New Perspectives in Science Education

We consider 4 problems concerning higher education system. The first problem deals with the demand for higher education and evaluates the size of admission to the universities using the model of a structure of households’ preferences with respect to professions provided by HE system. It is a multi-stage choice model which uses the Unified State Examination (USE) scores.
The second model develops the concept of the heterogeneity of the educational system on the basis of one parameter: input grades of university students. We consider a heterogeneity as one of the key elements of a different modeled higher education system. We develop a simple approach to measure the deviance of higher education systems, differentiating idealistic conceptualizations of higher education systems and how higher education institutions function in practice in terms of heterogeneity. We propose a mathematical model based on the construction of universities’ interval order. We use the Hamming distance to evaluate the heterogeneity of the educational system, and USE scores of Russian students to illustrate the application of the model. We show that institutions taking weak students turn the whole system of universities into a poorly structured nonhomogeneous system. In contrast, after ‘deleting’ the weakest part, the remaining set of universities becomes a well-structured system.
The third model deals with the performance based typology of universities. In recent decades national governments attempt to design and apply various taxonomies for structuring the university infrastructure in order to facilitate the development of efficient programmes for the advancement of higher education.
We provide a review of different approaches to university typologies, discusses the choice of indicators and mathematical tools for grouping universities using common criteria and evaluating their performance based on classical and modified DEA approaches. We develope a typology which was tested in the Russian context, taking into account indicators of research and educational activities implemented by domestic universities and their efficiency score. The typology is based on clustering universities by availability of resources and research and educational performance and the combination of these results with efficiency score keeping into account the universities’ heterogeneity. It may serve as a basis for content analysis of the wide range of universities, and for shaping targeted policies aimed at their particular groups.
The fourth model uses modified DEA technique to evaluate an efficiency of universities taking into account an observed non-homogeneity of the sample. In addition we use a reputation index as another parameter of universities’ productivity. We propose 13 criteria to evaluate reputational component. The threshold procedure of aggregation is used to evaluate reputational  component.  The application of the model is presented consisting in the analysis of 379 Russian universities.

Keywords: Higher Education System, universities, attractiveness of professions, heterogeneity of HES, typology and efficiency of universities;