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When adding, the binary system was used: if both thematrices had “0”, then in the total matrix the zero index was left. If there was 1 in either or both thematrices, the matrix also had 1. Then, based on the matrices, the visualization of professionalnetworks was designed (see Figure 1). Although all the calculations are based on data from networkmatrices, the visualization of the school network can be used by the school's management team toanalyze the current situation in the organization and plan professional development models 8.Figure 1. An example of professional interactions visualization14Third, apart from the networks of current professional leadership, the networks of potentialprofessional leadership were also analyzed.

Their role is to find internal resources and potentialleaders in the organization. The level of potential professional leadership was determined based onthe answers given to these questions:Which colleague would you like to see in a newly formed group aimed at solving someproblem in the field of teaching and upbringing?Which colleague do you see as a useful guest at your classes, lessons and events?Research FindingsThe structures of formal and informal leadership were compared, and the following datawere obtained during the analysis:Expectedly, the members of the management team demonstrate a higher level of current andpotential professional leadership.

The table below shows the aggregate leadership level based on the14The visualizations were designed by means of software UCINet: Borgatti, S.P., Everett, M.G. and Freeman, L.C.2002. Ucinet 6 for Windows: Software for Social Network Analysis. Harvard, MA: Analytic Technologiestwo indicators, depending on the position: the average level of the indegree centrality and theaverage number of reciprocal ties.Table 2 – Average indices of the indegree centrality based on the actual leadership questions 15PositionNumberofrespondentsAverage indegree centrality(standard deviation)Averagereciprocalnumberties(standarddeviation)PrincipalDeputy7152981principalTeacher3090011,6*2,9*(6,6)(2,0)10,1*2,5*(7,6)(2,2)4,2*1,1*(4,3)(1,3)Note. The Kolmogorov-Smirnov test for all indicators of centrality and mutual relationsshowed that the distribution is abnormal.

Therefore, here and below, the Kraskel-Wallis test is usedto calculate the statistical significance of the differences in the mean values.The study revealed a high level of hierarchy in the organizational structure. Employees with ahigh formal status (headmasters and their deputies) prevail in the network of informal interactions.For example, on average 10-12 employees turn to principals or their deputies, whereas to teachers –around 4. In other words, professional networks are largely centered on administration. In this casethere is a risk of the management team’s overwork: a large number of managers do not conductpedagogical work or have a low pedagogical workload and mention a high level of administrativeresponsibilities.

It is noteworthy that the number of reciprocal ties is about four times lower for allpositions. At the same time, the gap between the administration and teachers is quite comparablewith the indicators of the indegree centrality.Despite a high level of hierarchy, real professional and formal structures of general educationorganizations differ significantly. In each of the groups (principals, deputies, teachers) a high degree15*- p<0,01, 2 degrees of freedom, chi-square is 3837,5 and 1665,0ofof standard deviation from the average index is observed (for example, with an average number ofcurrent professional incoming ties of 4.2, the standard deviation level was 4.3). Thus, the formal roleof a leader does not a priori suppose any informal professional leadership. And vice versa - inprofessional networks one can find a significant number of teacher-leaders who do not have anyformal leadership position.

For all the positions, a high level of dispersion of professionalrecognition is characteristic.Although the dominance of the formal structure can be considered predictable, there areseveral more unexpected results:●in the networks of current attendance of the classes teachers without a formal status have thehighest share of the incoming connections (2,5 connections) compared to 1,4 shown by headmastersand 2,1 – by deputy headmasters who conduct lessons;Table 3 – Average indices of the indegree centrality in the questions about classes attendance for thecentral positions16PositionNumberofrespondentsAverage indegreecentrality (standarddeviation)Averagenumberreciprocal ties (standarddeviation)Principal4201,3 (2,3)0,2 (0,5)Deputy principal22731,9 (2,2)0,3 (0,6)Teacher288732,2 (1,9)0,5 (0,8)Note.

Only those respondents who conduct teaching activities were considered.Thus, if we recognize that the key process in school is teaching, and the main task ofprofessional growth is to improve the quality of lessons, it turns out that the management team isless involved in the processes of mutual monitoring and analysis of lessons.

Principals and deputiesare more likely to play the role of "resource holders", but the existing stereotype that the principal isa "teacher of teachers" is not supported by this study .16*- p<0,01, 2 degrees of freedom, chi-square is 251,5 and 165,0ofFurther, the role of heads of methodical associations, departments or laboratories was analyzed,since we assumed that they had the function of professional support as an official job. The studyshowed that the leaders of the school methodological association (hereinafter - SMA) are moresimilar to teachers without a formal status than to the administration.

So, on average, every formalleader with such status has 5.1 professional ties, the average indicator of mutual ties is 1.7.The complexities and risks of the existing system of professional support of teacherswithin general education organizations were analyzed:The study revealed a high level of professional isolation of teachers.

So, for example, in theaggregate network of actual leadership, more than 38% of teachers do not have reciprocal ties. Innetworks of potential leadership, this indicator is 46%. For networks of classroom visits (both up-todate and potential), this indicator is more than 66%. In other words, 2/3 of teachers are not involvedin the practice of mutual classroom observations, which can lead to emotional burnout andprofessional stagnation.Low involvement of SMAs in the instructional support of teachers. On average, there are 5-6teachers per SMA head, who belong to a specific methodical association. At the same time, theaverage number of actual professional reciprocal ties for this category of employees is 1.7. Thereciprocal links for classroom observations are 0.6. Thus, work on joint improvement of lessons mayseem not the key direction of the work of methodological associations.The role of teachers who have no administrative status was analyzed.

The study revealedthat teachers without a formal status have a high leadership potential. Although the averagemeasures indicate a high level of hierarchy and centrality of interactions around the administration,in teachers’ professional networks one can find a large number of "starring” teachers. That is, thoseprofessionals whose lessons and professional experience are important to their colleagues.Moreover, in the network of classes attendance by teaching staff members, which reflects a realexchange of experience, teachers with no formal status dominate (the average number of incomingconnections is 2.2, with average indices for headmasters and their deputies being 1.3 and 1.9,respectively).It was suggested that teachers who have three or more reciprocal professional ties possessleadership potential.

With the emergence of "star" network configurations, further development ofsustainable professional groups is possible. s a next step, the number of employees with theleadership potential was calculated at each of the positions.Among professional leaders, teachers who do not have a formal status are statisticallysignificant than administrators and managers. For example, among school leaders with a number ofincoming connections of 10 or about 10, 45% are teachers, not administrators. This situation showsthat in general education organizations there is an essential resource for the development of theinternal potential of the collective through the targeted use of pedagogical leadership.Table 4 – The number of potential professional leaders taking various job positionsPositionNumber of employeesTotal number ofShare of the totalwith 3 and morerespondentsnumber ofreciprocal tiesrepresentatives(proportion)Principals392 (6,6%)71554,8%Deputies1276 (21,5%)298142,8%Teachers4276 (71,9%)3090013,8%59443459617,2%TotalOn the one hand, the proposed table confirms the above: an administrative team is much moreinfluential than teachers.

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