The program reduced the variation in teacher practice within schools for all three core measures of teacher time allocation. Results are strong and significant in most specifications. The standard deviation within schools in time on instruction fell by -0.016 in the strongest specification. For classroom management activities, the standard deviation fell by -0.012 and for teacher off-task it fell by -0.018. For time on instruction with all students engaged, which improved very little for the whole sample, the change within schools is not significant. For the share of teaching time with a big group of students off-task, results are significant in some specifications, but not with full controls.

_e. Intent to treat - heterogeneous effects_ To assess heterogeneity in treatment effects across the distribution of teachers observed, we use the baseline data to create quartiles for each of the five key measures. It is plausible that the intervention will affect teachers differently according to where they stand in the distribution of our main variables. For example, if a teacher already achieves high time on instruction, it may be hard to improve further. Positive changes may be easier at the bottom of the distribution, where there is large room for improvement. Conversely, if being at the bottom of the distribution is a proxy for low capacity and/or motivation, achieving measurable change in teacher practice – particularly in the space of a single school year – may be more difficult. We use the following equations to estimate heterogeneous effects: �� = �� + ����,��� + �′��� + �����1�,��� + �����2�,��� + �����3�,��� + �����4�,��� + ���1�,��� + ���2�,��� + ���3�,��� + �� (3) where �� is the dependent variable for classroom observation i; ��,��� is the baseline classroom dynamic variable collected in November of 2014; �� represents a vector of pre-intervention characteristics at the school level; �� is an indicator for whether the classroom observed was in a school offered treatment; �1�,���, �2�,���, �3�,���, and �4�,��� are the quartiles (0-25%; 25-50%; 50-75%; and 75-100%) of the baseline classroom dynamic variables ��,���; and �� is the error term, clustered at the school level. The coefficients of interest are ��, ��, �� and ��. Results using specification (4)—OLS results with baseline and all covariates as controls—are presented in the table 9.

Overall, the results in Table 9 show no consistent pattern of heterogeneity connected with teachers’ starting performance. For time on instruction, the strongest effect was concentrated in the second quartile (increase of 8.3% of class time), while results for the other 3 quartiles are relatively homogeneous. For other dimensions, patterns varied. Time spent on classroom management and time off-task is relatively homogeneous, with a slightly stronger effect on quartile 3 for the first (3.1%) and on quartile 4 for the latter (2.6%). A large effect is observed on the share of time a large group of students is off-task in treatment classrooms at the 4th quartile (-7.4%), indicating that the intervention had strongest impacts in highly disorganized classrooms -- where students were disengaged a very high 75-100% of total class time. This is an interesting and potentially significant result, indicating how useful coaching support can be for teachers having particular difficulty in keeping students engaged.

The intervention was organized at the level of the school, so our hypothesis was that the program might impact schools differently, depending on their starting level of average classroom practice (or variance in classroom practice). Controlling for other factors, however, we found only weak evidence that the program affected schools with different average values at baseline differently. As seen in Annex Table 13, we found statistically significant correlations in expected directions for schools at the bottom of the distribution on several key variables: time on instruction rose 6.6 percentage points in schools in the bottom quartile of the distribution (which averaged between 35-59% of class time on instruction at baseline); time on classroom management fell the most for schools in the highest quartile of this distribution at baseline (averaging 2949% of time on classroom management); teacher time off-task fell the most for the top two quartiles of this distribution (10-43% of time off-task); and instructional activities with all students engaged rose the most in schools in the bottom quartile of this distribution (only 0-10% of instructional time with all students engaged). However, p-tests fail to confirm consistent patterns of heterogeneity in the overall distribution of the school-average results.

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