Design Methodology for Electronic Training Problems Aimed at Development of Mathematical Problems Solving Competence

Abstract

The aim of the study. The fourth industrial revolution demands highly qualified personnel as important factor of economic growth, which imposes serious requirements on the formation of key and subject competencies among graduates of higher educational institutions. A particularly important role is assigned to the mathematical competence which is required to solve complex and science-intensive problems. Given the growing share of e-learning and distance learning at the university, it is necessary to intensively develop the methodology for mathematical competence formation in the electronic environment, and create effective teaching tools on its basis. The current level of digitalization of education already allows organizing independent work of students in the electronic environment at a sufficiently high level. In the literature we can find various methods and tools, aimed at the formation of the cognitive component of competencies. However, the issue of skills’ development in the electronic environment is still underrepresented. The purpose of this study is to develop a methodology for creating electronic training problems, which aims at forming a practical component of mathematical competence – the competency of solving mathematical problems.Materials and methods. In the study we performed a comparative analysis of scientific and methodological literature, regulatory and methodological documents, as well as professional and federal educational standards of higher education. The development of a model of electronic training problems was carried out using methods of structural modeling. The developed methodology was implemented in the educational process, and the confirmation of its effectiveness was obtained by statistical analysis of the results of the pedagogical experiment.Results. We proposed a methodology for electronic training problems development aimed at formation of mathematical problems solving competency. The methodology is based on existing approaches to problem solving formalization. In the presented structural model of an electronic training problem, the aspects of problem solving discovered earlier by other authors, are supplemented by the contextual aspect. This aspect is intended for linking the regarded problem with the material, studied at the moment and, if possible, with future professional activity of a student. The proposed methodology for organizing feedback in an electronic training problem contributes to the formation of metacognitive skills among students through the elements of tutoring.Conclusion. On the basis of the proposed methodology, 8 electronic training problems were developed for the course “Probability and Mathematical Statistics” and tested in the educational process of the Siberian Federal University. The effectiveness of the electronic training problems for the development of mathematical problems solving competency was assessed in the course of a pedagogical experiment. The purpose of the experiment was to study the impact of the electronic training problems in the competency formation for particular topics of the course. Using student’s test for independent samples and the Mann-Whitney test we confirmed that the designed electronic training problems positively affect the formation of mathematical problems solving competency. In the future, the proposed methodology can be included in the teaching toolkit for the formation of mathematical competence in an electronic environment.