We explored whether the information shock contributed incremental impact to the program. Table 29 presents results for the 292 sub-sample that includes only the 156 schools that received the complete treatment. We can see that results are quite similar, but slightly higher. On SPAECE, results for Math range from 0.078 to 0.081 across specifications 3 to 5; for Portuguese, they range from 0.044 to 0.055. For the subsample of students who took ENEM in 2015 and 2014, results for Portuguese range from 0.055 to 0.056, and for Math the effect is 0.038 in specification 5.

These higher results reinforce the importance of the feedback bulletin. In the subsequent analysis, we focus on the 292-school sample.

_c. Intent to treat - heterogeneous effects_ The design of this program was inspired by evidence from large-scale classroom observations in Brazil and six other Latin American countries showing that average classroom practice varies tremendously across schools and across teachers within a school. The program’s goals were to help schools with the weakest average practice improve and to help the weaker teachers within schools to improve. Thus, interesting questions are whether the program differentially impacted teachers and schools at different levels of baseline performance – both in terms of classroom management and student learning.

We used quartile analysis to test two main hypotheses: that the program might have strongest effects on schools with: i) the lowest student learning performance at baseline; and ii) the worst classroom dynamics at baseline. Our complete results are included in Annex tables A19 to A23.

We did not find evidence that schools in the bottom quartiles of the learning distribution improved more (Annex Table A19). Although the logic of the teacher feedback and coaching program is that improvements in teacher practice can raise student learning, this program did not focus directly on the sources of low learning performance in schools or provide tailored strategies for improving learning in those contexts. It could be that schools with persistently low learning outcomes need more intensive interventions, and/or more sustained support.

However, we did find differential impacts on schools stratified by their classroom dynamics at baseline. The strongest finding is that learning gains were highest for schools with the worst performance on classroom management at baseline (i.e., top quartile of this distribution). Schools in the top quartile _averaged_ a very high 34% percent of total class time on classroom management, compared with the good practice indicator of 15% and the sample average of 24%. As Table 30 shows, schools in this top quartile of this distribution at baseline saw very significant increases on SPAECE of 0.17 SD in Math and 0.12 SD in Portuguese on SPAECE and on ENEM of 0.14 SD in Math and 0.15 SD in Portuguese as a result of the program. Table 30: Heterogeneous Impact of Program on Schools, by Share of Time on Classroom Management at Baseline (292 school sample)

|<br>Dependent Variable|(Quartile 1)<br> 0.00- 0.19|(Quartile 2)<br> 0.19- 0.23|(Quartile 3)<br> 0.23- 0.28|(Quartile 4)<br> 0.28- 0.49|p-value|
|---|---|---|---|---|---|
|**SPAECE** **1**<sup>**st**</sup> **Grade**||||||
|Spaece - Mathematics|0.007<br>[0.097]|0.035<br>[0.055]|0.057<br>[0.060]|0.167***<br>[0.061]|0.341|
|Spaece - Portuguese|0.060<br>[0.066]|-0.042<br>[0.040]|0.022<br>[0.051]|0.117***<br>[0.045]|0.064|
|N|7443|9777|9396|9773||
|**ENEM** **3**<sup>**rd**</sup> **Grade** **(controli**|**ng** **for** **ENEM** **t-1)**|||||
|ENEM - Portuguese|0.045<br>[0.053]|-0.016<br>[0.048]|0.024<br>[0.043]|0.146***<br>[0.047]|0.098|
|ENEM - Mathematics|0.014<br>[0.056]|-0.035<br>[0.053]|0.025<br>[0.057]|0.137***<br>[0.049]|0.103|
|N<br>Note: All specifications inclu<br>and previous achievment. St<br>1=Quartile 2=Quartile 3=Qu|5220<br>de student control<br>andard errors in b<br>artile 4. Statistical|6829<br>s for age, sex, rac<br>rakets, clustered <br>significance levels|6048<br>e, parental educa<br>at the school level<br> * p<0.1 ** p<0.0|6249<br>tion, paved street,<br> . P-value tests if Q<br>5 *** p<0.01.|cash transfer<br>uartile|

Even though there is an arithmetic inverse relationship between the average time spent on classroom management and time off-task and the average time spent on instruction, we did not find equally strong impacts on schools stratified by these other, related, variables. Schools in the second-to-bottom quartile of the distribution on the share of time “off-task” at baseline seem to have improved the most, and schools in the third quartile on the share of time on instruction at baseline improved seems to have improved most, but these impacts are not significantly different from the other quartiles (Annex Tables A20 and A21).

Given the program’s goal of stimulating more consistent teacher practice within schools, we also asked whether the program had stronger impacts in schools with larger variance on time on instruction at baseline, but we did not find evidence to support this (Annex table A22). Finally, we looked at schools with 34