Development of higher education in Russian regions: the number of scientific and pedagogical staff

This study was devoted to the assessment of indicators characterizing the number and structure of research and teaching staff at universities and other institutions of higher education in the regions of Russia. These indicators were the number of teachers working in higher education, per thousand residents and per hundred students, proportion of professors and associate professors in the whole number of teachers. Research used official statistical information for 82 regions of Russia. We used density functions of normal distribution as models. Study showed that on average, there was a little more than one teacher working in higher education organizations per thousand residents. It is proved that on average, every seventh teacher in all regions held the position of professor. Approximately two-thirds of all teachers held associate professor positions, there were five teachers per one hundred students.


Introduction
The increasing role of higher education, as indicated in the classical work (JASPERS, 1960), contributes to the significant social and economic development of In the twenty-first century, most States have created conditions that ensure mass access of the population to higher education (GURI-ROSENBLIT; SEBKOVA; TEICHLER, 2007). The total number of students in all countries in 2016 was 218 million, which is 1.5 times more than in 2006 (LA MOBILITE INTERNATIONALE, 2019). To solve the problems of higher education, a necessary condition is the availability of scientific and pedagogical personnel capable of teaching students according to appropriate programs.
Taking this into account, one of the urgent scientific problems is the assessment of indicators characterizing presence of personnel, that is, professors, associate professors, as well as other categories of teachers who ensure the availability of higher education (DOUGLAS, 2011;STIGLITZ, 2014 3 the current level of solving this problem is important both for state bodies regulating activities in this area, and directly for potential students. Despite the existence of extensive research on the problem of the development of higher education, until now, not enough attention has been paid to the regional peculiarities of solving this problem. The presence of organizations in the regions that teach students according to the relevant programs, as indicated in the works (ABEL; DEITZ, 2011;CIRIACI, 2014), increases the attractiveness of the regions, positively affects their economic growth and, most importantly, ensures the retention of school graduates in the regional labor market. All this determines the increased interest in the study of regional The structure of this work is below. The following section provides an overview of scientific publications of recent years that characterize such aspects of higher education as the number and structure of teachers in Russia, as well as the ratio of the number of teachers and students. The methodology, initial data and design of the study described in our article are presented below. The following sections present the simulation results and their discussion. The last sections contain conclusions and bibliographic references.
A number of scientific publications published in recent years have been devoted to the problem of assessing such an aspect of the development of higher education in Russia as the number and structure of the scientific and pedagogical staff of higher education organizations, as well as the current ratio of the number of teachers and students. A brief description of these publications is given in Table 1. Based on the information given in Table 1, it can be stated that the problem of research on the number and structure of teachers who carry out training in higher education programs is relevant in Russia. Most of the studies reviewed analyzed the number of teachers, students and the number of organizations in Russia as a whole. At the same time, a comprehensive assessment of the distribution of the number and structure of teachers according to all regions of Russia has not been sufficiently reflected in scientific publications. It can be noted that a comparative analysis of relative indicators that allow us to assess the regional characteristics of higher education organizations was not carried out in most studies. Thus, absolute indicators were given in 70% of the studies indicated in the table. Taking this into account, it seems appropriate to conduct a comparative analysis of the existing relative (specific) indicators characterizing the achieved level of activity of scientific and teaching staff in all regions of Russia.

Methodology
The scientific and pedagogical staff of higher education organizations, the number and structure of which is considered in this article, carried out training of students in 2020 the bachelor (four years of study), specialist degree (five years of study), as well as master's degree programs were taken into account.
The research process included five stages. At the first stage, initial data were formed that characterize the number of universities and other institutions of higher education and the number of research and teaching staff by region in 2020, as well as the number of students enrolled in higher education programs this year. In addition, empirical data on the number of inhabitants in these regions were formed. At the second stage, indicators were calculated that characterize the number of teachers per thousand residents of each of the regions and the specific weights of professors and associate professors in the total number of teachers of higher education organizations, as well as the number of teachers per one hundred students. At the third stage, the distribution of indicators by region was evaluated based on the development of mathematical models. At the fourth    (1) -the proportion of professors in the number of teachers working at universities and higher education institutions (2) -the proportion of associate professors in the number of teachers working at universities and higher education institutions (4) The quality of functions (1)-(4) we tested using such criteria: by the Kolmogorov-    10 An analysis of empirical data for 2020 showed that there are higher education organizations in all 82 regions of Russia. Accordingly, the scientific and teaching staff was also in each of the regions. Thus, the first hypothesis was confirmed. The data in table 3 show that the average number of teachers working in universities and higher education institutions by region is 1.2 per thousand inhabitants. In most regions, this indicator ranges accounting for one hundred students, was 5. The values of these indicators, typical for most regions, were in the range from 4 to 6%. That is, typical for Russian regions is from 25 to 17 students per teacher. This is slightly more than the average values for OECD countries, which range from 10 to 20 students per teacher (OECD/UIS/EUROSTAT, 2019).
To test hypothesis 2 on the differentiation of indicators by region, an analysis of the degree of variation of each of the indicators presented in Table 3 Table 3, and the minimum values are those that are less than the lower limits of the specified ranges. The results of this 11 analysis are shown in Table 4. Along with the lists of regions, this table also shows the values of indicators by region, as well as which of the federal districts the regions belong to.   14 that the territorial location of the regions does not significantly affect the maximum and minimum values of the indicators.
The practical significance of the study for the government is to take into account the territorial features in the development of higher education in the regions of Russia.
The results of the work can be used in the activities of federal and regional structures related to the support of educational processes, when justifying their planned activities, improving the quality of higher education by increasing the share of highly qualified teachers. For potential students, data on the distribution of research and teaching staff by region may be of particular interest.
The proposed methodology for modeling the estimation of the number of teaching staff can be used in conducting research on the development of higher education in countries with a large number of administrative units (states, provinces, regions, districts).
In particular, in the BRICS countries.
The new knowledge gained is of interest and can be used in the educational process at universities. The study was not limited to empirical data, as it was based on official statistical information for all 82 regions of Russia. Further research may be aimed at establishing gender characteristics describing the number and structure of teachers in higher education organizations in Russia.