institutions. Clearly, higher average scores in ENADE achieved by federal institutions programs are partly due to the better learning background of their incoming students. Therefore, the higher value-added of private programs may be due to decreasing returns to the educational production function, whereby it would be easier to obtain return from individuals with poor average educational background.

The above findings allow us to point out a set of factors that may explain why the raise in teacher tertiary education does not seem to have affect students learning in the last decade. Beyond the low educational background of incoming students and the raise in distance learning modality, the present analysis raises other key aspects. First, the preponderance of teachers with _licenciatura_ and the sharp fall in bachelor’s degree in specific areas of knowledge may not have benefited teacher quality. It is well documented that the majority of _licenciatura_ programs assigns little importance in developing core teaching competencies, like teaching techniques and planning and organizing classroom activities (Bruns et al, 2011). But it is also possible that they fail in providing the necessary knowledge on the specific subjects taught too. Second, lack of effects may lie in the mismatch between the specific subject training of the teacher and the discipline he teachers (e.g.: math teachers without the certification of _licenciatura_ or bachelor’s degree in math). The data presently available allow us to test this mismatch hypothesis, as described later.

Finally, the leading role of private institutions and of distance learning modality in the provision of pedagogy courses, while not directly affecting the quality of teaching in secondary education, can have effects on the quality of elementary and early childhood schools and, therefore, compromise the learning ability of students entering high school. This hypothesis will be investigated in an upcoming study.

# **3. Empirical literature on teacher training and student learning**

The quality of teachers and their effect on students' learning is a central theme of educational policy. The international literature indicates that a student with a low performance teacher might end the school year accomplishing less than half of the curriculum planned for the grade, while students with an excellent teacher may accomplish 50 percent more than expected curriculum (Farr, 2010; Hanushek and Rivkin, 2010). Thus, exposure to low-quality teachers for years running can lead to insurmountable deficits of students' learning.

Despite the recent evidence confirming the central role of teacher quality in students’ learning, there is still no consensus on how much schooling and teacher training contribute to a greater or lesser degree, to raise the quality of education. The first works on the productivity of teachers were developed based on the educational production function estimates from cross-sectional data, and regression analysis of aggregated levels of student performance in teacher training measures and several other controls.

In studies conducted until the mid-1990s for public schools in the United States, Hanushek (2003) identifies 170 estimates of the effect of teacher training measures on the performance of students, of which only 14% reported statistically significant results, 9% of which showing positive effects. This percentage drops to zero when the author considers only high-quality studies (based on the estimates of the "value added" by a student of the same state). The author suggests that the difficulty in capturing the effect of teacher education may be in part due to low variability of the indicator between American schools. In another compilation, spanning 63 studies applied to developing countries, Hanushek (2003) reports that 56% of estimates of the effect of teacher's education school performance were positive and significant.

Wayne and Youngs (2003) conducted an extensive review of the existing empirical literature until the early 2000s, when most of the evaluation studies of the effects of the education of teacher passes using student-level longitudinal data and involve broader sets of variables. Most of the work considered indicates that secondary school students learn more math when their teachers have higher training in mathematics, and no effect in relation to the lower grades and to other areas of knowledge. Moreover, the survey indicated that the quality of teacher education (measured by the raking of the institution) has positive relationship on the performance of the students.

Based on a review of a wide range of empirical studies, Rice (2003) reports positive effects on high school mathematics and science achievement of students whose teachers have obtained advanced degrees in these subjects, and reports mixed evidence regarding the impact of advanced degrees at the elementary 7