The method for evaluation of educational environment subjects' performance based on the calculation of volumes of m­simplexes

We propose the method for comprehensive performance evaluation of subjects of educational environments, specifically higher educational institutions, based on calculation of generalized volume of the m-simplex. The vertices of the m-simplex are found based on performance scores of subjects of educational environments by different categories. To find a comprehensive performance score of subjects of educational environments, it is proposed to calculate generalized volume of the constructed m-simplex, based on calculation of the Cayley-Menger determinant. The numerical methods for calculation of this determinant for different cases of location of vertices of m-simplex were considered. A list of five major categories of evaluation of higher education institutions was compiled and selection of indicators for these categories was performed. The method of comprehensive performance evaluation of the subjects of educational environments based on calculation of generalized volume of m-simplex was verified in the developed information-analytical system. This method was compared with the ideal point method and the weighed scores method. The feature of the proposed method is its self-sufficiency, because the method does not require solution of ancillary problems in calculation of a comprehensive score, such as selection of weight coefficients and the ideal point, involvement of experts, etc. It was shown that the proportional changes in a comprehensive score, calculated by the proposed method, correspond to small changes of certain categories. The method of setting a tendency of activity development of subjects of educational environments by calculating the derivative of a comprehensive score in time was presented. The methods for performance evaluation of subjects of educational environments can be used in scientific and educational institutions, as well as in private companies that are engaged in creation of high-tech applied information technologies