Table 4 shows statistics for outcome and teacher education variables, and relevant available covariates in this sample. The average math score dropped from 475.6 to 450.8 points in this period, a reduction of 0.31 standard deviation from the average obtained in 2009. This decrease came together with the increase of the dispersion of results among students, captured by the rise in the standard deviation. Portuguese average score, on the other hand, rose from 477.1 to 490.2 points, an increase of 0.15 standard deviation from the average obtained in 2009, and there was a reduction in the dispersion of scores.

Table 4 – Summary Statistics for Student and School Variables, by year, 2009 and 2011.

||||2009<br>|||||2015<br>|||
|---|---|---|---|---|---|---|---|---|---|---|
|Covariate|obs.|mean|sd.|min.|max.|obs.|mean|sd.|min.|max.|
|||_S_|_tudent le_|_vel varia_|_bles_||||||
|Math score|523,043|475.6|79.6|345.2|939.5|793,728|450.8|85.8|285.4|999.5|
|Portuguese score|523,043|477.1|90.0|224.3|835.6|793,728|490.2|66.4|303.3|795.4|
|Female|523,043|62.5%|48.4%|0%|100%|793,728|59.3%|49.1%|0%|100%|
|Black|466,681|11.2%|31.5%|0%|100%|784,540|12.5%|33.1%|0%|100%|
|Mother secondary|456,105|38.2%|48.6%|0%|100%|755,439|46.2%|49.9%|0%|100%|
|Car|463,789|44.7%|49.7%|0%|100%|793,621|42.0%|49.4%|0%|100%|
|Computer & Internet|463,685|41.7%|49.3%|0%|100%|793,614|56.3%|49.6%|0%|100%|
|Work|446,886|47.3%|49.9%|0%|100%|793,614|34.7%|47.6%|0%|100%|
|Private primary|466,374|14.0%|34.7%|0%|100%|793,614|15.5%|36.2%|0%|100%|
|Evening classes|459,708|40.2%|49.0%|0%|100%|793,613|25.6%|43.7%|0%|100%|
|||_S_|_chool lev_|_el varia_|_bles_||||||
|Infra PNE|11,355|0.193|0.395|0.000|1.000|11,355|0.305|0.460|0.000|1.000|
|Class hours|11,355|4.4|0.5|3.0|8.0<br>|11,355|4.8|1.1|2.7|12.9|
|Class size|11,355|34|6|11|214<br>|11,355|31|6|7|222|
|Participation ENEM|11,355|35.9%|17.4%|1.3%|100%|11,355|54.5%|19.4%|3.8%|100%|
|Math classes higher<sup>*</sup>|11,336|93.0%|18.9%|0%|100%|11,317|95.1%|13.7%|0%|100%|
|Math classes higher field<sup>**</sup>|11,336|71.8%|32.7%|0%|100%|11,317|76.4%|27.9%|0%|100%|
|Portuguese classes higher<sup>*</sup>|10,857|94.9%|15.5%|0%|100%|11,323|96.9%|10.3%|0%|100%|
|Portuguese classes higher field<sup>**</sup>|10,857|84.3%|26.1%|0%|100%|11,323|82.1%|25.4%|0%|100%|

_Note._ Students in the 3rd year of public regular secondary school that participate in ENEM. _Infra PNE_ : _Indicator for school infrastructure_ from Observatory of theNational Education Plan (Observatório PNE). *% classes taught by teacher with higher education. **% classes taught by teacher with higher education in the field. _Source._ ENEM,and School Census microdata.

In the same period, the percentage of classes taught by teachers with higher education increased by about 2 percentage points for both math and Portuguese. This result was accompanied by the increase of 4.6 percentage points in the percentage of math classes taught by teacher with higher education in this field, and the decline of almost 2.2 percentage points in the indicator for Portuguese classes. That is, the growth of teacher-specific training for the discipline, from an aggregate point of view, does not seem to have had a positive relationship with student performance.

Some important changes occurred in the period that may be correlated with students’ results. Regarding the educational offer conditions, the percentage of students attending evening classes decreased from 40.2% to 25.6%, the average duration of classes increased from 4.4 to 4.8 hours, the average number of students per class decreased from 34 to 31, and the school infrastructure indicator increased from 0.193 to 0.305. In relation to students’ profile, the percentage of students who have already worked decreased from 47.3% to 34.7%, the percentage of students with mothers with complete secondary education rose from 38.2% to 46.2%, and the percentage of students with computer and Internet access at home increased from 41.7% to 56.3%. The other covariates showed minor variation.

Table 5 presents the percentiles of the _percentage of classes taught by teachers with higher education_ and _with higher education in the field_ in years 2009 and 2015. While more than 80% of the schools already had all math and Portuguese classes taught by higher-educated teachers in 2009, big changes occurred in the lowest percentiles. For example, 95% of the schools had more than half of its math classes taught by teachers with higher education in 2009 and six year later the same proportion of schools had more of 66.7% of its math classes taught by teachers with that degree. For _higher education in the field_ indicator, more than half of schools already had all Portuguese classes with teachers trained in this discipline but the proportion of math classes with teachers trained in math is much far from being complete. In general, 9