Application of multivariate statistical methods for assessment of educational competencies

Abstract

Assessment of educational competencies of students in the Russian Federation higher education institutions is one of the most important objectives of the efficient training of competitive specialists in a smart environment, since the third-generation Russian educational standards prescribe the implementation of competence-oriented learning in higher education institutions. This aspect is important for the smart education system as well. The main features of a competence can be distinguished using Bloom’s taxonomy according to which each competence is assessed according to six characteristics: knowledge, understanding, application, analysis, synthesis, and assessment. The goal of this paper is to build a model of probabilistic assessment of the students’ competencies quality level on the basis of the multivariate normal distribution. That said, we see probabilistic assessment as the use of mathematical statistics’ ideas related to the statistical methods of experimental planning to minimize the differences in obtaining the final results in educational systems in response to uncontrolled factors and at the same time to increase maximally the possibility of obtaining the guaranteed result. The proposed model was tested in the smart education context during the learning process in the Toglyatti State University (Russian Federation, city of Toglyatti), on the basis of the distance technology of teaching the discipline “Econometrics (advanced level)”. Testing was carried out for 2.5 years (5 semesters). A total of 274 students participated in the experiment.