Equity measures in basic education

Given that learning is integral to upholding the constitutional right to education, as discussed in the UNESCO report by Tawil and Locatelli (2015); to monitor a basic education system effectively, it is necessary to measure students´ learning. Measurement methodology directly influences student learning outcomes and impacts the pedagogical strategies of the educational system. Consequently, the design of assessment mechanisms must prioritize the improvement of student learning rather than merely focusing on the act of measurement itself. Measures for both learning quality and equity should be established. For large student groups, the distance from the empirical distribution to a reference distribution can gauge quality. Handcock and Morris (1998) have fully addressed how to calculate this distance using relative distribution. When the number of students considered is small, such as when analyzing the quality of student results in a specific school, the available information may not be sufficient to define the empirical distribution of learning. In these situations, the quality of learning measurement can be assessed by first categorizing students' proficiencies into different learning levels. Four levels are frequently used: Below Basic, Basic, Adequate, and Advanced. Each level gets a quality score, typically like school grades from 0 to 10. This classification and scoring method were commonly used in American state educational systems (Erpenbach, 2009) and Brazil (Soares, 2009). In this study, equity is considered a general characteristic of the students´ performance measurement. Equity exists in the group when the quality measure of the various social groups into which the students are divided is socially equivalent. Usually, considering each relevant social group's performance isn't feasible for sample size reasons. Thus, it's essential to combine these groups into fewer categories to calculate the equity measure. This methodology corresponds to the statistical implementation of Crenshaw's (2013) principle of intersectionality. It was implemented in this work in two distinct ways. First, students were classified using the quintiles of the empirical distribution of performance, and the equity measure is defined as the difference between the average proficiency scores of students in the extreme quintiles. In the second, initially, students are grouped by gender, SES, and race. These groups are first ordered and then aggregate into five equally sized groups. The equity measure is the difference between the quality measure means in the extreme groups. The Brazilian data from the 2019 SAEB were used to validate this proposal. First, it is observed that the two methodologies for defining the reference groups produce convergent results. This is expected considering that the results in educational performance tests are greatly influenced by social capital, especially in Brazil as shown by Nogueira and Nogueira (2002). Since, however, there are students with low and high performance in all social groups, the equity measure made with the social referenced groups produces a lower result than that obtained when the quintiles of the performance distribution are used to create the groups. Due to the presence of students with varying performance levels within all social groups, evaluating equity through the social groups methodology results in lower equity values compared to using performance quintiles. This reflects the presence of students from all social groups across all quintiles. However, socially excluded groups, like poor black boys, are primarily found in the lower-performance quintiles. The data analysis also reveals that in Brazil, where there is quality, there is no equity, confirming earlier findings by Ernica et al. (2024). Brazilian education policies historically focused only on improving results, leading to performance gains for a few students and increasing inequalities. This finding shows how the public policy of rewarding schools with high values is especially mistaken when the aim is to reduce inequalities. Crenshaw. K. W. Mapping the margins: Intersectionality, identity politics, and violence against women of color. In: The public nature of private violence. Routledge, 2013. p. 93-118. Ernica, M., Rodrigues, E. C., & Soares, J. F. (2025). Desigualdades educacionais no Brasil contemporâneo: definição, medida e resultados. Dados, 68(1), e20220109. Erpenbach, W. J. (2009). Determining Adequate Yearly Progress in a State Performance or Proficiency Index Model. Council of Chief State School Officers. Handcock, M. S., & Morris, M. (1998). Relative distribution methods. Sociological Methodology, 28(1), 53-97. Nogueira, C. M. M., & Nogueira, M. A. (2002). A sociologia da educação de Pierre Bourdieu: limites e contribuições. Educação & Sociedade, 23, 15-35. Soares, José Francisco. Índice de desenvolvimento da educação de São Paulo–Idesp. São Paulo em Perspectiva, v. 23, n. 1, p. 29-41, 2009. Tawil, S., & Locatelli, R. (2015). Rethinking education: Towards a global common good. UNESCO