Analysis of learning inequalities in the elementary education of Espírito Santo through the inequality and learning indicator (IDeA)

ABSTRACT

This paper investigates learning inequalities by socioeconomic status, gender, and race in elementary education in Espírito Santo using the Inequality and Learning Indicator (IDeA). It assumes the right to education as an implicit theoretical framework and employs a mixed methodological approach, combining documentary research on the foundations of the IDeA with descriptive and correlational quantitative analyses considering the 78 municipalities of the state as units of analysis. The results reveal persistent educational inequality in Espírito Santo and suggest that socioeconomic, racial, and gender factors exacerbate these disparities, especially in regions with higher levels of learning. The urgency of developing school attendance and learning indicators aimed at reducing these inequalities is emphasized, promoting a more inclusive and equitable educational system.

Keywords:
Performance Indicators; Educational Inequalities; Right to Education

RESUMO

Este artigo investiga as desigualdades de aprendizado por nível socioeconômico, sexo e raça no ensino fundamental do Espírito Santo por meio do Indicador de Desigualdades e Aprendizagens (IDeA). Assume o direito à educação como referencial teórico implícito e adota uma abordagem metodológica mista, combinando pesquisa documental sobre as bases que sustentam o IDeA com análises quantitativas descritivas e correlacionais que consideram os 78 municípios do estado como unidades de análises. Os resultados obtidos revelam uma persistente desigualdade educacional no Espírito Santo e sugerem que os fatores socioeconômicos, raciais e de sexo ampliam essas disparidades especialmente em regiões com níveis mais elevados de aprendizado. Destaca-se a urgência de desenvolver indicadores de atendimento escolar e aprendizagem que visem reduzir essas desigualdades, promovendo um sistema educacional mais inclusivo e equitativo.

Palavras-chave:
Indicadores de Desempenho; Desigualdades Educacionais; Direito à Educação

RESUMEN

Este artículo investiga las desigualdades de aprendizaje por nivel socioeconómico, sexo y raza en la educación primaria en Espírito Santo utilizando el Indicador de Desigualdades y Aprendizajes (IDeA). Asume el Derecho a la Educación como un marco teórico implícito y emplea un enfoque metodológico mixto, combinando investigación documental sobre las bases del IDeA con análisis cuantitativos descriptivos y correlacionales que consideran los 78 municipios del Estado como unidades de análisis. Los resultados revelan una persistente desigualdad educativa en Espírito Santo y sugieren que los factores socioeconómicos, raciales y de género agravan estas disparidades, especialmente en regiones con niveles más altos de aprendizaje. Se destaca la urgencia de desarrollar indicadores de asistencia escolar y aprendizaje destinados a reducir estas desigualdades, promoviendo un sistema educativo más inclusivo y equitativo.

Palabras clave:
Indicadores de Rendimiento; Desigualdades Educativas; Derecho a la Educación

INTRODUCTION

Education is enshrined as the first of the social rights recognized by Brazil's Federal Constitution of 1988 (Art. 6), which determines that quality standards be guaranteed as one of the fundamental principles of education (Subsection VII, Art. 206) (Brasil, 1988). However, the full exercise of this right still faces significant obstacles, manifesting itself most clearly in the educational inequalities that permeate our society.

From the perspective of educational assessment, Soares (2006) explains that an educational system is considered equitable when the distribution of performance among groups of students defined by their social and demographic characteristics is equivalent to the overall distribution of students. In this context, the quality of education would not be susceptible to external factors specific to each student. However, we must acknowledge the existence of factors that can foster substantial disparities among different groups of students, directly impacting their educational outcomes. Among these, Soares, Rodrigues, and Ernica (2019) highlight three main sources of inequality: socioeconomic status (SES), race, and gender.

Regarding the first, studies show that schools with better educational outcomes are those that serve a smaller percentage of students in vulnerable situations (Freitas, 2007; Almeida, Dalben and Freitas, 2013; Alves and Soares, 2013; Soares and Xavier, 2013; Chirinéa and Brandão, 2015; Matos and Rodrigues, 2016). Regarding the multiple dimensions of race, the academic literature indicates that White students have higher educational performance than non-White students (Soares and Delgado, 2016; Bof, Oliveira and Barros, 2018; Sousa and Roncalli, 2021). Regarding gender, female students generally perform better on language tests than male students. For mathematics, this relationship is usually reversed, although the educational equity is higher than in language arts (Soares and Collares, 2006; Menezes Filho, 2012; Machado, 2014; Ernica and Rodrigues, 2020).

To assess exclusions caused by low academic performance and educational inequality, considering socioeconomic status, race, and gender, the Inequality and Learning Indicator (IDeA) was launched in 2019. According to its creators, its development was "motivated by the conviction that defending the right to education requires tools to verify its realization" (Soares, Rodrigues and Ernica, 2019, p. 2).

Recognizing that it is essential to bring to the debate proposals and reflections that help guarantee this right, with social equity, and valuing all diversity, this article seeks to address the following research question: How are educational inequalities manifested in Espírito Santo? Thus, the initial objective of this article is to present the methodological foundations of the IDeA, through an analysis and discussion of the construction of its algorithm. To support this initiative, learning disparities related to SES, gender, and race in the municipalities of Espírito Santo will be analyzed using primary school as the object of study, and the right to education as an implicit theoretical framework.

METHODOLOGY

This article adopts a mixed-methods approach, employing a sequential exploratory strategy (Creswell and Clark, 2015), which initially emphasizes a qualitative phase, through a literature review on the IDeA, followed by a quantitative phase, comprising analyses of educational inequalities present in the 78 municipalities of Espírito Santo. These inequalities are examined in relation to SES, gender, and race, as expressed by the indicator.

According to Kripka, Scheller and Bonotto (2015, p. 58), documentary research in qualitative analysis "is that in which the data obtained are derived strictly from documents, with the aim of extracting information contained therein to understand a phenomenon." Thus, the sources are official technical notes produced to help understand the algorithm of the indicator and provide guidelines for its responsible use (Fernandes and Felicio, 2019; Ernica, Rodrigues and Soares, 2023). These documents are organized on the IDeA website.¹ This platform contains a vast repository of content and other resources that can help foster debate about educational inequalities, such as articles, technical reports, and videos on education, inequalities, and their effects.

The quantitative analysis involved the application of descriptive and correlational techniques. For the former, in addition to the results of classical descriptive statistics (mean, standard deviation, and coefficient of variation—CV), scatter plots and geospatial maps are presented to facilitate the visualization of data according to their distribution by educational level and location, respectively. For the latter, Pearson's correlation coefficient was used, and the assumption of data normality was verified using the Kolmogorov-Smirnov test. Comparisons of means were also performed using Student's t-test (Gujarati and Porter, 2011).

The results for the 78 municipalities in the state for the 5^th and 9^th grades of primary school in Portuguese and mathematics were considered as units of analysis, based on the 2013, 2015, and 2017 editions of the Prova Brasil tests, the most recent data available on the IDeA website at the time of the study. In all analyses performed, basic functions of the R language were used (R Core Team, 2020). Descriptive and correlational analyses were performed using the MASS package (Venables and Ripley, 2002). The graphs and maps were constructed using the ggplot2 (Wickham et al., 2016) and geobr (Pereira and Barbosa, 2019) packages.

To promote the transparency and replicability of this study, all source codes used in the analysis, the database used, and the generated images are available in a public repository on GitHub. Interested parties can access these resources at the following link: https://github.com/denilsonjms/PhD-Thesis.

INEQUALITY AND LEARNING INDICATOR

The IDeA indicator was developed from an initiative to measure students’ learning levels and their disparities across social groups as defined by three main sources of inequality: SES, race, and gender. IDeA was conceived within the context of the project Educational Inequalities in Contemporary Brazil, based at the Center for Public Policy Studies (NEPP) at the Universidade Estadual de Campinas (UNICAMP). It was presented on June 25 and 26, 2019, during the "Seminar on Democracy, Education, and Equity: An Agenda for All²," organized by the Tide Setubal Foundation in partnership with the Teaching and Research Institute (INSPER) and the United Nations Educational, Scientific and Cultural Organization (UNESCO) in Brazil.

According to Soares, Rodrigues, and Ernica (2019), who conceived the IDeA indicator, it is based on the 1988 Federal Constitution and was created to help verify the effective realization of the right to basic education, by producing information on student learning and addressing two aspects through which this right is not being fulfilled:

• exclusion due to low levels of learning;

• exclusion due to learning inequality.

Thus, the indicator enables Brazilian society to describe and evaluate its education system, informing the formulation of public policies to address its specific needs.

To do so, the IDeA algorithm uses a non-symmetric measure of the difference between two probability distributions — in this case, regarding the learning of different groups — known as the Kullback-Leibler (KL) divergence.³ Thus, based on data extracted from the Prova Brasil test, administered between 2007 and 2017 and grouped into four sets of three successive editions (2007–2009–2011; 2009–2011–2013; 2011–2013–2015, and 2013–2015–2017), the level of learning in Portuguese and mathematics and learning inequalities for the social characteristics considered (race, gender, and SES) were calculated for 5^th and 9^th grade students (Ernica, Rodrigues and Soares, 2023).

The reference learning distribution in IDeA was calculated based on the academic performance of a typical Organisation for Economic Co-operation and Development (OECD) country, in line with the methodological process used to set the targets for the Basic Education Development Index (Ideb),⁴ to equate the scores achieved by that country in the Programme for International Student Assessment (PISA) with a possible score on the Prova Brasil (Ernica, Rodrigues and Soares, 2023). Then, using partitioning clustering techniques from cluster analysis,⁵ it was possible to group the municipalities into five bands on the KL scale, whose values, defined based on the 2013–2015–2017 test triad, are presented in Table 1.

Table 1
Values defined for the bands of the Kullback-Leibler divergence scale for the 2013-2015-2017 Prova Brasil test series.

Level of learning	5th grade	9th grade
High	> -0.27	> -0.45
Upper-middle	-0.6 < x < -0.27	-0.60 < x < -0.45
Medium	-1.06 < x < -0.6	-0.83 < x < -0.60
Low-medium	-1.35 < x < -1.06	-1.16 < x < -0.83
Low	< -1.35	< -1.16

It is worth noting that the negative numbers used in these standardized measures indicate the distance between them and the desired level of learning, which is expressed by the value "zero." Thus, the further the negative index is from this value, the lower the learning outcomes. Positive indices indicate that learning in the municipality exceeds the reference situation (Ernica, Rodrigues and Soares, 2023).

For the social factors analyzed, values close to "zero" indicate equality, positive values show the existence of atypical situations, and negative values signal inequalities. Thus, the larger they are in magnitude, the more pronounced the inequalities will be. For the social factors of SES and race, three main interpretive ranges were defined: inequality, equity, and atypical situations. The first of these was subdivided into three ranges: inequality, high inequality, and extreme inequality. For the gender factor, only the inequality and equity ranges were considered, assuming the absence of atypical situations. In this case, inequalities are categorized into three levels: low inequality, inequality, and high inequality.

According to the IDeA technical note, this division into categories was performed through cluster analysis using the k-means method.⁶ The values defined as thresholds for the categories of the KL scale, considering atypical situations, of equity, and of levels of learning inequality by social groups, are presented in Table 2.

Table 2
Values defined for the bands of the Kullback-Leibler divergence scale for atypical situations, of equity, and levels of learning inequality by social group.

			Extreme inequality	High inequality	Inequality	Low inequality	Equity	Atypical situations
SES	5th grade	Portuguese	[--, -0.962)	[-0.962, -0.506)	[-0.506, -0.00151)	-	[-0.00151, 0.00151)	[0.00151, --)
		Mathematics	[--, -1.01)	[-1.01, -0.541)	[-0.541, -0.00151)	--	[-0.00151, 0.00151)	[0.00151, --)
	9th grade	Portuguese	[--, -0.876)	[-0.876, -0.468)	[-0.468, -0.00108)	--	[-0.00108, 0.00108)	[0.00108, --)
		Mathematics	[--, -0.907)	[-0.907, -0.477)	[-0.477, -0.00108)	--	[-0.00108, 0.00108)	[0.00108, --)
Race	5th grade	Portuguese	[--, -0.899)	[-0.899, -0.54)	[-0.54, -0.00151)	--	[-0.00151, 0.00151)	[0.00151, --)
		Mathematics	[--, -0.934)	[-0.934, -0.549)	[-0.549, -0.00151)	--	[-0.00151, 0.00151)	[0.00151, --)
	9th grade	Portuguese	[--, -0.849)	[-0.849, -0.488)	[-0.488, -0.00108)	--	[-0.00108, 0.00108)	[0.00108, --)
		Mathematics	[--, -0.852)	[-0.852, -0.502)	[-0.502, -0.00108)	--	[-0.00108, 0.00108)	[0.00108, --)
Gender	5th grade	Portuguese	--	[--, -0.599)	[-0.599, -0.205)	[-0.205, -0.00151)	[-0.00151, 0.00151)	[0.00151, --)
		Mathematics	--	[--, -0.636)	[-0.636, -0.216)	[-0.216, -0.00151)	[-0.00151, 0.00151)	[0.00151, --)
	9th grade	Portuguese	--	[--, -0.628)	[-0.628, -0.235)	[-0.235, -0.00108)	[-0.00108, 0.00108)	--
		Mathematics	--	[--, -0.597)	[-0.597, -0.19)	[-0.19, -0.00108)	[-0.00108, 0.00108)	--

The results of the indicator's readings can be viewed on the IDeA website, where, through an educational platform, users can generate graphs showing learning levels and inequality by Brazilian municipalities, states, and regions, and can also apply filters based on classifications for these levels or the number of inhabitants in the municipalities, for example.

INEQUALITY AND LEARNING INDICATOR (IDEA) ANALYSIS FOR THE MUNICIPALITIES OF ESPÍRITO SANTO

Espírito Santo has shown significant progress in educational measures, as determined by standardized testing since the beginning of this century. The most recent learning measure proposed by IDeA, for example, which uses data from the Prova Brasil exams for the 2013–2015–2017 period, indicates that, for 5^th grade students, in both Portuguese and mathematics, municipalities with medium-high or high learning levels predominate in the state. For 9^th grade, in Portuguese, there is a prevalence in the state of municipalities with medium or higher learning levels. In mathematics, most municipalities have low or medium-low learning levels.

However, Espírito Santo still exhibits concerning levels of regional inequalities, which have been the subject of study by researchers from different scientific fields (Barros et al., 2010; Ferrari and Castro, 2011; Leite and Magalhães, 2012; Grassi and Araújo, 2013; Campos, Silva and Valpassos, 2019) and are also evident in the educational sphere, as can be seen from an analysis of IDeA data. Tables 3, 4, and 5, for example, constructed from information obtained from the IDeA portal, show the frequency distribution by social groups in the state, considering the classification regarding inequality in learning Portuguese and mathematics for the 5^th and 9^th grades, respectively.

Table 3
Distribution of municipalities in Espírito Santo by level and learning inequality based on the socioeconomic status factor.

Grade level assessed	Classification	High		Medium-high		Medium		Low-medium		Low		Total
		Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)
5th Grade	Equity	0	0	0	0	0	0	0	0	0	0	0	0
	Inequality	39.74	3.85	24.36	42.31	1.28	15.38	0	1.28	0	0	65.38	62.82
	High inequality	16.67	11.54	10.26	16.67	2.56	2.56	0	1.28	0	0	29.49	32.05
	Extreme inequality	3.85	0	1.28	3.85	0	1.28	0	0	0	0	5.13	5.13
	Total	60.26	15.38	35.90	62.82	3.85	19.23	0	2.56	0	0	100	100
9th grade	Equity	0	0	2.56	0	2.56	0	3.85	0	0	2.56	8.97	2.56
	Inequality	15.38	5.13	24.36	10.26	26.92	16.67	6.41	38.46	1.28	6.41	74.35	76.93
	High inequality	3.85	1.28	6.41	5.13	3.85	3.85	1.28	6.41	1.28	1.28	16.67	17.95
	Extreme inequality	0	0	0	1.28	0	1.28	0	0	0	0	0	2.56
	Total	19.23	6.41	33.33	16.67	33.33	21.79	11.54	44.87	2.56	10.26	100	100

Table 4
Distribution of municipalities in Espírito Santo by level and learning inequality by race.

Level assessed	Classification	High		Medium-high		Medium		Low-medium		Low		Total
		Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)
5th Grade	Equity	0	0	2.56	0	1.28	0	0	0	0	0	3.84	0
	Inequality	24.36	2.56	16.67	29.49	0	12.82	0	0	0	0	41.03	44.87
	High inequality	17.95	6.41	15.38	20.51	2.56	6.41	0	1.28	0	0	35.89	34.61
	Extreme inequality	17.95	6.41	1.28	12.82	0	0	0	1.28	0	0	19.23	20.51
	Total	60.26	15.38	35.89	62.82	3.84	19.23	0	2.56	0	0	100	100
9th grade	Equity	0	0	5.13	0	2.56	3.85	2.56	3.85	0	0	10.25	7.7
	Inequality	6.41	0	12.82	6.41	23.08	8.97	2.56	26.92	0	5.13	44.87	47.43
	High inequality	5.13	3.85	10.26	3.85	7.69	5.13	2.56	10.26	0	3.85	25.64	26.94
	Extreme inequality	5.13	2.56	5.13	6.41	0	3.85	3.85	3.85	2.56	1.28	16.67	17.95
	Atypical situations	2.56	0	0	0	0	0	0	0	0	0	2.56	0
	Total	19.23	6.41	33.33	16.67	33.33	21.79	11.54	44.87	2.56	10.26	100	100

Table 5
Distribution of municipalities in Espírito Santo by level and learning inequality by gender.

Level assessed	Classification	High		Upper-middle		Medium		Low-medium		Low		Total
		Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)	Port. (%)	Math. (%)
5th Grade	Equity	0	11.54	2.56	32.05	0	7.69	0	1.28	0	0	2.56	52.56
	Low inequality	58.97	3.85	26.92	30.77	2.56	11.54	0	1.28	0	0	88.45	47.44
	Inequality	1.28	0	6.41	0	1.28	0	0	0	0	0	8.97	0
	High inequality	0	0	0	0	0	0	0	0	0	0	0	0
	Total	60.26	15.38	35.90	62.82	3.85	19.23	0	2.56	0	0	100	100
9th grade	Equity	0	2.56	0	3.85	0	5.13	0	11.54	0	5.13	0	28.21
	Low inequality	19.23	3.85	32.05	12.82	30.77	16.67	10.26	32.05	2.56	5.13	94.87	70.52
	Inequality	0	0	1.28	0	1.28	0	1.28	1.28	0	0	3.85	1.28
	High inequality	0	0	0	0	1.28	0	0	0	0	0	1.28	0
	Total	19.23	6.41	33.33	16.67	33.33	21.80	11.54	44.87	2.56	10.26	100	100

Overall, the highest percentages for high or extreme inequality are concentrated in municipalities with high or medium-high levels of learning. For the SES and race factors, it is worth noting the low percentage of municipalities in a situation of equity in both grade levels and in both subjects. For these factors, it is also possible to observe that the distribution of municipalities by levels of inequality in the Portuguese and mathematics is similar, indicating a possible association between them.

Specifically for the SES factor, Table 3 indicates that more (less) vulnerable students tend to perform worse (better) on the Prova Brasil, a fact that, in turn, confirms a hypothesis widely discussed in studies on educational assessment (Alves and Soares, 2013; Alves, Gouvêa and Viana, 2014; Soares, Soares and Santos, 2020).

Although this is an expected finding, the absence of effective public policies to address it remains surprising. Alves, Soares, and Xavier (2014) demonstrated that the performance gap on the Prova Brasil between students in the first and fifth quintiles of the measure they propose for SES can reach two years of schooling. In other words, students with lower SES levels who are in the 9^th grade, for example, would have a level of knowledge equivalent to that expected of students in the 7^th grade. This gap is reflected in increased school dropout rates and highlights the inefficiency of our public schools in ensuring equal opportunities for the students who attend them.

Regarding the race factor, Table 4 indicates that, in the state as a whole, White students generally have higher learning levels than non-White students, following a national trend also noted in the academic literature (Soares and Delgado, 2016; Bof, Oliveira and Barros, 2018; Sousa and Roncalli, 2021). However, for the 9^th grade, two municipalities with high learning levels exhibit behavior contrary to what is expected: Domingos Martins and Ibatiba. In these municipalities, non-White students have, on average, higher learning levels than White students, which is an atypical situation.

It is worth noting that both are small municipalities,⁷ whose populations are predominantly White, a reflection of immigration — primarily German and Portuguese, respectively — that shaped their territories. According to data from Management and Innovation Secretariat (SEDU, 2022), of the enrollments in basic education that include a declaration of color/race, 63.35% of the students in Domingos Martins and 56.65% in Ibatiba identify as White, which, in itself, reflects an atypical situation, considering that the average percentage of students who identify as White in the state is only 34.34%. However, although this is not the focus of this article, it highlights the importance of investigating the processes that shape the practices and subjectivities adopted by educational agents in these municipalities, which may explain this phenomenon. For the other social factors investigated, no atypical situations were found.

It is also important to highlight the number of municipalities experiencing extreme inequality in this regard. For 5^th and 9^th graders, in both subjects, approximately one in five and one in six municipalities, respectively, are in this situation, with a higher concentration in municipalities that have high or medium-high levels of learning. Soares and Alves (2013) suggest two possible explanations for this phenomenon:

• practices and attitudes within schools may favor White students;

• performance differences are amplified in more favorable contexts, that is, in schools with better infrastructure, better teachers, and students on regular schooling trajectories.

Considering gender, in mathematics, learning equity predominates in 5^th grade. For the 9^th grade, the vast majority of municipalities exhibit low inequality. In both grades, the learning scores achieved by male students in mathematics are slightly higher than those achieved by female students. However, for Portuguese, where municipalities with low inequality predominate, the opposite effect occurs; that is, female students tend to achieve better results than male students, following a national trend also noted in the specialized literature (Soares and Collares, 2006; Menezes Filho, 2012; Machado, 2014; Ernica and Rodrigues, 2020).

Although there is no consensus in the educational literature to explain these differences, some authors have formulated hypotheses that may account for them. Senkevics and Carvalho (2015), in the national context, and Sammons et al. (2008), in the international context, argue that family socialization may contribute to gender inequalities in elementary education. According to the authors, the more rigid, restricted, and controlled routine in families’ daily lives could favor women's success in school activities. Eurydice (2010) suggests that, on the one hand, girls read more books and thus excel in items based on literary texts. In contrast, boys have higher self-esteem regarding their mathematical ability. Soares and Alves (2013, p. 507) indicate that the presence of more girls in school can create "a more orderly academic environment conducive to learning." However, the academic literature still lacks more conclusive studies on this topic.

It is also worth noting that the social characteristics analyzed individually also influence student learning collectively. Soares and Delgado (2016), in an effort to consider groups formed by multiple factors, showed that the group of Black girls from low SES backgrounds would take 78 years to reach the benchmark distribution for reading achievement. In mathematics, this timeframe would be 57 years. For the group of White boys from high SES, this timeframe would be 14 and nine years, respectively. Although still far from the ideal, the gap between these groups is troubling, and will not close unless new policies to reduce inequalities are urgently implemented.

Figures 1 and 2 below illustrate how inequalities by social group and learning outcomes in Portuguese and mathematics are interrelated for 5^th and 9^th grade students, respectively. To this end, in addition to the frequency distribution and dispersion graphs between the variables, the Pearson correlation coefficient is presented to quantify this association.

Figure 1
Correlation between learning levels in the 5^th grade and inequalities by socioeconomic status, race, and gender.

Figure 2
Correlation between learning levels in the 9^th grade and inequalities by socioeconomic status, race, and gender.

It can be observed that performance in Portuguese and mathematics is strongly correlated, meaning that when one is high (or low), the other also tends to be high (or low). However, on average, the learning indicator for Portuguese was higher than that for mathematics in both situations. For 5^th grade, the standardized means were -0.282 (standard deviation —SD = 0.152; CV = 53.95%) and -0.478 (SD = 0.214; CV = 44.83%), respectively. The difference between these standardized means was statistically significant (t[139] = 6.560; p < 0.001). For 9^th grade, the standardized means were -0.630 (SD = 0.208; CV = 33.048%) and -0.825 (SD = 0.271; CV = 32.795%), respectively, and the difference between these standardized means was also statistically significant (t[143] = 3.588; p < 0.001).

It is also worth noting that, for 9^th grade, the level of learning in both subjects was found to be statistically correlated with SES-based inequalities, indicating that the higher (lower) the average academic performance in a municipality, the more (less) pronounced the SES-based educational inequalities experienced there generally are. In mathematics, the learning index was also found to be statistically correlated with existing inequalities when considering race.

Regarding the associations within each social factor, analyzed in isolation, it is seen that the inequality indices in mathematics and Portuguese are also significantly correlated. Thus, the greater (or smaller) the inequality due to a given social factor in one subject, the greater (or smaller) the inequality tends to be due to that same factor in another. The only exception occurs for gender in 9^th grade. Furthermore, in both grades, the correlation between the inequality indices for SES and race stands out, which was expected, considering that there is a historic disparity in income distribution by race in Brazil.

The high CV index calculated for the learning measures indicates a high variability in scores, which in itself would be an indication of territorial inequality. However, to conduct a geospatial analysis of this type of inequality, considering students’ educational levels measured via IDeA, Figures 3 and 4 were constructed for the 5^th and 9^th grades, respectively.

Figure 3
Geospatial analysis of changes in educational levels, measured via IDeA, for the 5th grade.

Figure 4
Geospatial analysis of changes in educational levels, measured via IDeA, for the 9^th grade.

The maps show that in both subjects and both grades analyzed, educational outcomes are not uniformly distributed across all regions of Espírito Santo. The concentration of municipalities with higher learning indices in the central mesoregion, compared to the northwest and south regions, suggests the existence of significant regional disparities.

These results are consistent with those obtained by Soares et al. (2020), who empirically demonstrated that, within the state, educational opportunities manifest in distinct ways and are not associated with the wealth of each region. In fact, the southern coastal mesoregion of Espírito Santo, which stands out negatively in the learning indices presented, concentrates the municipalities with the highest Gross Domestic Product (GDP) per capita in the state, such as Itapemirim (2020 GDP per capita = R$ 93,609.55) and Presidente Kennedy (2020 GDP per capita = R$ 301,474.89), a reflection of the mineral extraction industry, royalty revenues, and special participations from oil and gas extraction.

FINAL CONSIDERATIONS

The initial objective of this article was to demonstrate the methodological foundations underpinning the IDeA indicator, through an analysis and discussion of the construction of its algorithm. To support this initiative, the study analyzed learning disparities related to socioeconomic status, gender, and race in the municipalities of Espírito Santo, using primary education as the object of study, and taking the right to education as an implicit theoretical framework.

The results indicate that education remains an unequally distributed social product. Specifically regarding socioeconomic status and race, the percentage of municipalities achieving equity was negligible in both of the subjects and grade levels examined (5^th and 9^th grades). Inequalities regarding gender were less pronounced. Furthermore, it is important to highlight the striking regional disparity in learning in Espírito Santo, which persists regardless of the wealth generated by the municipalities. It should be noted, however, that the inequality indicators for the social factors analyzed did not show differences in distribution across mesoregions, exhibiting patterns that are consistently repeated throughout the state. This suggests that, regardless of each municipality's educational performance, socioeconomic, racial, and gender factors tend to widen existing disparities, especially in regions with higher levels of learning. Thus, effective public policies must be implemented to address these disparities.

The Basic Education Development Index (Ideb), an indicator adopted by the National Educational Plan as the official benchmark for the quality of Brazilian education (Brasil, 2014), is not sensitive to these inequalities, proving insufficient to capture their complexity within the Brazilian educational landscape. With the deadline approaching for meeting its targets, a new indicator for monitoring basic education is being developed. Following the publication of Ordinance No. 556 on October 2, 2020, within the scope of the Anísio Teixeira National Institute for Educational Research and Studies (INEP), a working group was established to prepare a technical study to support an updating of the indicator (Brasil, 2020).

In this context, it is imperative that a new quality indicator, which may replace Ideb, incorporate targets specifically aimed at reducing educational disparities. To do so, a comprehensive assessment must be conducted of the various existing inequalities and effective strategies developed to address them.

Based on this assessment, we suggest reformulating the current system of targets, orienting it not only toward test results but also toward reducing inequalities, with a focus on municipal departments of education and higher-level authorities, rather than on individual educational institutions. This new approach is based on the principle that all social segments must attain minimum educational standards in an inclusive and equitable manner, in accordance with the principles established in the Constitution.

• 1
  These documents are available on the IDeA website: https://portalidea.org.br/. Accessed on: May 21, 2026.
• 2
  For more information about the event, see https://www.insper.edu.br/agenda-de-eventos/desigualdades-educacionais/. Accessed on: May 21, 2026.
• 3
  For more information on Kullback-Leibler divergence, see Kullback and Leibler (1951) and Anderson and Burnham (2002).
• 4
  For more information on the process of aligning PISA and Prova Brasil performance data, see Brasil (2009).
• 5
  For more information on Cluster Analysis, see Theodoridis and Koutroumbas (2001).
• 6
  For more information on Cluster Analysis, see Jain, Murty, and Flynn (1999).
• 7
  Domingos Martins and Ibatiba have an estimated population of 34,120 and 26,762 inhabitants, respectively, according to the Brazilian Institute of Geography and Statistics (IBGE, 2021).
• Funding:
  This study was developed within the scope of the project From standardized exams to the right to learning: experiences for improving the quality of High School in the State Network of Espírito Santo, funded by the Espírito Santo Research and Innovation Support Foundation (FAPES), through FAPES Notice No. 28/2022 – Universal (Process/Protocol No. 53875.821.17880.15022023).

Data availability statement:

The research data is available in a public GitHub repository: https://github.com/denilsonjms/PhD-Thesis.

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Edited by

• Responsible Editor:
  Edla Eggert https://orcid.org/0000-0002-1980-7053

Publication Dates

• Publication in this collection
  07 Aug 2026
• Date of issue
  2026

History

• Received
  19 Mar 2024
• Accepted
  18 June 2025