecologists, is described. The paper gives an illustration of its methodological component formation on the example of the implementation of a group research project, including construction and analysis of graphical and analytical multiple regression models. Mathematical modeling was carried out on the basis of monitoring data of social-economic and medical-ecological indicators of the Kirov region for 2007-2016 together with students-ecologists of Vyatka State University. The procedure of scientifically based choice of factors in the model, their classification by the method of correlation pleiades, which allow effective analyzing both strong and weak correlation links, prevailing in the relationship between a person and the environment are described in detail. Mathematical modeling of the links between the health indicators of the population of the Kirov region and habitat factors was carried out using multiple correlation-regression analysis. The possible nonlinearity of the studied bonds is taken into account. The process of sequential selection of the best model of multiple regressions is presented, taking into account such criteria as determination coefficient, Zarembka test, standard regression error and approximation error. Conclusion. The listed criteria are satisfied by linear, inverse, power and exponential models. Among them high-quality selection of the regression equation is ensured by an exponential model that has statistically significant parameters and allows interpretation from the ecological point of view. Based on the analysis of the constructed mathematical models, some conclusions are formulated, which are of scientific and practical interest for residents of the Kirov region and consistent with the results of other researchers. In particular, it was found that the health status of the population of the region is more significantly influenced by social-economic factors of the environment in comparison with medical and environmental indicators. The inclusion of mathematical modeling in the content of higher education of future ecologists promotes the formation of a scientific worldview, the applied and professional orientation of teach-ing mathematics, and the strengthening of motivation to study mathematical content. Participation of students at group research projects devoted to the application of mathematical modeling in the future professional activity ensures the implementation of interdisciplinary study, mastering the methods and logic of scientific research.