Theoretical and empirical framework

According to ^{Ingersoll (2001}), in conceptual terms, teacher turnover is connected to the leaving of their jobs, which can happen either voluntarily or involuntarily, and, as a rule, it assumes replacement. However, the author emphasizes that frequent research on teacher turnover, in the international context, has observed it primarily under the dimension of leaving the profession/attrition, either by leaving or by retirement. Thus, these studies ignore the data on teachers leaving a school to enter another one, since this movement, called migration, does not affect the systemic picture of occupations. The national studies conducted by ^{Torres (2015}) reports this dimension. The author situates it as a less important condition, denoting its more common frequency in productions on public service and teaching work.

The concept of teacher turnover presented by ^{Ingersoll (2001}) is the text reference. For the author, turnover means the leaving of teachers from a school, which encompasses leaving the profession, retirement, and migration. Two premises based the choice of this definition. The first is related to the social function of schools and the uniqueness of teachers’ work. Giving the above, it is possible to assume that the incidence of high turnover rates, either because of leaving the profession, retirement, or migration from one school to another, produces similar effects on the operationalization of teachers’ social function and the social labor relations within it. Therefore, it would be inadequate to ignore any of the dimensions that encompass it.

The research objective is related to the second assumption, which is to understand the phenomenon in the context of basic education schools. It is distinguished, therefore, from studies that aim to produce a general and systemic balance of occupations, such as those from the Ministry of Labor and Employment [Ministério do Trabalho e Emprego] (MTE, 2013), and in partnership with the Inter-Union Department of Statistics and Socio-Economic Studies [Departamento Intersindical de Estatística e Estudos Socioeconômicos] (Dieese, 2014a, 2014b) for which turnover is important in the dimension of leaving the profession. Migration was excluded from the analysis.

Another relevant aspect refers to the assumption of replacing teachers when they leave since it is understood that turnover is prejudicial not only because of the departures and replacements in the teaching staff of a school but also because of the gap it opens up for the occurrence of uncovered vacancies. This interpretation, as presented in Table 1 (in the section reserved for the methodological aspects of this article) was crucial to the process of testing and proposing an indicator.

Regarding teacher turnover, ^{Ingersoll (2001}) emphasizes the prevalence of the individual dimension, explaining a theoretical body of magnitude, which seeks explanatory factors from the teacher's own characteristics, to categorize a profile with a greater predisposition to leave the profession. The author argues that, although research of this nature has been important for its understanding, the absence of other explanatory factors related to schools´ characteristics and organizational conditions has been prejudicially ignored. This leads to the investigation of the teacher turnover phenomenon as something isolated from its context of origin, which eventually shapes the school as a victim of demographic trends and ignores the possibility of a high concentration of turnover in particular types of schools. For the author, the identification of organizational sources of high turnover would allow us to observe not only staffing problems but also, and especially, weaknesses in reaching the school's goals and in terms of team cohesion.

It is worth noting that studies about the history of the teaching career attribute to teacher mobility, through successive inter-school transfers, a feature of the very constitution of the teaching career (^{Vicentini & Lugli, 2009}). They explain that, at the end of the nineteenth century, teachers, especially in São Paulo, chose the schools where they would teach based on the accumulated score in their career, according to the valuation credited to the school of origin. This score would be associated with the distance of the school from the urban centers. This process resulted in a high degree of teacher turnover in the more isolated schools. Moreover, it would produce a hierarchization among schools and, therefore, raise their degree of social prestige and that of their teachers. If we compare this conclusion with the research findings in the public sector in ^{Campos and Malik (2008}), it is possible to observe that the prestige of the organization, even today, relates to low professional turnover rates.

School principals, according to ^{Pereira and Oliveira (2016}), point out that teacher turnover comprises of one of the prominent current problems to be faced in 32.6% of Brazilian public schools. Pereira (2017) further states that its incidence is a factor associated with teacher working conditions.

However, the Brazilian educational research scenario still poorly explores the teacher turnover theme. A document survey, which bases this statement, was carried out, by digital means, in the online archive of Brazilian universities and by searching the Brazilian Digital Library of Theses and Dissertations (BDTD) [Biblioteca Digital Brasileira de Teses e Dissertações]. The survey also included the Scientific Electronic Library Online (SciELO), Scientific Information System Redalyc [Revistas Científicas de America Latina, el Caribe, España y Portugal], the Scientific Periodicals Online (SciELO), and the Redalyc System (Red de Revistas Científicas de América Latina e El Caribe, Espanha e Portugal), the Scientific Periodicals Electronic Library (Spell) and Google Scholar. Specific descriptors were used as references (professional turnover, teacher turnover, migration, attrition, departure, and teacher evasion). One of the criteria adopted in this document survey was the selection of research conducted in Brazil that showed the centrality of study on the turnover phenomenon, since many occurrences addressed it peripherally. The selected researches were drawn from the three areas of knowledge: Education (^{Azevedo, 2012}; ^{Cunha, 2015}; ^{Pereira & Oliveira, 2016}; ^{Silva, 2007}); Administration (^{Siqueira & Alves, 2016}); and Economics (^{Duarte, 2009}; ^{Kasmirski, 2012}). This classification was supported by the idea that the genesis of the research imprints its own characteristics to the researched phenomenon and, likewise, indicates its relevance in different areas.

Thereby, it is possible to note that the four studies carried out within the scope of Education, even when referring to theories outside the area, maintain articulations, in different degrees, with theoretical and empirical references that emphasize the uniqueness of the teaching profession and the social function of the school.

On the other hand, studies from Economics and Administration discuss the theme starting, essentially, from theoretical references of organizational theories and organizational behavior, conceiving the school as an organization susceptible to generalization. In this sense, they do not capture particular delineations, both concerning the social function of the school and with the singular, immaterial, and interactive nature of the teaching work (^{Tardif & Lessard, 2014}). It is necessary to ponder that frequent changes in the framework of a school imply abdicating the collective, procedural, and continuous character that intentional and planned human development requires. It is also worth noting that the achievement of the school's goals demands the maintenance of a long-term bond between the teacher and the student, to ensure the student's commitment and motivation for daily participation in an immaterial work and the conversion of the social obligation to study into a subjective interest. Moreover, it is necessary to consider that the social function of the school is not restricted to the individual (and sometimes antagonistic) conceptions, aspirations, and decisions of each worker; on the contrary, such function aims, above all, to articulate them, through a process of constant search for possible consensus, to implement a collective and socially assumed commitment to materialize a common educational and social project.

In conceptual terms, although coming from different perspectives, the seven studies are all unanimous in defining teacher turnover on a global level.

In terms of the methodological choices, one study is essentially qualitative (^{Azevedo, 2012}) and the others express quantitative techniques of analysis. Among the studies that use quantitative methods, regarding the analysis unit for the definition of explanatory variables, one analyzes turnover essentially from the organization's perspective; two focus on the workers' individual dimension, two of them cover both dimensions and one looks at the phenomenon from the perspective of the class, articulating it to the researched school and municipality. The research that presents only qualitative methods of analysis associates the phenomenon's incidence with some factors related to the organization and the worker.

This body of research reiterates the assumption that high levels of turnover can cause disruptions in the educational functioning of the institution and teachers’ work. It also provides robustness to the decision to work with the global concept of teacher turnover.

The analysis of these studies, besides guiding part of the decision-making process of this research, seems to validate the need for a path that situates the singularities of the teacher turnover in education in the Brazilian context and, when appropriate, in the public sphere. At this point, it is important to recognize the distinctive characteristics of the public sphere concerning the private one regarding the purposes and work relations, which are regulated by their own statute and not by a contract. The public sector, unlike the intention of generating profit, involves complex relationships, both from the point of view of remuneration and time allocated to work and power relations. Furthermore, it is subordinated to the public interest to ensure rights that cannot be violated or conceived as privileges (^{Supiot, 1995}).

Because of the prevalence of efforts, in the researches surveyed, to observe the teacher's individual aspects as factors associated with the incidence of teacher turnover - and, therefore, of the design of a profile prone to it -, it is possible to reiterate the relevance of research that broadens its observation, in the school dimension.

At last, the efforts made to measure teacher turnover provide a “window” of opportunity for the sophistication of related indicators.

Methodological issues

The development of the teacher turnover measure at the school level took place in five stages. The first phase was to define the concept of teacher turnover, which, while remaining consistent with the theoretical assumptions, guided the subsequent methodological procedures.

The second stage comprised gathering methods (strategies and formulas) for calculating the indicator. At this point, given the limited empirical support available, we also consulted researches that analyzed turnover in other professional categories in the public sector. Thus, the theoretical and empirical background raised - expressed in the studies of ^{Campos and Malik (2008}), ^{Medeiros et al. (2010}), ^{Sancho et al. (2011}), ^{Paranaíba (2014}), ^{Torres (2015}), and ^{Diógenes et al. (2016}) - was added to the research repertoire on teacher turnover, related to the scientific productions of ^{Pereira and Oliveira (2016}), ^{Cunha (2015}), ^{Kasmirski (2012}), and ^{Duarte (2009}). Similarly, the measuring strategies used by MTE and the Brazilian Institute of Geography and Statistics (IBGE) [Instituto Brasileiro de Geografia e Estatística] in the Monthly Industrial Survey of Employment and Wages (PIMES) [Pesquisa Industrial Mensal de Emprego e Salário] were considered, due to the robustness of the efforts for the visibility of the phenomenon at the national level. Finally, we also considered ^{Nomura and Gaidzinski’s (2005}) calculation method for the Health area.

Formulas for measuring teacher turnover

After analyzing these studies, in the third stage, we selected five formulas for testing the results based on hypothetical situations of teacher turnover in schools. The empirical test showed that, despite their similarities, none of the formulas generated results that accurately captured the concept of teacher turnover adopted in this study. Therefore, we proposed new formula. Figure 1 shows the six formulas under comparison.

Source: Developed by the authors.

Note: (1) The mathematical notations of the formulas are presented according to the original works.

FIGURE 1 FORMULAS SELECTED TO CALCULATE TEACHER TURNOVER¹ 

The understanding that teacher turnover indicator should capture only the departure movement based the formula proposed in this study. Therefore, it considers the number of departures in the reference year of the analysis in relation to the total number of teachers in the comparison base year (previous year). The rate is calculated by a ratio between the number of teachers who, in the reference year, left the schools they worked in the previous year. The result is multiplied by 100 to express it as a perceptual rate.

Results and discussion

This section presents the results that aim to answer questions regarding the level of teacher turnover in basic education schools, the magnitude of the phenomenon between public and private schools, and the discussion of some explanatory factors. Table 2 presents the turnover rates by public administrative branch and by type of private maintainer for the municipality of Curitiba-PR. Although the research unit of analysis refers to schools, the results of this table show values at the level of teachers to allow for the analysis of the magnitude of the phenomenon with the size of the staff of each sphere analyzed.

TABLE 2 TEACHER TURNOVER RATE BY ADMINISTRATIVE DEPENDENCY AND TYPE OF PRIVATE SPONSOR, CURITIBA-PR, 2017 (ANALYSIS OF THE TEACHERS’ LEVEL) 

Administrative dependence	Number of teachers in 2016	Number of teachers who departed in 2017 from the schools they worked in 2016	Turnover rate 2017
Federal	379	46	12.1%
State	8,811	4,697	53.3%
Municipal	10,400	2,457	23.6%
Private partner school	1,352	447	33.1%
Private community, confessional or philanthropic school	976	227	23.3%
Private profit-making school	6,548	1,919	29.3%
Total	28,466	9,793	34.4%

Source: Developed by the authors from the microdata of the 2016 and 2017 School Census/Inep.

The teacher turnover rate in the city of Curitiba in 2017 was 34.4%, according to Table 2. This rate is close to the turnover rate of the overall workforce in Brazil (35.3%) reported by the MTE (MTE, 2013) and that obtained by Dieese (Dieese, 2014a) for the turnover of teaching professionals (31.5%). Even though the context and the work on which it focuses and the effects and ways of measuring the phenomenon differ, safeguarding the proper distances, this comparison allows us to situate the results found in a broader scenario.

The stratification by the administrative department shows that the phenomenon is more common among teachers in the state public school network (53.3%). The municipal network which has the largest number of teachers among the categories analyzed (36.5% of the total) has a significantly lower turnover (23.6%). The federal network has the lowest rate observed in 2017 (12.1%). Private school categories have a group of teachers of quite a distinct size. For-profit schools employ 23% of the city's teaching workforce and showed a turnover of 29.3%. The partner institutions had a teacher turnover rate of 33.1%. To summarize, by adding the number of teachers in 2016 and departures in 2017, it was found that: public schools have a combined turnover of 36.7%; and private schools, 29.2%. The higher rate among public schools is clearly influenced by the state network, which has a large part of its personnel composed of teachers with temporary contracts (Table 3). Either way, the findings in Curitiba show a difference from ^{Ingersoll´s (2001}) research on the North American context, in which the private sphere showed higher turnover rates. The overall rate presented by the author (13.2%) was also much lower.

Aiming specifically at the municipal dependency, there is a similarity to the rate achieved in ^{Cunha’s (2015}) study for the municipal school network in Rio de Janeiro (from 20 to 30%).

Continuing the same unit of analysis, Table 3 presents a deeper analysis of the findings with disaggregation of the turnover rate by type of employment relationship and stage/modality of education in which the teachers work.

Even though the type of governmental/stable/tenured contract is predominant in Curitiba’s public network (82.4%), the state school network has almost 40% of its teachers on a temporary basis. This temporary contracting modality called PSS (Simplified Selective Process) implies periodic voluntary and involuntary departures of these teachers from the state schools. Not by chance, the turnover rate among temporary staff is quite high (83.3%). In addition, the temporary contract produces work relations different from those of the professionals with whom these teachers work simultaneously. If, as shown earlier, the statutory personnel´s professional consciousness is linked to the recognition of obligations arising from a professional statute, on the other hand, the contracts subject this professional consciousness to a logic of obedience to the employer (^{Supiot, 1995}). These contracts further subject work to the logic of the market, changing power relations, remuneration, and time allocated to work in the sense of continuity of function (Supiot, 1995).

Recognizing this strong duality between the type of contract and its consequences, including the collective work to accomplish a common educational project and the need for team cohesion within schools, leads us to think about the fact that the rate among stable teachers in the state network (34.8%) continues to be the highest among public school networks in Curitiba.

TABLE 3 TEACHER TURNOVER RATE BY CHARACTERISTICS, CONTEXT AND WORKING CONDITIONS, CURITIBA-PR, 2016 AND 2017 (TEACHERS’ LEVEL ANALYSIS) 

Characteristics	TOTAL				Federal		State		Municipal		Private partner school		Private community. confessional or philanthropic school		Private profit-making school
	Frequency		Turnover		Frequency	Turnover	Frequency	Turnover	Frequency	Turnover	Frequency	Turnover	Frequency	Turnover	Frequency	Turnover
	N	%	%		%	%	%	%	%	%	%	%	%	%	%	%
Employment relationship	-
1 - Governmental/stable/tenured contract	16,156	82.4	27.1		84.3	11.5	61.9	34.8	99.8	23.6
2 - Temporary contract	3,404	17.4	82.4		9.7	24.3	37.9	83.3	0.2	40.9
3 - Third-Party Contract	15	0.1	86.7		0.3	-	0.2	92.9	-
4 - CLT Contract (Brazilian Consolidation of Labor Laws)	25	0.1	8.0		5.8	-	0.0	66.7	-
Total	19,600	100.0	36.8		100.0	12.0	100.0	53.3	100.0	23.6
Stage / Modality	-
Daycare	5,927	18.0	25.4		3.9	6.7	-		39.2	23.7	38.7	29.3	7.9	25.8	13.2	30.5
Pre-School*	1,405	4.3	26.3		-		-		-		16.5	22.3	11.0	16.2	13.8	28.4
Elementary School - Early Years	7,822	23.8	22.9		-		-		50.3	22.8	2.9	35.9	27.1	21.2	25.7	23.4
Elementary School - Last Years	7,318	22.2	40.9		15.5	28.8	42.5	50.7	4.9	21.9	2.1	24.1	24.7	17.1	20.3	21.7
High School	5,562	16.9	42.3		16.5	9.5	35.2	48.6	-		-		15.8	18.2	16.8	27.3
EJA (youth and adult education - YAE)	1,225	3.7	47.7		-		8.4	49.5	1.0	27.0	-		-		1.9	51.7
Vocational Education	2,536	7.7	45.0		64.0	9.4	13.0	47.3	0.2	76.5	-		13.6	46.6	8.2	52.3
Special Needs Education	1,121	3.4	35.3		-		0,8	53.3	4.4	24.8	39.8	41.6	-		0.0	100.0
Total	32,916	100.0	33.8		100.0	12.3	100.0	49.4	100.0	23.3	100.0	33.1	100.0	23.0	100.0	28.3

Source: Developed by the authors from the microdata of the 2016 and 2017 School Census/Inep.

Note: (*) The data for preschool teachers in Curitiba´s municipal network were reported in the 2016 School Census as "nursery". THerefore, there is no information for this segment.

Such finding is consistent with the results of ^{Medeiros et al. (2010}) and ^{Linhares, (2014}), which express a relationship between professional turnover in the public sector and the precariousness of employment relationships. ^{Sancho et al. (2011}) also explain the relationship between contract instability and turnover incidence, observing it at higher levels when related to non-statutory employment contracts in public administration.

In terms of teacher turnover in the different stages/modalities of education, Table 3 shows that in the aggregate of the teaching staff in the municipality (regardless of administrative dependency and private school category), the rate varies from 22.9% (elementary school - early years) to 47.7% (Youth and Adult Education - YAE). The numbers show that the context of the education networks and categories of private schools strongly influence this variation. Teachers working in the nursery segment, for example, have a turnover rate of 6.7% in federal schools, 23.7% in the Municipal Center for Early Childhood Education (CMEIs)[Centro Municipal de Educação Infantil], and 30.5% in for-profit schools. The data reveal a great discrepancy in teachers’ turnover in the early (22.9%) and last years of elementary school (40.9%). The distribution of responsibility explained this for the supply of these educational stages in the State of Paraná between state and municipal schools. State network handles the public offer of the last years of education, and in this network, the turnover rate is 50.7%. In fact, the turnover rate is higher than 40% in all stages/modalities that are mostly offered by the state network (High School = 48.6% and EJA/YAE = 49.6%). It is worth noting that Vocational Education has a general turnover rate of 45%. However, this is the modality in which the largest number of teachers in federal schools work, with a turnover rate of 9.4%. In the state schools, the turnover rate is 47.3%; in community, confessional, and philanthropic schools, it is 46.6%; and in for-profit schools, it reaches 52.3%. In Special Needs Education, the overall rate is 35.3%. In this modality, 39.8% of the teachers of partner institutions work, and in these institutions, the turnover is 41.6%.

Nevertheless, as previously mentioned, a broader understanding of teacher turnover requires observing it from the point of view of the correlation of organizational forces that contribute to its production. Therefore, the following investigations take the school as the analysis unit. Table 4 presents a set of descriptive measures of teacher turnover rate by school for each category considered in the analysis.

The data reveals that turnover is highest in the 163 Curitiba-based state schools. In 2017, these schools had an average turnover of 55.4%. Approximately 75% of schools have rates higher than 48.7% (first quartile value). It is also in this network that the phenomenon is more homogeneous (Coefficient of Variation - CV = 21.9%). In contrast, the lowest rates were found in the five federal schools in Curitiba (12.3%). In these schools, the range of the rate oscillated between 0.9% and 19%. The municipal network has a much larger number of units than the other public networks in the city (390), and the average turnover rate was 24.9% in the year under study. Even though there is significant heterogeneity in the distribution of values (CV = 56.8%), it is important to consider that turnover in this network is significantly lower than in the state network and in private schools (partnership and for-profit). Approximately 75% of municipal schools had a turnover of up to 29.7% (third quartile values).

Regarding the private sector, the data in Table 4 show that the three analyzed categories have distinct characteristics, starting with the number of schools. It is notable that, in the year under analysis, this sector employed 31.2% of teachers and offered 34.2% of Curitiba's basic education enrollments (27.2% of enrollments in for-profit schools). In 2017, turnover was of similar magnitude among for-profit and partner schools (average of 33.1% and 35.1%, respectively). Turnover rates higher than 50% in at least 25% of these schools (see third quartile values) are a significant highlighted incidence. On the other hand, emphasizing the heterogeneity of these schools, it is possible to observe schools with no incidence of turnover, and at least 25% of them, with turnover rates lower than 15%. Finally, the numbers reveal that the best performance on teacher turnover, in the private sector, is among the community, confessional and philanthropic schools (non-partner school). The average for the 28 schools in this category is 22.2%, and approximately 75% of these schools have turnover rates of up to 25%.

The data reported in Table 4, for the national scenario, diverge from ^{Pereira and Oliveira (2016}) results, which identify the municipal administrative dependency as the public sphere with the highest median value and the most dispersed teacher turnover rates.

Moreover, the meaning attributed to the obtained rates needs a closer approximation with the elements of a particular reality, to broaden the spectrum of the phenomenon understanding, and aiming to increase the explanatory potential about its incidence in the public school system. Therefore, in this research, we chose to define Curitiba's Municipal Education Network as the universe of explanatory investigation.

It is necessary to consider that Curitiba´s municipal network is composed of two types of teaching units: Municipal Center for Early Childhood Education (CMEI) and elementary schools. In terms of the offering, the CMEIs include enrollments only in early childhood education (mostly nursery school), while schools can offer preschool and elementary school (predominantly early years). The teachers who work in these units, although the common entrance criterion is a public examination of tests and titles, are amid a historical duality that segments them into two distinct careers: one called “teaching professional” and another, more recent, called Early Childhood Education teacher. Even though the “Early Childhood Education teacher” career gives the teacher a professional status not foreseen for the previous “educator” career, this duality maintains the absence of equality in working conditions among teachers in the same school system. This culminates in the distinction, not only of minimum training requirements for admission and workplace but also between career plans, weekly workday, time allotted to activity hours,¹⁰ and remuneration. The main differences between these careers are presented in Figure 2.

Source: Developed by the authors based on Municipal Law n° 14,580 (2014) and Municipal Law n° 14.544 (2014).

Note: [1] It is worth noting that both career plans, in effect until 2017, are suspended by Municipal Law n° 15,043 (2017) whose scope extends the suspension to all career plans of the Curitiba municipal civil service.

FIGURE 2 COMPARATIVE BETWEEN TEACHING CAREERS IN THE MUNICIPAL EDUCATION NETWORK OF CURITIBA, 2016 

In the face of this, it seems essential to examine the incidence of turnover disaggregated by unit type. In 2017, the CMEIs had a higher average turnover rate and higher dispersion than the schools. Table 5 is the base for this inference.

Moreover, the values for CMEIs from the third quartile surpass the incidence obtained among schools, reaching the maximum value of 100%, while the limit for schools does not exceed 72%.

Graph 1 presents a brief historical series in an attempt to situate these findings in a broader time frame. Observing the turnover trajectory for each type of teaching unit shows a gradual drop in rates from 2013 to 2017, except for 2016.

Source: Developed by the authors based on School Census/Inep microdata from 2012 to 2017.

Notes:

(1) Teachers registered as “educational assistant/assistant” in the 2013 to 2015 School Censuses were included in this analysis given their frequent occurrence on the occasion of the “educator” career.

(2) The turnover rate was calculated by the school. The values presented are the median rate for schools in each category in the analyzed years.

GRAPH 1 TEACHER TURNOVER RATE OF SCHOOLS BY TEACHING UNIT TYPE, MUNICIPAL NETWORK OF CURITIBA¹, 2013 TO 2017 (MEDIAN VALUES)² 

Likewise, the comparative analysis between CMEIs and schools allows us to observe a movement of progressive closeness between the rates, again except for 2016. However, until 2016, the median rates for CMEIs were higher, reaching a value 20% higher than that obtained for schools.

Given these results, it is possible to infer that the distinguishing marks for the characteristics of each type of teaching unit and the teachers’ working conditions, including those related to the careers of the teachers who work there, may have some explanatory weight on the incidence of teacher turnover, since the findings, in historical series, reveal its highest magnitude in CMEI.

Schools that are more distant from the city's more central areas and the implementation of an incentive policy to stay in school employing monetary bonuses to teachers are other potential explanatory factors.

As for the location of units in relation to the city's most central areas, its objectification takes place through the municipal education network by a metric assigned to each school/CMEI, which is used to accumulate the teacher's score to compete in the annual process of internal relocation among teaching units. This measure, called weight value (WV), ranges from 1 to 8, 1 being assigned to the most central schools and its increasing progression associated with the increasing distance of the unit in relation to the city's ground zero (downtown).

On the other hand, the policy of incentives to remain in schools, regulated in 2001 and put into effect starting in 2003, was instituted because of the difficulty in occupying positions and due to the high turnover of professional personnel in certain teaching units. This policy provides, through a decree, the definition of units considered difficult to be occupied. For these units are expected the payment of a percentage cash bonus to be paid to the public employees for as long as they remain in the unit. In 2016, the units covered by the policy represented about 34% of the total number of schools and CMEIs observed. This bonus, which induces permanence in these schools, varies from 10% to 30% of the starting career salary.

Table 6 presents the turnover rates for these variables. Its results show that there is a complex relationship between turnover rate and distance, implementation of hard-to-staff policy, and bonus percentages.

TABLE 6 TEACHER TURNOVER RATE, BY UNIT TYPE AND DISTANCE FROM GROUND ZERO AND % OF BONUSES POLICY, MUNICIPAL NETWORK OF CURITIBA, 2017 (SCHOOL-LEVEL ANALYSIS) 

Aspect	Type of teaching unit
	CMEI			School
	N	Mean (%)	Standard deviation (%)	N	Mean (%)	Standard deviation (%)
Total teaching units	205	25.4	16.7	185	24.3	10.7
Distance from city's ground zero (WP)
1	2	22.7	10.3	2	32.4	7.2
2	10	32.6	24.5	17	29.7	11.9
3	25	22.9	13.9	37	23.6	11.1
4	62	22.7	14.8	42	22.4	11.0
5	47	28.3	18.3	40	25.0	10.4
6	30	23.9	13.0	22	24.7	9.9
7	12	23.6	19.2	10	22.6	11.8
8	17	31.0	20.6	15	22.9	7.7
Implementation of hard-to-staff policy
Não	137	27.8	19.0	122	25.1	11.6
Sim	68	20.6	9.1	63	22.9	8.6
Percentage of bonuses - permanence in school
0	137	27.8	19.0	122	25.1	11.6
10%	28	22.0	9.0	25	23.2	8.2
20%	23	17.2	7.5	21	22.7	10.2
30%	17	23.0	10.4	17	22.6	7.3

Source: Developed by the authors based on data obtained from documents and regulations issued by the Municipal Secretariat of Education (SME) and microdata from the 2016 and 2017 School Census.

Concerning distance, it is important to emphasize that among those teaching units with weighted values from 1 to 3, located in more central regions of the city, only 7.7% have the hard-to-staff policy implemented. This percentage is 6.7% in units of level four, 43.7% in level five, 49.1% in level six, 90.9% in level seven, and 93.8% in the most distant units (level eight), the latter being implemented in all schools and 88.2% of CMEIs.

Thus, considering the distance and coverage of the hard-to-staff policy, we observe that the average turnover rate among CMEI is lower for the most centralized units (22.7%), reaching 31% in the most distant schools (level 8). It is interesting to note that the highest rate is found in level 2 (32.6%), which alludes to more central locations, with less policy coverage, but inserted in vulnerable contexts from the socioeconomic and cultural point of view. A similar movement is perceived in schools, which show higher rates for schools closer to the central region of the city (weighted values 1 and 2). Rates lower than average are found in more distant schools, and those under Weight Values 7 and 8 also have greater policy coverage.

The results for the variable “policy implemented” show that the average is significantly lower between the two groups whose policy was implemented, denoting also less internal dispersion (CV of 44% among the CMEIs and 37% among the schools).

Considering the percentages of bonuses, the turnover rates among schools are lower as the percentage increases, so higher bonus percentages may be related to a decrease in the incidence of the phenomenon. Although this is not a common regularity among the CMEIs, their rates for the different percentages are lower than the overall average (24.3%).

Given the obtained results, it is possible to state that distance, implemented policy and bonus percentage are intervening factors in the turnover level, but do not keep a linear relationship. At this point, it is worth reminding the study by ^{Campos and Malik (2008}), which shows the matters of distance and prestige of the institution as variables that explain part of the incidence of professional turnover in the public sector.

Anyhow, the relationship between these variables needs to be problematized under the lens of the teaching work conditions that are operated in the units considered hard-to-staff by the municipal management, because they are not filled up every year. Thus, we have the policy as an element that induces attractiveness but disconnected from the investigation of the issues that produce the difficulty in staffing the vacancies.

To summarize, the above-mentioned analyses of the policy in question - together with ^{Kasmirski’s (2012}) finding that local policies of additional monetary payments added to the remuneration per job location show potential for reducing migration among schools - evoke the need for studies that observe, in-depth, its effects on the incidence of teacher turnover, taking as reference the universe of schools in the Municipal Education Network (RME)[Rede Municipal de Ensino].

Concluding remarks

The teacher turnover in schools, at high levels, may constitute an obstacle to the fulfillment of the educational objectives expressed in an educational and social project. This is the basic assumption of this article. The phenomenon was thought of in the light of the singularity of the teaching work, as it alludes not only to the departure of a professional from his/her workplace and eventual replacement, but to the rupture of a political, continuous, intentional, interactive, and collective work, with a view to broader human development.

Regarding the implications for educational policies, taken as necessary actions for the effectiveness of the constitutional right to education, the expressed results reiterate the need to reveal, by an indicator, the incidence of the teacher turnover phenomenon in basic education schools.

The conclusion of the general analysis of teacher turnover in Curitiba, by administrative department, and for the set of schools that comprise it, is that the phenomenon's measuring reveals an incidence at high levels. If the undertaken theoretical construction made it possible to highlight its negative effects on the school’s social function and a work of a unique nature, revealing average incidence rates that can vary from 12.3% to 55.4%, depending on the sphere in which they occur, reiterates the need to give it visibility to raise it as a pertinent theme to be included in the local political agenda.

Among the research limits, it is important to emphasize that, although we recognize the possibility of a relationship between turnover and differentiated forms of school management, since this relationship tenses, to different degrees, the teaching work, and the power relations inherent to the school, this is a dimension not observed in this study. The relationship among peers, which may explain the interest in departing from or remaining in a school, was not assessed either.

It is important to highlight the possibility of replicating the indicator for other Brazilian contexts, since it was developed from a database made available annually by Inep. This creates endless possibilities for diagnosis, analysis, and discussion. Therefore, it can be set as an agenda for future work: a) efforts that seek to identify organizational factors that contribute to turnover production, as a condition for the political decision that aims at its reduction; b) studies that capture the specificities that generate the stressed dissimilarity in the incidence of the phenomenon between CMEIs and schools; c) explanatory analyses with a broad set of independent variables and more sophisticated statistical modeling; d) analyses of the indicator's historical series to know the trajectory of the aimed phenomenon incidence, among other results, at the construction of “tolerable” parameters of teacher turnover in basic education schools.