teachers believe, _the relationships index_ which measures teacher beliefs about their relationships with students, colleagues and the head teacher is important.<sup>32</sup> Analysis of the Post-CIF and Post-LASSO regressions show that in a more parsimonious model, offering extra help to lagging students (teacher practice) and the Relationships index (teacher beliefs) are statistically significant at the 1% level. Moving from the 25<sup>th</sup> to the 75<sup>th</sup> percentile in terms of teachers offering extra help to lagging students, is linked to student learning gains of 0.19 SD. Similarly, going from the teacher at the 25<sup>th</sup> percentile to the 75<sup>th</sup> percentile on the Relationships Index is associated with an increase in student learning gains of 0.14 SD.

# **5. Conclusion**

Research on teacher effectiveness has struggled to identify observable teacher characteristics that can help explain variation in student performance. In this study, we apply machine learning methods to this problem. Using matched student-teacher data for Grade 2 and 3 students from across 392 schools in Tanzania, we use two ML approaches, Conditional Inference Forest (CIF) and LASSO, to predict student learning gains.

We find that ML approaches outperform the standard OLS model by 14-24 percent in out-of-sample predictions. Further, even though both CIF and LASSO take different model-building approaches, they produce largely consistent results. As expected, student baseline scores are the most predictive of student learning gains, signaling mean reversion in the data.

Our key finding is that specific elements of what teachers know (teacher preparation); what teachers do (teacher practice); and what teachers believe (teacher beliefs) are more strongly predictive of student learning gains than other teacher, student, and school factors, especially in Math. For Math, CIF results show that the teacher practice of providing written feedback on homework/tests and reviewing key concepts at the end of class (measured through student surveys); the teacher belief that they can help disadvantaged and struggling students learn; and teacher preparation around teaching foundational concepts are the most important predictors of student learning gains. However, one counter-intuitive result that merits further investigation is that teachers who score high on fostering critical thinking in classroom observations (for instance by asking more open-ended questions) have lower student learning gains.

For Kiswahili, even though teacher (and other observable) covariates matter less for predicting student learning gains, teacher preparation on teaching foundational skills, teacher practice of providing additional support to struggling students, and teacher belief that they have good relationships within school still emerge as important. Consistent with existing literature, commonly used teacher characteristics such as education, experience, assessment scores etc. do not emerge as important predictors of student learning gains. Outside of teacher variables, rural schools (for both Math and Kiswahili) and older students (for Kiswahili) have stronger student learning gains; but these factors are still less important than the top teacher factors.

> 32 Examples of questions include (= 1 if 'Agree'; = 0 if 'Disagree'): (i) I have a good relationship with my students, (ii) I have a good relationship with my colleagues, (iii) I have a good relationship with my Head Teacher.

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