Relationship between educational performance and students quantity: a regional empirical analysis with data of the SARESP

This study contains an empirical investigation about the existence or otherwise of a relationship between the students number in schools and the educational performance in mathematics. Do schools with larger numbers of students achieve better results? To answer this question, we used data of the SARESP, grouped according to the regions of the state of São Paulo, to perform a correlation analysis between the number of students per school, who participated in the evaluation, and the average in mathematics achieved. The correlation coefficients were calculated and interpreted considering information referring to the years 2008 and 2013. From the scatter plots and correlation coefficients, computed using software R, associated to the number of student that participated of the evaluation in 2008 and 2013 and performance in mathematics, it was possible identify that are regions of the State in which schools with higher quantities of students performed better. On the other hand, in other regions the correlation coefficient explained a weak relation for such variable. Thus, the same assertion cannot be maintained for all regions in the two years considered in this research. The presence of regional characteristics and other variables associated with the number of students per school and educational performance can play a significant role in the investigation by all association between both variables.