Introduction

Since the IDEB - Índice de Desenvolvimento da Educação Básica (Basic Education Development Index) (BRASIL, 2019b) was established as a potential indicator of the quality of basic education ( ^{BRASIL, 2007} ), it is not difficult to accept the idea that one of the information desired by managers and citizens is to know in which programs to apply resources, to improve performance in this indicator. The bibliography in the area suggests that it cannot be said that programs contemplating a component (variable) ( ^{WOOLDRIDGE, 2016} , p. 23) or even a factor (combination of variables) (HAIR et al ., 2009, p. 101) would have the primacy in explaining student performance in general assessment systems and expected progression to the following years. Analysts have long suggested that there is a considerable combination of components, with distinct associations for each context and moment, making the issue complex ( ^{OLIVEIRA, 2010} ; ^{DITTRICH, 2010} ). One may see that the term quality, when attributed to education, becomes polysemic, given that it can be interpreted from different perspectives ( ^{GUSMÃO, 2013} ; ^{ALVEZ; SILVA, 2013} ).

Factors related to personal and family characteristics of students, from macroeconomic and social structures to those that can be identified with the structures of public service provision, present in the locations where the activities are developed, are among the most indicated as influencing the results of educational systems ( ^{OLIVEIRA, 2010} ). The latter characterize the conditions for effective production of public policy in a territory ( ^{MORAES, 2018} ), results of public choices made by political actors responsible for managing public services in localities ( ^{SECHI, 2015} ).

There is considerable academic interest in studies on IDEB as an indicator of quality, with the evaluation of expenditure efficiency as the most frequent focus. Few published studies try to explain IDEB influencers in municipal elementary education networks. This finding indicates a gap to be filled by studies capable of supporting citizen assessments and decisions by those responsible for managing educational programs and policies in the municipalities.

Given this context, this article aims to identify and evaluate variables with a higher level of association with the IDEB of elementary education students, initial and final years, enrolled in public municipal networks in São Paulo, in 2017. Based on the literature visited and referred to in the following topic, the study uses variables obtained from official databases of the Union and the State of São Paulo, applying simple and multivariate analysis techniques by Ordinary Least Squares (WOOLDRIGE, 2016, p. 70) to identify those that influenced, with a higher level of statistical significance (HAIR et al ., 2009), the IDEB of fundamental education, of the municipal networks of the State of São Paulo, in 2017.

With the increasing availability on official government websites of educational databases, this study uses data from the TCE - State Audit Court ( ^{SÃO PAULO, 2019} ), from IBGE - Brazilian Institute of Geography and Statistics (BRASIL, 2020a), from STN – National Treasury Secretariat (BRASIL, 2020b), IDEB – Basic Education Development Index (BRASIL, 2019a), INEP – Institute of Studies and Research Anísio Teixeira (BRASIL, 2019b) as well as MS – Brazilian Ministry of Health (BRASIL, 2019e).

In the regression model, there are 33 variables indicated in the literature, which had data available at the municipal level in the cited sources for 2017. The stepswise procedure ( ^{FAVERO, 2015} , p. 44) defined the variables that represent the most statistically significant influence ( p-value > 0.05 ) on the 2017 IDEB of elementary education municipal networks in São Paulo. The previous result of IDEB, from 2015, human development index, income dimension of the year 2010, teacher effort rate, student dropout rate and average remuneration per student of the staff of municipal networks, point out as the most explanatory influencers for more than 66% of the IDEB of the municipalities.

The novelty of this study refers to the low availability of publications with similar objectives. The study opportune due to the renewal, in 2020, of the Law of the Fund for the Maintenance and Development of Basic Education and the Valorization of Education Professionals – Fundeb (BRASIL, 2019d), which placed educational policies and their financing on the public agenda. One should consider that federal transfers are the most relevant in the financing of education in Brazilian municipalities, aggravating the care taken in the renewal of the aforementioned Law. Another point concerns the assessment of the quality of primary education from the perspective of quality management of public spending (BOUERI et al ., 2015).

In addition to this introduction, this article visits studies published on IDEB and the quality of education, contextualizing and supporting the findings. Next, it presents the methodological choices, results and conclusions.

The IDEB, publications, and the quality of public education

Methodological aspects

This study can be classified as descriptive, explanatory and exploratory, given the objective of identifying the variables with significant correlation with the IDEB, in 2017, of municipal elementary education networks in the State of São Paulo, as it analyzes “if and how two or more variables are related to each other in a population” ( ^{STEVENSON, 1981} , p. 341). To do so, it uses the technique of multivariate regression analysis (HAIR et al ., 2009, p. 149-220) by Ordinary Least Squares ( ^{WOOLDRIDGE, 2016} ) and the stepwise procedure that “presents the property of automatically excluding explanatory variables whose parameters are not show statistically different from zero” ( ^{FÁVERO, 2015} , p. 44).

The city of São Paulo was excluded, considering its population equivalent to 42% of the others and a public budget, for 2017, equivalent to 49.4% of the sum of the budget of all municipalities in the state (BRASIL, 2020b). The remaining 644 were grouped by their population estimated by IBGE 2017, into five bands, as disclosed by the National Treasury Secretariat (BRASIL, 2020b):

Range 1 – up to 30,000 inhabitants

Range 2 – between 30,001 and 50,000 inhabitants

Range 3 – between 50,001 and 300,000 inhabitants

Range 4 – between 300,001 and 1,000,000 inhabitants

Range 5 – above 1,000,000 inhabitants

The variables used, indicated in the literature and with available data, are described in Table 1 below, regarding the denotation used in the regression, description and source.

The requirements of normality, homoscedasticity and linearity (HAIR et al ., 2009, p. 82-88; CORRAR, PAULO; DIAS FILHO, 2014, p. 40-46) and the absence of multicollinearity (HAIR et al ., 2009, p. 160; FÁVERO et al. , 2014, p. 131; ^{FÁVERO, 2015} , p. 45-62) of the variables of the final regression, were verified and found adequate by the visual histogram test, by the White, Shapiro-Wilk and linear correlation tests and the variance inflation factor or VIF ( variance inflation facto r) (HAIR et al ., 2009, p. 190-191; FÁVERO et al ., 2014, p. 131-142; ^{FÁVERO, 2015} , p. 45-62). Data, charts, graphs and statistical analyzes were developed using Microsof Excel (2010) and STATA (14) [Computer Programs].

Results and analyses

The resident population, enrolled students and the respective IDEB for the year 2017 (average, lowest and highest value and standard deviation) in the municipal primary education network of the 644 municipalities, are contained in Table 2 below, in the population groups already identified.

In Table 2 above, one can see that 21% of São Paulo residents, except for the capital, live in municipalities with up to 50,000 inhabitants. These municipalities are home to more than 27% of students enrolled in elementary education schools managed by local municipalities. They also have the lowest and highest IDEB value in 2017 in the municipal primary education network in the state. It is observed that, while there are municipalities with IDEB at levels higher (7.80) than the state average (6.25), in these cities there is also the lowest IDEB (4.35).

Table 3 , below, presents the variables that were excluded from the multivariate regression by the stepwise procedure ( ^{FÁVERO, 2015} , p. 44) for having low statistical significance ( p-value > 0.05), with the dependent variable in the regression model.

Twenty-eight of the 33 initial variables were removed from the regression model. The existence, or not, of the Municipal Council of Education (conedu: p-value = 0.0519), the non-response rate (tnr17: p-value = 0.0688) and the age-grade distortion rate (tnr17: p -value = 0.0887). These variables would have been included in the equation if the significance level was set at 10% ( p-value < 0.1). In this regard, the explanatory power of the final regression equation would have a R2 ( R-squared ) = 0.7037.

In Table 4 , below, the data from the regression equation offered by the STATA application are shown, explaining the variables that influence IDEB, of São Paulo municipalities in the year 2017.

Table 4 shows that the econometric model obtained as multivariate regression has considerable statistical significance ( Prob. F > 0.0000) and that can explain 66.24% ( R-squared = 0.6624) of the behavior of the dependent variable, that is, the 2017 IDEB of the municipal networks in São Paulo. As these variables individually have statistical significance at 5%, they indicate an excellent combination of focus on managing the improvement of the IDEB in fundamental education in each municipality.

The regression equation for estimating the IDEB of the municipal elementary education network in 2017 in the municipalities of São Paulo, considering the variables with statistical significance, is defined as follows:

The HDI Income dimension (idhr10) is positively related to the IDEB of São Paulo municipalities. It is estimated that the 1.16-point increase in the IDHR will reflect the 1-point increase in the respective municipality’s IDEB. Families that are better equipped with economic resources have better conditions of access to schools in which their children perform better in IDEB. This result is in line with the discovery by Gomes et al. (2016) and Dittrichi (2007). Overcoming the antagonistic dichotomy between income and learning is a challenge for the Brazilian state that was not even overcome by the NGP (LOURENÇO, et al ., 2016, p. 40). Evidence contrary to the statement by ^{Oliveira (2010)} for whom “student performance is not directly related to the economic and social differences of the municipalities.” ( ^{OLIVEIRA, 2010} , p. 129).

Variable ied17 reflects the proportions of professors who develop a lower level of effort in the function. It shows that the greater the proportion of professors with less effort, the better (or higher) IDEB in the municipality. It is possible to assess the level of influence of physical and intellectual impairment for the necessary adaptation to the challenge of being a primary school teacher in the analyzed networks. Teachers with up to 150 students per shift have students with better performances in the Prova Brasil.

As municipalities with more than 1 million inhabitants and those with up to 30,000 inhabitants have better financial capacity to hire a greater number of teachers (more than 1 million inhabitants) and by the smaller number of students and fewer displacements (up to 30,000 inhabitants), these present the best performance in this indicator. These results corroborate the findings of ^{Oliveira (2010)} , ^{Dittrich (2010)} and ^{Vidal and Vieira (2011)} , who stated that “The Physical Infrastructure and Pedagogical Resources dimension is a critical field in Rio de Janeiro municipalities, demanding a closer look of political managers.” ( ^{VIDAL; VIEIRA, 2011} , p. 128).

The dropout rate by elementary school students is negatively correlated with the 2017 IDEB, as expected. The coefficient in the estimated regression equation (-0.349953) indicates that the IDEB of São Paulo municipalities can improve 1 point for every 3% decrease in the dropout rate. The estimated column in table 7 shows that just over 3,600 students dropped out of elementary school in 2017, in these education networks. Of these, municipalities in ranges 1 to 4, with a high standard deviation, show that this is not a problem at all. This finding corroborates the statement by Rezende and Januzzi (2008, p. 144) that the reduction in school dropout is still one of the relevant dimensions of the development of education in the country and by ^{Dittrichi (2010)} for whom managers should:

[...] commit to part of the solution of the problems detected by the evaluations, implementing policies that aim to guarantee to the group of schools with the lowest performances, especially when this performance is linked to the socioeconomic level, that there is an effective policy for differentiated improvement of these schools, so that such privileged conditions can compensate part of the unfavorable structure of the students of these schools. ( ^{DITTRICHI, 2010} , p. 267).

Thus, there is potential for improvement in IDEB in municipalities with higher school dropout rates, that is, programs that induce students to stay in schools have the right address.

One may observe that municipalities with up to 30,000 inhabitants have an average of 8,400 reais; however, the highest value is 5 times higher than the average and almost 30 times higher than the lowest value for this category of municipality. Municipalities with a population between 50 thousand and 300 thousand inhabitants have the lowest average value of 6.0 thousand reais, which shows a gain in scale in the educational networks. The lowest value of average expenditure per student is 532 reais, representing 8.5% of the average and the highest value is 39 times higher than this, in the same range of municipality. These same cities, on the other hand, according to additional analyses, have a high average budget expenditure per student with purchases of materials and services (md17), an indication that they may be hired by outsourcers of educational services. In the other population groups, the mean, highest and lowest values are relatively stable, given that the standard deviation is much lower in relation to the first two population groups.

In a complementary analysis, it was found that the average expenditure on staff of the municipal primary education networks (ma17) has high statistical significance with the adequacy of teacher training (afd17), with the teacher effort index (ied17), with the proportion of faculty with higher education (dsu17), with the teacher regularity index (ird17), with the average remuneration of the professor (rmd17), with the number of students per class (atu17) and with the average amount per student received by the municipality transfers to FUNDEB (fundebal7). Adequate training for the contents (afd17) at the level of higher education (dsu17) of teachers is combined to enhance the efforts of municipal education systems, with the learning processes of students. This finding emphasizes the role of total expenditure on education, which should be directed primarily to teacher remuneration and how these are related to complementary aspects of the teacher’s performance, relevant to the education system. This finding corroborates the considerations by Gomes et al . (2016), and Jacomini and Pena (2016), Lourenço et al. (2016) and Gomes et al . (2019), for whom programs, materials and educational spaces work together for quality when well managed (GOMES, et al. , 2019, p. 292-293).

As shown in Table 9 above, the level of univariate correlation between the variables that make up the regression model is low to weak; on the other hand, the level of statistical significance of this correlation is high ( p-value < 0.05) for most of the correlations. This analysis consolidates these variables as the main causes of the variation in the IDEB in the year 2017, of elementary education networks in São Paulo municipalities that combine to produce an event or phenomenon ( ^{FÁVERO, 2015, p} , p. 44 ; HAIR et al ., 2009, p. 100).

Discussion

Public policies are complex phenomena and their analysis requires technical training, knowledge with a scientific basis, as well as dedication to their proper understanding. As stated by ^{Sechi (2015} , p. 1):

The analysis of public problems aims to improve the public decision-making process with the use of methods and techniques of problem analysis ( problem analysis ) and solution analysis ( soution analysis ) to assist in decisions and in the structuring of policies, laws, programs, campaigns , projects or public actions.

The results of this study show that the result of the elementary education policy in São Paulo municipalities measured by IDEB is influenced by an interesting and small combination of variables. The pre-existing condition, measured by the IDEB of the previous evaluation (2015), with strong explanatory power of the current score, represents the strength of the educational context present in each municipal network, as the main aspect of change in the quality of fundamental education in these realities. The biggest challenge is to break the inertia in the quality of education observed.

The results showed that the educational policy of considering structural variables such as the Human Development Index (HDI), income component of municipalities, is non-discretionary for network managers, and cannot be directly transformed by direct actions. This implies analyzing the socioeconomic and cultural condition of families in order to integrate them into the process of stimulation and development of students.

On the other hand, the average expenditure on the remuneration of public servants in education (teachers, employees and managers of the local network) is one of the variables with a strong impact and consequences in the 2017 IDEB of the networks. It must be appreciated that this is a consolidated concern in the management of fundamental education policies, given the inclusion of aspects of valuing education professionals when the FUNDEF is renewed for FUNDEB (BRASIL, 2019d) and also identified by Gomes et al . (2016) and Lourenço et al . (2016). Equalizing remuneration for the set of municipalities, as well as valuing the teacher for a fair remuneration consistent with their social role, is the first step.

The data consistently show that the teaching effort influences the 2017 IDEB results of these municipal networks. Decreasing the number of classes, teacher displacements and the number of students per class are evidences that the quality of educational services in environments that are easier to manage and teaching performance are key aspects for the quality of learning and the student’s permanence in the network. Teachers’ remuneration and their performance in the classroom are crucial for the quality of teaching, which will be observed with their own programs and actions to reduce the teacher’s effort, in fulfilling their noble mission of educating. Structuring teaching careers that encourage the permanence of the teacher with a bond in a single municipality is a good way to go.

The dropout rate is also a condition that can be worked on with specific programs. The identification of dropout conditions, their motivations and the student’s profile can be established by specific programs. The 644 municipal networks that consume more than 17.6 billion reais a year have the potential to establish teams of monitoring abandonment, as a concrete action for the improvement of IDEB, since “one could observe the reception or association of IDEB with the notion of educational quality.” ( ^{SANCHES, 2017} , p. 151).

Conclusion

This study sought to identify which variables influenced, with statistical significance, the 2017 IDEB of São Paulo municipalities. With the use of 33 variables and the Ordinary Least Squares (MQO) method with the stepwise procedure, unprecedented knowledge of interest to managers and those responsible for implementing educational policies in the municipalities was produced.

The results show that the initial condition of teaching in the evaluation cycle (IDEB 2015), the average expenditure per student with the remuneration of education professionals, the level of teaching effort, the dropout rate in municipal networks and the development index human dimension income (IDHR) form the set of variables that can explain more than 66% of the variation of the IDEB in the year 2017.

Evaluating the intrinsic relationships as well as the details of how these variables are operationalized and implementing actions in plans, programs and projects to strengthen the dimensions reflected by these variables has the potential to bring improvements to education in the State’s municipalities with a higher level of effectiveness , if compared to the others that were not included in the regression model. These considerations are strengthened by the studies referred to and the results of this work, pointing to the improvement of the management of education systems as a relevant step towards the quality of education. The decrease in the number of students per class and/or the number of teacher work shifts are clear examples that are achievable by managers who managed public expenditures in the order of 16 billion reais in 2017, to serve a population of more than 1.8 million students. The implementation of programs to reduce school dropout in municipalities where this problem is relevant is a desirable action with significant results.

The smallest but present significant influence (0.05 < p-value > 0.10) of variables such as the age-grade distortion rate, the non-response rate (tnr17) as well as the existence or not , of the Municipal Council of Education (in 8 municipalities there is no such Council, according to data from this research), as variables with the potential to influence the IDEB of São Paulo municipalities in 2017.

The studies published, as well as the results of this work, corroborate the implementation of actions with a strong potential to change the not-so-adequate conditions of fundamental education in municipal public networks, in the state of São Paulo. In this sense, new studies with primary data of a qualitative and quantitative nature can be developed to deepen the assessment of the best paths for education in São Paulo and Brazil. As the teacher component of elementary education in the municipalities appeared insistently in the results of this study and in others indicated in the literature, a first investigation into how the careers of professionals in elementary education are structured, developed and operationalized seems to be the most urgent. Aspects of the definition and development of the teaching career are the most pressing.