Teaching styles and achievement: student and teacher perspectives

Teaching Styles and Achievement: Student and Teacher Perspectives∗ Ana Hidalgo-Cabrillana Universidad Autonoma de Madrid Cristina Lopez-Mayan† Universitat Autonoma de Barcelona Euncet Business School January 28, 2017 Abstract We analyze the relationship of the teaching style with student achievement. As a novelty, we explore whether the effect of the teaching style differs when class work is reported by teachers or students. We find that who reports the practices matters. Teamwork and student discussions -modern practicesare strongly related to better achievement, and individual work and rote learning -traditional practicesare detrimental. But these effects are significant only using students’ reports. Heterogeneous effects of teaching practices arise by subject or gender, but mostly using students’ reports, suggesting differences in the perception of teaching styles. Only results by socioeconomic status are robust to who reports practices: students from low socioeconomic background lose from traditional teaching and gain from modern teaching. JEL classification: I20; I21; J24 Keywords: Students and teacher reports; Test scores; Teacher quality; Modern and traditional teaching ∗We are indebted to Manuel Arellano, Jordi Caballé, Raquel Carrasco, and Jesús Fernández-Huertas Moraga for their insightful comments at different stages of this research. We also thank valuable comments by seminar attendants at University of Edinburgh, Centre for Economic Performance (LSE), Universidad Carlos III de Madrid, Bank of Spain, Universidad Autónoma de Madrid, Universitat de Barcelona; and attendants at RES Conference in Bristol, EALE Conference in Ghent, EEA-ESEM Congress in Toulouse, SAEe in Palma de Mallorca, WinE Mentoring Retreat in Toulouse, ESPE Conference in Braga, IAAE Conference in London, IWAEE in Catanzaro, RWI Research Network Conference on the Economics of Education in Berlin, Encuentro de Economía Aplicada in Gran Canaria, Jornadas de Economía de la Educación in Valencia, and Annual Meeting of the Portuguese Economic Journal in Azores. We are very grateful to the Instituto Nacional de Evaluación Educativa for its support with the database. We acknowledge financial support from Fundación Ramón Areces (Ayudas a la Investigación en Ciencias Sociales 2012 ) and from the Spanish Ministry of Economy and Competitiveness (Grant ECO2013-44920P). †Corresponding author: clopezmay[email protected]; Euncet Business School; Ctra. de Talamanca Km 3; 08225 Terrassa (Barcelona), Spain. 1 Introduction Teacher effectiveness, measured through teacher fixed effects, has a significant impact on student’s cognitive achievement (Rockoff (2004), Rivkin et al. (2005), Hanushek and Rivkin (2006), Hanushek (2006, 2011)) and on student’s development of non-cognitive skills (Jackson, 2013)1. However that finding contrasts with the lack of consistent evidence on the relationship between observed teacher characteristics and student achievement (Hanushek and Rivkin, 2006). Among the exceptions, Rockoff (2004) and Rivkin et al. (2005), which find small effects of the first years of experience, and Dee (2007), which obtains that opposite-gender teachers reduce achievement. A related line of research has found that how teachers actually work in class does a better job than teacher’s characteristics to explain student achievement (Van Klaveren (2011), Schwerdt and Wuppermann (2011), Lavy (2016), Bietenbeck (2014))2. A potential concern however is that those papers measure teaching practices using the students or the teachers as the unique source of information. Since teaching is a complex process, using only the perspective of one of the agents involved may be problematic if the individuals perceive in-class work differently. In that case, using one or another perspective will not be neutral for the results.3 In this paper we use the teacher’s and the student’s perception of teaching practices in order to analyze to what extent different teaching styles affect student achievement. We distinguish two types of teaching styles: traditional and modern. Broadly speaking, the traditional style is characterized by the use of rote learning and individual work and the modern style by teamwork and involvement of students in discussions and presentations. We use data from a national assessment program conducted in 2009 in Spain, “La Evaluación General de Diagnóstico” (EGD). This program evaluates fourth grade students (nine years old) in mathematics and reading. All the students from each class perform the test and in most schools the EGD evaluates two classes. Classes in fourth grade are organized around the main teacher, the tutor, who teaches most of the subjects, including usually math and reading.4Students have the same classmates for the entire school day. The EGD allows linking each student with her tutor and collects rich information about them, including how classes work. The teacher and the students answer the same set of questions about teaching practices. We use those answers to measure the use of traditional and modern teaching styles in class according to the perspective of the teacher and 1Hanushek (2011) quantifies that an effective teacher is equivalent to advancing knowledge in one academic year. 2Teaching practices affect other important outcomes. Recently Algan et al. (2013) find that the use of a modern teaching style promotes the formation of social capital. 3In health economics for instance different observers perceive the same child health differently, leading to different estimates of the income gradient in child health (Johnston et al., 2010). 4Throughout the paper, we use the terms “teacher” and “tutor” interchangeably. 1 the students. We follow the Zemelman et al. (2005)’s taxonomy to classify the teaching practices as traditional or modern. As we discuss later, traditional and modern practices can be complements rather than substitutes and so the aggregate measures do not imply a trade-off between using one or another style. Our empirical strategy exploits the between-class within-school variation in teaching practices and test scores to identify the effect of different teaching styles on student achievement. This type of analysis is challenging because the non-random allocation of students to schools and to classes within school introduces bias in the estimate of teaching practices. By exploiting within-school variation, we deal with the bias from the endogenous selection between schools. The within-school sorting should not be a major concern since the Spanish schooling system is neither track-based in primary education, nor characterized by the practice of “teacher shopping” by parents. We conduct an exhaustive analysis to show the lack of systematic assignment of teachers and students with certain attributes to the same class. Nevertheless, we also control for a rich set of teacher variables and student characteristics in order to minimize the potential bias due to unobserved traits. This paper is closely related to the literature identifying the best teaching style.5Schwerdt and Wuppermann (2011) and Van Klaveren (2011) study the effect of the percentage of time spent in lecture-style teaching using the Trends in Mathematics and Science Study (TIMSS) wave of 2003 for US and Netherlands, respectively. Both papers use a betweensubject within-school strategy to control for unobserved student traits. Schwerdt and Wuppermann (2011) find that shifting time from problem solving to lecturing results in an increase in student achievement. This result is in line with Brewer and Goldhaber (1997). However, Van Klaveren (2011) find no relationship between time lecturing and student performance. Lavy (2016) analyzes the effect of traditional and modern teaching on student achievement in Israel using panel data of pupils in fifth and eighth grade. His identification strategy is based on the within-school change in exposure to teaching practices among students attending both grades. Lavy (2016) concludes that traditional and modern practices have a positive effect on test scores and do not necessarily crowd out each other. Bietenbeck (2014) analyzes the effect of traditional and modern teaching practices on math and science test scores using the TIMSS wave of 2007. He estimates a student fixed-effect model, where identification relies on the different student exposure to teaching practices between math and science. Traditional teaching has a positive effect on overall test scores while modern teaching is not significant. After splitting overall scores by cognitive skills, modern practices have a positive effect on reasoning, while traditional 5Using an experimental approach, Dobbie and Fryer (2013) and Fryer (2014) find that other school practices -teacher feedback, data-driven instruction, increasing instructional time, high-dosage tutoring and culture of high expectationsincrease achievement of students from charter and public schools. 2 teaching increases knowing and applying skills. In sum, these studies show that teaching practices matter. In the last years, the proposals to reform education in different countries advocate a greater use of modern teaching practices in detriment of a traditional learning style.6But this recommendation contrasts with the still scarce and not conclusive results to identify the best teaching style. This paper provides more evidence on this issue and extends beyond those previous papers in the following. First, in contrast to previous literature, we estimate the effect of teaching practices using both the perspective of the teacher and her students. Previous works use only one of these perspectives, usually the students, to measure in-class work. Information reported by students and teachers have different advantages and disadvantages (Goe et al., 2008). Students’ reports about teaching are useful because they provide the perspective of students, the recipients of the teaching practices. However, student responses are subject to bias. Students do not know all the aspects of teaching. Pupils may also answer about in-class work influenced by personality characteristics of the teacher or by their grades. In contrast, teacher self-reports have the advantage that teachers know their own abilities, the class context, and how they work in class. However, teacher responses are also subject to potential biases. Teachers may misreport their practices to adjust them to the “social desired" practices or because they believe that they are applying a certain practice when actually they are not. Therefore, since both student’s and teacher’s responses on teaching practices are self-reported measures with different potential reporting bias, using both sources of information will improve our understanding of the role of teaching practices on student achievement. Goe et al. (2008) recommend assessing teacher effectiveness gathering data from more than one source, especially if one of these sources are students’ reports. Second, we analyze the effect of teaching practices on performance of younger students. Previous papers analyze that effect for students at eight grade. Research on early development outcomes -for instance Heckman (2008)- highlights the importance of understanding at the earliest stages how the education process successfully improves student achievement in order to prevent future dropouts and improve outcomes later in life (Chetty et al., 2011). Finally, none of the previous studies has analyzed the impact of the teacher characteristics and the teaching practices on the achievement of Spanish students. However, it is essential to provide evidence on the role of the teacher because the Spanish educational system faces serious problems, such as the high dropout rate (23.5% in 2013 according to Eurostat, far away from the 10% target of Europe 2020 strategy) and the lack of excellence 6For example, the recent reforms in Finland (http://www.minedu.fi/OPM/Verkkouutiset/2015/03/ curricula.html?lang=en) and UK (https://www.gov.uk/government/news/new-curriculum-will-makeeducation-system-envy-of-the-world) 3 (as shown by the low performance of Spanish students in PISA). Although these problems are measured at the end of secondary schooling, they may come from earlier educational stages. Education is a cumulative process and thus it is important to analyze how schooling inputs affect learning outcomes in primary education. We find that the use of modern practices is related to better overall student achievement, while the traditional teaching if any is detrimental. Those effects are larger when the teaching style is measured using the practices reported by the students. We also find that modern teaching increases scores in reading and math while traditional teaching is particularly detrimental for reading scores. However those different effects arise using the students’ answers rather than the tutor’s answers. Traditional teaching is especially harmful for students from low socioeconomic background. They are also the students who benefit the most from modern teaching. The effect of the teaching style hardly differs, when the teacher reports the practices, for boys and girls, students from public and private schools, and students with the same or different tutor in the previous grade. However when the students inform about the practices, the effects are different: (i) boys do no benefit from using any particular teaching style, while girls gain from modern practices and lose from traditional ones; (ii) modern and traditional practices are related respectively to higher and lower scores in public schools but not in private ones; and (iii) students with the same tutor in the previous grade benefit less from the modern style than students with a different tutor. The fact that those different effects arise when the practices are reported by the students rather than by the tutor suggests that the heterogeneity may result from different perceptions of the in-class work. In line with previous literature, pupils’ achievement is not correlated to teacher’s gender or experience. However, having a teacher with more than three years of college is negatively correlated with achievement, suggesting a pattern of negative selection into primary education in Spain. The rest of the paper is organized as follows. Section 2 describes the database and explains the construction of the teaching measures. Section 3 explains the empirical strategy. Section 4 presents the results and the sensitivity analysis. Section 5 concludes. 2 Data We use data from “La Evaluación General de Diagnóstico”, the national assessment program conducted in 2009 by the Instituto Nacional de Evaluación Educativa (INEE), the public institution for the evaluation of the Spanish education system. The EGD evaluates the competencies of fourth-grade students in mathematics and reading using a standardized test following the PISA methodology. In reading, the EGD evaluates the competencies in 4 understanding texts and the literacy to write the own ideas and in mathematics, it assesses the ability to do basic math and to apply the mathematical reasoning in solving problems. The EGD evaluates 28,708 pupils from 900 schools selected with a two-stage stratified sampling method to ensure that the results are representative both at the national and regional level, and for public and private schools. In the first stage, for each stratum, schools are selected with probabilities proportional to their fourth grade enrollment. In the second stage, one or two fourth grade classes are randomly sampled. All the students from the selected classes are evaluated but the tests of pupils in special situations are not included in the final EGD database (students with serious special needs or immigrant students who recently entered the Spanish schooling system). The EGD scales test scores so that the average in each domain (mathematics and reading) is 500 and the standard deviation is 100. In order to interpret coefficients as fractions of a standard deviation we standardize scores to have a mean of zero and standard deviation of one. The EGD does not provide actual test scores. The student’s overall achievement is available through five plausible values, or imputed values. Providing plausible values rather than actual test scores is a standard practice in international assessment programs (Programme for International Student Assessment, TIMSS). In this type of evaluations, each student answers a limited number of test questions. Then, those answers and the student’s family background are used to estimate the proficiency distribution of the student by applying the Item Response Theory. Plausible values then are random draws from that distribution. The EGD includes rich information about students and about the tutor of each fourthgrade class. The tutor teaches most subjects, including usually the core ones -math and reading. Students have the same classmates for the entire school day. Indeed, students are assigned to a class in first grade and they usually continue with the same classmates until sixth grade, the last grade of primary education. The whole fourth-grade class spends a large fraction of the school day with the tutor. The tutor is also the person who follows the performance of the students, monitors the class climate and meets with parents. Aside from the relatively standard set of tutor characteristics, the EGD provides information about (i) the teaching practices used in class; (ii) whether the tutor teaches both math and reading, only math, only reading, or none; and (iii) the tutorial work, such as the number of meetings with parents and whether the tutor was the tutor of the class in third grade as well. The original sample contains 28,708 pupils, 1,358 classes and tutors -since there is one different tutor per classand 900 schools. From this sample, we drop (i) students with missing math or reading scores; (ii) classes with an extremely small number of students (less than five); (iii) students who take the test but did not fill in the questionnaire or whose tutor did not answer her questionnaire; (iv) classes whose tutor does not teach math or 5 reading to ensure that teachers in the final sample are the instructors of at least one of the analyzed subjects; and (v) students and teachers with missing information in basic variables such as gender, parents’ education, years of experience, and teaching practices. As we discuss later, our identification strategy relies on within-school variation, so we also rule out the schools with only one sampled class. The final sample contains 12,113 students, 736 classes/tutors and 368 schools. Of the 368 schools, 69% are public and the remaining 31% are private and semi-private (private schools publicly funded). Despite the reduction in size, the final sample is not significantly biased with respect to the initial one and is still representative of the target population of fourth-grade students in Spain as Tables A.1 and A.2 in the Appendix show. Table 1 presents the characteristics of the fourth grade tutors in primary school in Spain. They are mostly women, have more than twenty years of experience, teach both mathematics and reading, and were tutor of the same class in third grade. Regarding educational qualification, 17% of the tutors hold more than a three-years university degree (five-years degree, master or PhD), which is the minimum educational level required by Spanish authorities to teach in primary education. Tutors meet with parents an average of three times per school year -presumably, once per quarterand it is more usual that the tutor asks for the meeting. The average number of pupils per class is 21.14 with a standard deviation of 4.85. We compute the class size as the total number of surveyed students in the class in the initial sample. Table 2 reports students’ characteristics. Half of fourth-grade pupils are girls and 6% has repeated at least once. The proportion of non-Spanish pupils is 7%, coming mainly from Latin America, Non-Western Europe and Morocco. Most students started school at three years old or less, which is the usual age to begin school in Spain. Regarding household composition, 7% of the students live with a single parent and 85% live with at least one sibling. Although mothers are slightly more educated than fathers they are unemployed or inactive in a higher proportion than fathers7. Table 3 shows that on average girls perform better than boys in reading, while boys perform better in math. Students in private schools perform better on average in both subjects than students in public schools. 7For household composition we construct two categories: living in single-parent household, and living with siblings. For parents’ education, we consider the following categories: primary or less, compulsory, high school, vocational training, and university. Regarding parents’ labor status, we consider these categories: self-employed, employee, unemployed, and inactive. 6 2.1 Teaching practices The information about teaching practices is derived from the question, “How often do you use the following teaching practices in your lessons this school year?”. On a point-four scale, possible answers are “Never or almost never”, “Sometimes”, “Almost always”, and “Always”. Teachers respond about each of the following practices: (a) “Most of the time I teach by telling”, (b) “Students present works or topics to classmates”, (c) “While I teach, I ask students questions about the lesson”, (d) “While I teach, students ask me doubts”, (e) “I promote discussions”, (f) “Students work on exercises and activities proposed by me”, (g) “Students work individually”, (h) “Students work in small groups”, (i) “I give different exercises or activities to best/worst students”. We do not consider this last item because it reflects the level of students in class and it would lead to a problem of reverse causality in the estimation. According to the taxonomy by Zemelman et al. (2005), practices (b), (e), and (h) are classified as modern, and practices (a), (f), and (g) as traditional (Table 4). It is not possible to unambiguously match items (c) and (d) as traditional or modern. In principle, item (c) may be thought as traditional and item (d) as modern, but classifying (d) as traditional and (c) as modern is reasonable as well. The EGD data supports the theoretical classification derived from the Zemelman et al. (2005)’s taxonomy. Table 5 shows the correlation among the tutor’s answers to all items. Modern items (b), (e), and (h) are positively correlated with coefficients around 0.26. The same pattern appears for traditional items (a), (f), and (g), with coefficients ranging from 0.13 to 0.30. Items (d) and (c), classified as modern and traditional in this Table, are positively correlated with the respective modern and traditional items. At the same time, (d) is positively correlated with traditional items, and (c) with modern ones (see the bottom left of Table 5). This clear pattern of positive cross-correlations does not appear for the rest of items. Moreover, the correlation between (c) and (d) is quite high (0.47). Therefore, we exclude items (c) and (d) from the baseline measure of teaching practices. In Section 4.3 we check the robustness of the results to include those items. Following Lavy (2016) and Bietenbeck (2014), for the ease of interpretation, we rescale the answers to each item by assigning a numerical value as follows: 0 to “Never or almost never”, 0.33 to “Sometimes”, 0.67 to “Almost always”, and 1 to “Always”. Thus, like in previous works, responses are interpreted as the proportion of the time used in that practice. The aggregate measure of traditional teaching practices is the mean of the teacher’s answers to items (a), (f) and (g); and the aggregate measure of modern teaching practices is the mean of the teacher’s answers to items (b), (e) and (h). Table 6 shows that teachers report that they use traditional and modern practices, respectively, 66% and 43% of the class time on average. 7 We should note that both indexes do not imply a trade-off between using one or another style in class. Teaching practices can be complements rather than substitutes (De Witte and Van Klaveren, 2014). For instance, one possible activity proposed by the teacher (item (f), traditional) may be to promote discussions in class (item (e), modern). Indeed, Table 5 shows a positive correlation between these two items. Moreover, the question about in-class work does not impose any restriction on the complementarity or substitutability among the practices because the answer on the frequency of use for one practice does not restrict the answers for the rest of practices. We thus do not restrict the aggregate measures either. This explains that the means of traditional and modern indexes sum above one for each respondent (Table 6). In the estimation we include jointly the traditional and modern indexes and the estimated coefficient of one of the indexes should be interpreted as the effect on test scores holding constant the other one.8We then assess the sensitivity of the results to restrict that the total proportion of time using all practices must be equal to one or, in other words, that all teaching practices are substitutes. Table 7 shows that the correlation between the traditional and modern indexes is zero. This may be explained by the opposite cross-correlations among individual items (see the bottom left of Table 5). The EGD survey also asks students about teaching practices. The question is “In general, how is in-class work?”. The list of practices provided to the students correspond exactly with items (a) to (h) from the teacher questionnaire. Students answer using the same four-point scale explained above. We also rescale the students’ answers to each item by assigning a proportional value from zero to one. We construct the modern and traditional indexes by averaging the responses of the students in the class -excluding the student’s own responseto the modern and traditional items. Using the students’ or the teacher’s reports about teaching practices to estimate their effect on test scores may be subject to different biases or measurement errors. In principle, teachers’ reports may seem more accurate because teachers know their own abilities, the class context, and how they work in class, while the students do not know all the aspects of teaching. In addition, the question to the students is about class work in general and, although the tutor teaches most subjects, we cannot disregard that some students might answer thinking on another teacher. Pupils may also answer influenced by personality characteristics of the teacher or by their grades. However, teachers may misreport their practices either intentionally (to adjust them to the “social desired" teaching) or unintentionally (believing that they are using a certain practice when they are actually not). Since it is not clear whether the students’ or the teachers’ answers are less subject to bi8Lavy (2016) and Bietenbeck (2014) also use this approach. 8 reading, although only the positive relationship of the modern teaching with reading scores is large and measured precisely. A 10% increase in the use of modern practices is associated with 3% of a standard deviation increase in reading test scores. When the students report the practices, the modern style is related to higher scores in both subjects, although the effect is larger for reading (4.1%) than for math (2.7%). A 10% increase in the use of traditional practices reduces scores by 2.6% of a standard deviation but the estimate is significant only for reading. Compared with the results in Table 14, math scores benefit from having a tutor with an intermediate level of experience, while reading scores benefit from having either the least or the most experienced tutors. The negative relationship between achievement and having a tutor with more years of education appears in both subjects with a similar magnitude. Compared with a tutor who only teaches math, a tutor who teaches only reading is detrimental for math scores while she does not affect performance in reading. Table A.3 in Appendix shows that the estimates of the student characteristics present some differences across subjects. It arises the usual gender gap: girls obtain higher scores in reading and lower in math than boys. The older the student started at school, the lower the scores, especially in reading. Latin American students obtain the lowest scores in math and reading, even though Spanish is their mother tongue. Parents’ education is positively correlated with scores and the association is larger for reading. It is interesting to mention that the parents’ labor status is not correlated with scores except if the mother is employee. The positive association may suggest that employee mothers spend less time with children than inactive and unemployed mothers but the time spent is of higher quality. In Table 16 we explore whether the effect of the teaching style is different according to the socioeconomic background of the students as measured by the Index of Economic, Social and Cultural Status (IESCS) included in the EGD database. This index was created on the basis of the highest levels of education and occupational status of the student’s parents; the number of books at home; and an index of other home resources12. We stratify the sample by high or low socioeconomic status -student’s IESCS above or below the median of the IESCS distribution, respectively. Using the students’ answers, students of low IESCS gain from modern teaching and lose from traditional one in the two subjects, although the effects are stronger in math. Using the tutor’s answers, students from high socioeconomic status also gain from the modern teaching but this effect only arises in reading. To gain deeper knowledge about the effect of the teaching practices on achievement, we explore whether there are differences by the gender of students, the type of school and the type of tutor. By type of tutor we refer to whether the students had or not the same 12The index of other home resources was created on the basis of whether there is a quiet study space, internet access, TV, and stories and novels at home. For more details on the IESCS, see INEE (2010). 15 tutor in third and fourth grades. Each panel in Table 17 shows the results of estimating for math and reading jointly and separately. In Panel A the estimated coefficients of modern and traditional teaching do not reveal differences across male and female students if the tutor reports the practices: the modern teaching has the same positive and significant effect for reading scores of boys and girls. However, if we use the students’ reports, striking differences appear. For girls, the use of traditional practices is strongly associated to lower scores in math and reading, while the effect for boys is negligible and not significant. In contrast, girls’ reading scores benefit from using the modern style while boys’ scores do not. Nor boys’ neither girls’ math scores are significantly correlated with using modern teaching practices. In Panel B we stratify the sample by public and private schools. Using the tutor’s answers, no significant differences appear except the positive relationship between reading scores and modern teaching for students in public schools. With the students’ answers, the use of modern practices is significantly associated to higher math and reading scores in public schools but not in private ones. Traditional teaching decreases reading scores but only among students from public schools. In Panel C we split the sample among the students who had the same tutor in third and fourth grades and the students who had a different tutor. Table 1 shows that 74% of the tutors were also the tutors of the class in third grade. According to the practices reported by the teacher, the modern teaching is significantly related to higher scores in reading for the students with the same tutor in third and fourth grades. For students with a different tutor, the estimate is also positive but it is not significantly different from zero. When the teaching practices are reported by the students, several differences arise. The modern style is positively related to math and reading scores but with a lower magnitude for students with the same tutor in third and fourth grade. The traditional style is strongly related to lower scores in reading but only for students who did not have the same tutor in the previous grade. 4.2 Differences in students’ and teachers’ responses From previous findings we conclude that the effect of the teaching style is heterogeneous across subjects and several subsamples mainly if the teaching practices are reported by the students. This suggests that the heterogeneous effects may not be the consequence of differences in the effect of the teaching style. Instead, they may partly result from a different perception of the traditional and modern styles for instance by boys and girls, or students from public and private schools. First, to explore whether observed characteristics lead to differences in the teaching 16 practices reported by students and teachers, we estimate the following model: TP T ut jcs −T PStu jcs =γ0+γ0 1Tcs +γ0 2Xcs +φs+publics+εics (5) where TP T ut jcs and T PStu jcs are the teaching practices indexes for the style j={modern, traditional}as reported by the tutor and the students, Tcs is the vector of tutor characteristics and class size, Xcs is the vector of the average characteristics of students from class cat school s,publicsis a dummy variable for public school and φsis a school fixed effect. Xcs includes the average scores in math and reading to explore whether differences in the perception of the practices are related to student ability -for instance, high achievers may perceive class work more accurately and respond more similar to her teacher. Unexpectedly, tutor and average class characteristics are not significantly correlated to the difference in modern and traditional indexes. Only ability explains differences in the indexes: students from classes with higher average scores in reading report a lower use of the modern teaching than the tutor. For the sake of brevity we do not show this table but it is available upon request. Second, to explore whether differences in students’ responses are explained by certain observed characteristics, we estimate the following model: ModPStu ics −TradP Stu ics =β0+β0 1Xics +β0 2Tcs +β0 3Xcs−i+φs+publics+εics (6) where ModPStu ics and TradP Stu ics are the modern and traditional indexes reported by student i,Xics is the vector of individual characteristics, including reading and math test scores, and Xcs−iis the vector of average class characteristics and test scores excluding the student’s own value. We use the first plausible value for test scores but results do not change using the other ones. Table 18 shows the results. Girls and students with high-performing classmates tend to overreport the use of traditional practices. Repeaters, students with higher scores in reading and from public schools tend to overreport the use of the modern style. Unfortunately, due to the lack of appropriate data it is difficult to provide a clear interpretation of the mechanisms explaining those differences in the perception of the use of modern and traditional practices. 4.3 Sensitivity analysis In this Section, we conduct several sensitivity tests in order to address potential reservations about our findings. First, the baseline specification includes the traditional and modern indexes jointly because they do not imply a trade-off between using traditional or modern methods in class. A possible concern is whether including jointly the indexes creates a collinearity problem that may influence the results because some traditional items are 17 correlated -although weaklywith some modern items (see Table 5). Table 19 shows that collinearity is not an issue because the results do not change if the indexes are included separately in the regression. Second, we analyze whether the results hold after considering alternative ways of measuring teaching practices. Rather than aggregating the items, in Table 20 we estimate a specification that includes the six teaching practices. We do not observe any particular item leading our main findings. The baseline estimates are the result of individual effects that either compensate or reinforce each other. In Panel B of Table 21 we assess the sensitivity of the results to include items (c) “While I teach, I ask students questions about the lesson”, and (d) “While I teach, students ask me doubts”. The baseline indexes do not include those items because, as we discuss, its classification as traditional or modern is ambiguous. In Panel B1 we redefine the traditional and modern indexes including (c) as traditional and (d) as modern, while in Panel B2, we consider (c) as modern and (d) as traditional. The new estimates are consistent with the baseline results. The estimated coefficients do not change too much but if any they move slightly towards a higher positive effect of the modern style and a lower negative effect of the traditional practices. Then the baseline estimates, obtained without including items (c) and (d), may be seen as conservative or lower bound estimates of the relationship between teaching styles and student achievement. In Panel C of Table 21 we construct a new measure of teaching practices that restricts that the total class time allocated to the six traditional and modern practices listed in Table 4 must sum to one. In the baseline indexes, we rescale the answers to each practice from zero to one in order to interpret the responses as the proportion of the time used in the practice. Without imposing any restriction on the total time engaged in teaching practices, the traditional and modern indexes from a class can sum more than one. Indeed, according to the teacher’s reports on practices, this happens in 74% of the classes. As discussed in Section 2.1, in the baseline measures we do not impose that the proportion of the time using modern and traditional practices is equal to one because different practices may be complements rather than substitutes. However, measurement error or careless responses (for instance, answering “always” to all items) may also result in traditional and modern indexes that sum above one. In order to assess whether this concern affects the results, we rescale the answers of each individual such as they sum to one. That is, for each individual we aggregate the numerical values assigned to the answers of the six items in Table 4 and weight each answer by the inverse of that sum. In this way, we keep the relative frequency in the use of practices while imposing that the proportion of the time using traditional and modern practices fulfills the time budget constraint. In other words, we impose that all practices are substitutes. The restricted share of the class time using modern practices is 18 then the sum of the weighted time allocated to the three modern items. The proportion using traditional practices is the remaining weighted time and so the new specification includes only one of the measures. Note that these new measures of the teaching style are more restrictive than the baseline measures. Panel C shows that the estimates of the share of time using modern practices are similar to the baseline estimates. We can conclude that measurement error or careless responses about in-class work are not a concern for our findings. Third, we analyze whether the results are robust to adding the class average of all student characteristics -excluding the student’s own valueto the baseline specification13. Panel D of Table 21 shows that controlling for those additional variables hardly changes the effect of the teaching style on student achievement. This supports our previous evidence that within-school sorting is not a big concern. If the main results were driven by this type of selection, controlling for sociodemographic characteristics of the class would lead to different results. Finally, we may think about using the teaching indexes reported by the students as instrument for the indexes reported by the teacher to correct for potential measurement error bias. Note that this approach would not correct for the possible bias introduced by the endogenous selection of the teaching style. However, the first stage estimates show that the instruments behave weakly (results are available upon request). The correlations among the indexes reported by the students and the teachers is not very large, although they are not so low to flag a weak-instruments problem (see Table 7). However, both the F-statistics for the joint significance of the instruments and the extremely low values of the partial R2point to the weakness of the instruments.14 5 Conclusions We analyze to what extent using traditional or modern teaching styles in class is related to the student achievement in math and reading in primary education. As a novelty, we measure in-class work using two different sources of information -students and tutor. To deal with the non-random assignment of teachers and students to schools, our identification strategy relies on between-class within-school variation of teaching styles. We show also robust evidence of the lack of systematic selection of students and teachers within-school. We provide new insights on the effect of using traditional and modern teaching practices on achievement. We show that using the teacher’s or students’ reports may lead to different 13Regarding the student’s origin we control for the percentage of non-Spanish students in the class. 14If the partial R2is much smaller than the R2, the instruments are weak because they are adding little extra to explaining the endogenous regressors after accounting for the rest of variables. 19 conclusions about the relationship between student achievement and teaching style. If we only used the tutor’s reports, we would conclude that the teaching style does not matter for the overall student achievement. Alternatively, if we only used the students’ reports, we would conclude that students benefit from modern teaching and lose from traditional one. In addition, we find heterogeneous effects of the teaching style for math and reading, boys and girls, students from public and private schools, and by type of tutor but they mainly arise when the practices are reported by the students. As we discuss, using students and teachers reports have different pros and cons but since they are both self-reported measures, we should use more than one source of information to draw adequate policy implications about the role of the teaching practices on student achievement. Only when splitting the sample by socioeconomic status, results are quite robust to the source of information used. Students from low socioeconomic background especially lose from traditional teaching, but they also benefit the most from modern teaching. These effects arise in reading regardless of the source of information and in math when the students report the practices. This result suggest that educational policies on teaching practices would be more effective if they are targeted to students from low socioeconomic background. We also show that student achievement is not correlated to teacher’s gender or experience, but it is negatively correlated with the teacher’s degree. We discuss that this may reflect a pattern of negative selection into primary education of the teachers holding a five-years degree or more. Spanish educational authorities should take into account this misallocation problem when enacting the educational requirements to teach in primary education. As a final remark, we should note that our findings -like the previous onesrefer to the effect of the traditional and modern teaching styles on student achievement as measured by test scores. However test scores do not capture all aspects of student learning. Test-based measures can identify the practices more effective to increase test skills in detriment of other practices not so effective for the test but that may give also valuable skills to the students. Indeed if questions from math and reading tests capture different skills, this might explain why the effect of teaching styles is different across subjects. Thus a more complete understanding of the relationship between in-class work and student outcomes will require analyzing the effect of teaching practices on other student outcomes. 20 References Algan, Y., P. Cahuc, and A. Shleifer (2013): “Teaching Practices and Social Capital,” American Economic Journal: Applied Economics, 5, 189Ű210. Bietenbeck, J. C. (2014): “Teaching Practices and Cognitive Skills,” Labour Economics, in press. Brewer, D. J. and D. D. Goldhaber (1997): “Why don’t schools and teachers seem to matter?” The Journal of Human Resources, 32, 505–523. Chetty, R., J. N. Friedman, N. Hilger, E. Saez, D. W. 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(2011): “The Economic Value of Higher Teacher Quality,” Economics of Education Review, 30, 466–479. Hanushek, E. A. (2006): School resources, in Handbook of the Economics of Education, edited by Eric A. Hanushek and Finis Welch. Amsterdam: North Holland, vol. 2, chap. 14, 865–908. Hanushek, E. A. and S. Rivkin (2006): Teacher Quality, in Handbook of the Economics of Education, edited by Eric A. Hanushek and Finis Welch. Amsterdam: North Holland, vol. 2, chap. 18, 1051–1078. 21 Heckman, J. J. (2008): “Schools, Skills and Synapses,” Economic Inquiry, 46, 289–324. INEE (2010): “Evaluación General de Diagnóstico 2009. Educación Primaria. Informe de resultados,” Instituto Nacional de Evaluación Educativa. Jackson, C. K. (2013): “Non-Cognitive Ability, Test Scores, and Teacher Quality: Evidence from 9th Grade Teachers in North Carolina,” NBER Working Paper 18624. Johnston, D. W., C. Propper, S. E. Pudney, and M. A. Shields (2010): “Is There an Income Gradient in Child Health? 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Today’s Standards for Teaching and Learning in America’s Schools, Heinemann, third ed. 22 Figures Figure 1: Difference in the teaching indexes between tutor and students 0123 Density -.5 0 .5 Tutor minus Students Modern index 0123 Density -.5 0 .5 Tutor minus Students Traditional index 23 Tables Table 1: Tutors’ characteristics Mean Std. Dev. Classes† Female 0.75 0.44 736 Experience (years): Less than 5 0.10 0.30 736 5 - 9 0.10 0.30 736 10 - 14 0.07 0.25 736 15 - 19 0.09 0.29 736 20 - 24 0.10 0.30 736 25 - 29 0.15 0.36 736 30 or more 0.39 0.49 736 5-years degree or more 0.17 0.38 736 Instruction: Reading and Math 0.88 0.32 736 Reading 0.05 0.21 736 Math 0.07 0.25 736 Person asking for a meeting: Parents 0.22 0.41 734 Teacher 0.33 0.47 734 Number of meetings with students’ parents 3.04 0.97 731 Teacher at 3rd and 4th grades 0.74 0.44 729 Class size 22.53 3.54 736 Schools 368 †The number of tutors is equal to the number of classes since there is one different tutor per class. 24 Table 11: Within-school sorting: effect of class characteristics (II) Teaching index (Tutor’s answers) Teaching index (Students’ answers) Traditional Modern Traditional Modern Mother’s education: Compulsory -0.04 -0.10 0.01 -0.06 (0.13) (0.12) (0.09) (0.12) High School 0.02 -0.09 -0.03 -0.11 (0.17) (0.14) (0.10) (0.14) Vocational training -0.15 -0.07 -0.04 -0.06 (0.17) (0.14) (0.10) (0.14) University 0.06 -0.13 -0.02 -0.06 (0.16) (0.14) (0.11) (0.15) Father’s education: Compulsory 0.09 0.04 0.00 0.03 (0.14) (0.13) (0.09) (0.11) High School 0.13 -0.01 0.06 0.00 (0.15) (0.13) (0.08) (0.11) Vocational training 0.10 0.04 0.05 0.00 (0.14) (0.13) (0.08) (0.11) University -0.03 0.07 0.03 -0.01 (0.14) (0.13) (0.09) (0.11) Mother’s labor status: Employee 0.06 0.00 -0.05 -0.03 (0.09) (0.09) (0.06) (0.07) Unemployed 0.14 -0.08 -0.05 -0.01 (0.13) (0.11) (0.09) (0.10) Inactive 0.12 -0.05 0.01 -0.04 (0.13) (0.12) (0.07) (0.08) Father’s labor status: Employee 0.02 -0.14∗∗ -0.01 0.02 (0.08) (0.07) (0.05) (0.07) Unemployed -0.07 -0.26∗∗ -0.04 -0.08 (0.14) (0.12) (0.08) (0.11) Inactive 0.12 -0.16 -0.18 -0.01 (0.24) (0.20) (0.12) (0.17) % non-Spanish 10-20% 0.00 0.01 0.01 0.03 (0.03) (0.03) (0.01) (0.02) More 20% -0.01 0.04 0.01 0.03 (0.04) (0.04) (0.02) (0.03) % single parent -0.01 -0.17 0.00 -0.06 (0.13) (0.13) (0.07) (0.12) % siblings 0.08 0.00 0.02 0.08 (0.10) (0.08) (0.05) (0.07) % female -0.02 0.03 0.04 0.01 (0.08) (0.08) (0.05) (0.06) % repeater 0.08 0.01 -0.02 0.14 (0.14) (0.14) (0.09) (0.12) F-test 0.43 0.69 0.49 0.47 p-value 0.99 0.83 0.97 0.98 School fixed effects Yes Yes Yes Yes R20.68 0.71 0.70 0.69 Classes 736 736 736 736 Reference outcomes: primary education, self-employed, <10% non-Spanish. Standard errors clustered at the school level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. F-test: joint significance of the class characteristics. 31 Table 12: Within-school sorting: effect of class size Traditional teaching Modern teaching Class size -0.01 -0.03 -0.02 -0.00 (0.02) (0.03) (0.01) (0.03) (Class size)20.00 0.00 0.00 0.00 (0.00) (0.00) (0.00) (0.00) F-test 0.38 0.59 1.27 0.25 p-value 0.69 0.56 0.28 0.78 School fixed effects No Yes No Yes R20.00 0.66 0.01 0.69 Classes 736 736 736 736 Teaching practices reported by the tutor. Standard errors clustered at the school level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. F-test: joint significance of class size and (class size)2. 32 Table 13: Within-school selection of teaching style: Effect of teacher characteristics Dependent variable: Teaching index Tutor’s answers Students’ answers Traditional Modern Traditional Modern Female -0.02 0.01 -0.02∗0.00 (0.03) (0.02) (0.01) (0.02) Years of experience (ref: <5): 5 - 9 0.03 0.01 -0.01 0.01 (0.04) (0.04) (0.02) (0.03) 10 - 14 0.04 0.00 -0.02 -0.03 (0.05) (0.05) (0.03) (0.04) 15 - 19 0.03 0.01 -0.01 -0.02 (0.05) (0.05) (0.02) (0.03) 20 - 24 0.02 -0.00 -0.00 -0.02 (0.05) (0.05) (0.02) (0.03) 25 - 29 0.01 0.01 -0.02 -0.03 (0.04) (0.04) (0.02) (0.03) 30 or more 0.05 0.01 -0.00 -0.04 (0.04) (0.04) (0.02) (0.02) 5-years degree or more -0.03 -0.00 -0.00 0.01 (0.03) (0.03) (0.01) (0.02) Instruction (ref: Math): Reading and Math -0.02 -0.01 -0.01 0.03 (0.06) (0.05) (0.03) (0.03) Reading -0.00 0.01 0.01 0.04 (0.08) (0.07) (0.03) (0.04) Person asking for a meeting: Parents 0.01 -0.01 -0.01 0.01 (0.04) (0.03) (0.02) (0.02) Teacher -0.01 0.00 -0.00 0.02 (0.03) (0.03) (0.01) (0.02) # of meetings with parents 0.02 -0.00 -0.01 0.01 (0.02) (0.02) (0.01) (0.01) Teacher at 3rd and 4th grades -0.01 -0.01 0.02 0.02 (0.03) (0.03) (0.02) (0.02) Class size -0.00 0.00 0.00 0.00 (0.01) (0.01) (0.00) (0.01) Constant 0.55∗∗∗ 0.51∗∗∗ 0.74∗∗∗ 0.30∗∗ (0.18) (0.16) (0.10) (0.14) F-test 0.46 0.06 0.59 0.71 p-value 0.96 1.00 0.88 0.78 School fixed effects Yes Yes Yes Yes R20.69 0.69 0.71 0.69 Classes 724 724 724 724 Standard errors clustered at the school level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. F-test: joint significance of teacher characteristics and class size. 33 Table 14: Estimation results Tutor’s answers Students’ answers (1) (2) (3) (4) (5) (6) Traditional teaching 0.00 0.04 0.00 -0.19 -0.21 -0.26∗∗ (0.10) (0.10) (0.10) (0.13) (0.13) (0.13) Modern teaching 0.08 0.08 0.14 0.38∗∗∗ 0.47∗∗∗ 0.34∗∗ (0.10) (0.10) (0.09) (0.14) (0.14) (0.13) Math dummy 0.00 -0.00 -0.00 -0.00 -0.00 -0.01 (0.01) (0.01) (0.01) (0.01) (0.01) (0.01) Class size 0.01∗0.01 0.01 0.00 (0.01) (0.01) (0.01) (0.01) Teacher variables: Female 0.03 0.01 0.02 0.01 (0.02) (0.02) (0.03) (0.03) Years of experience (ref: <5): 5 - 9 0.02 0.03 0.01 0.02 (0.04) (0.04) (0.05) (0.04) 10 - 14 0.07 0.07 0.04 0.07 (0.06) (0.05) (0.06) (0.06) 15 - 19 0.07 0.09∗0.07 0.09∗ (0.05) (0.05) (0.05) (0.05) 20 - 24 0.01 0.01 -0.00 0.02 (0.05) (0.05) (0.05) (0.05) 25 - 29 0.06 0.06 0.04 0.05 (0.05) (0.04) (0.05) (0.05) 30 or more 0.07∗0.08∗0.08∗0.10∗∗ (0.04) (0.04) (0.04) (0.04) 5-years degree or more -0.07∗∗∗ -0.07∗∗∗ -0.08∗∗∗ -0.07∗∗∗ (0.03) (0.03) (0.03) (0.03) Instruction (ref: Math): Reading and Math -0.10∗-0.04 -0.08 -0.03 (0.06) (0.05) (0.05) (0.05) Reading -0.15∗∗ -0.13∗∗ -0.15∗∗ -0.12∗ (0.06) (0.06) (0.06) (0.06) Person asking for a meeting: Parents -0.01 0.01 -0.03 -0.01 (0.03) (0.03) (0.04) (0.03) Teacher -0.02 0.01 -0.03 0.00 (0.03) (0.03) (0.04) (0.04) # of meetings with parents -0.02 -0.02 -0.02 -0.02 (0.02) (0.02) (0.02) (0.02) Teacher at 3rd and 4th grades 0.02 0.05∗0.02 0.03 (0.03) (0.02) (0.03) (0.03) Constant 0.08 -0.14 -0.27 0.16∗0.06 0.04 (0.08) (0.20) (0.20) (0.09) (0.20) (0.20) Student characteristics No No Yes No No Yes School fixed effects Yes Yes Yes Yes Yes Yes Observations 24226 23844 23492 22086 21734 21524 R20.16 0.16 0.23 0.15 0.15 0.22 Dependent variable: Student test scores in Math and reading. Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. Student’s characteristics: female, country of origin, repeater, mother and father’s education, mother and father’s labor status, single-parent household, siblings, born in 4th quarter, age at starting school, private tutor/family helps with homework. 34 Table 15: Heterogeneous effects across subjects Tutor’s answers Students’ answers Math Reading Math Reading Traditional teaching 0.08 -0.07 -0.26 -0.26∗ (0.12) (0.10) (0.18) (0.14) Modern teaching -0.03 0.30∗∗∗ 0.27∗0.41∗∗ (0.13) (0.10) (0.15) (0.16) Class size 0.01 0.01 0.00 0.00 (0.01) (0.01) (0.01) (0.01) Teacher variables: Female -0.01 0.04 -0.01 0.03 (0.03) (0.02) (0.04) (0.03) Years of experience (ref: <5): 5 - 9 -0.03 0.10∗-0.05 0.10∗ (0.05) (0.05) (0.06) (0.06) 10 - 14 0.01 0.12∗0.02 0.12 (0.07) (0.07) (0.07) (0.08) 15 - 19 0.12∗∗ 0.05 0.10∗0.08 (0.05) (0.06) (0.06) (0.07) 20 - 24 0.04 -0.02 0.03 0.00 (0.05) (0.06) (0.06) (0.07) 25 - 29 0.06 0.07 0.03 0.08 (0.06) (0.06) (0.06) (0.06) 30 or more 0.07 0.08 0.07 0.12∗∗ (0.05) (0.05) (0.06) (0.06) 5-years degree or more -0.06∗∗ -0.08∗∗ -0.07∗∗ -0.08∗∗ (0.03) (0.03) (0.03) (0.03) Instruction (ref: Math): Reading and Math -0.07 -0.02 -0.07 0.00 (0.06) (0.07) (0.07) (0.07) Reading -0.17∗∗ -0.08 -0.19∗∗ -0.05 (0.07) (0.08) (0.08) (0.08) Person asking for a meeting: Parents 0.01 0.00 -0.01 -0.01 (0.04) (0.03) (0.04) (0.04) Teacher -0.00 0.03 -0.01 0.02 (0.04) (0.04) (0.04) (0.04) # of meetings with parents -0.03 -0.00 -0.03 -0.00 (0.03) (0.02) (0.03) (0.03) Teacher at 3rd and 4th grades 0.05∗0.04 0.04 0.01 (0.03) (0.04) (0.03) (0.04) Constant -0.07 -0.47∗0.28 -0.21 (0.26) (0.25) (0.30) (0.28) Student characteristics Yes Yes Yes Yes School fixed effects Yes Yes Yes Yes Observations 11746 11746 10762 10762 R20.24 0.26 0.23 0.24 Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗ p < 0.05, ∗∗∗ p < 0.01.35 Table 16: Heterogeneous effects: student socioeconomic background Math and Reading Math Reading High IESCS Low IESCS High IESCS Low IESCS High IESCS Low IESCS A. Tutor’s answers: Traditional teaching 0.21 -0.13 0.25 -0.00 0.16 -0.25∗∗ (0.14) (0.10) (0.17) (0.13) (0.14) (0.13) Modern teaching 0.13 0.14 0.04 -0.10 0.21∗0.39∗∗ (0.11) (0.14) (0.15) (0.19) (0.12) (0.17) Math dummy -0.02 0.01 - - - - (0.02) (0.02) - - - - Observations 11834 11658 5917 5829 5917 5829 R20.19 0.21 0.22 0.22 0.22 0.25 B. Students’ answers: Traditional teaching -0.14 -0.33∗0.05 -0.56∗∗ -0.33 -0.10 (0.20) (0.18) (0.27) (0.22) (0.23) (0.20) Modern teaching 0.09 0.49∗∗∗ -0.11 0.55∗∗∗ 0.28 0.44∗∗ (0.18) (0.18) (0.22) (0.20) (0.21) (0.22) Math dummy -0.01 0.00 - - - - (0.02) (0.02) - - - - Observations 11102 10422 5551 5211 5551 5211 R20.19 0.20 0.22 0.22 0.22 0.24 Each column in each panel represents a separate regression. IESCS: Index of Economic, Social and Cultural Status. High and low IESCS refer to student’s IESCS above or below the median of the IESCS distribution. Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. All regressions control for teacher and student characteristics, and school fixed effects. 36 Table 17: Heterogeneous effects: student gender, type of school and type of tutor Math and Reading Math Reading A. Gender of students Boys Girls Boys Girls Boys Girls Tutor’s answers: [11844] [11648] [5922] [5824] [5922] [5824] Traditional teaching 0.04 -0.06 0.06 0.05 0.02 -0.16 (0.11) (0.13) (0.14) (0.16) (0.12) (0.14) Modern teaching 0.11 0.17 -0.07 0.05 0.30∗∗ 0.29∗∗ (0.12) (0.12) (0.17) (0.15) (0.14) (0.13) Math dummy 0.12∗∗∗ -0.13∗∗∗ - - - - (0.02) (0.02) - - - - Students’ answers: [10860] [10664] [5430] [5332] [5430] [5332] Traditional teaching 0.02 -0.56∗∗∗ 0.01 -0.57∗∗ 0.04 -0.55∗∗ (0.18) (0.21) (0.22) (0.27) (0.19) (0.24) Modern teaching 0.13 0.44∗∗ 0.12 0.29 0.14 0.60∗∗ (0.18) (0.18) (0.22) (0.21) (0.19) (0.24) Math dummy 0.12∗∗∗ -0.13∗∗∗ - - - - (0.02) (0.02) - - - - B. Type of school Public Private Public Private Public Private Tutor’s answers: [15000] [8492] [7500] [4246] [7500] [4246] Traditional teaching -0.07 0.29 -0.03 0.45 -0.12 0.14 (0.10) (0.21) (0.11) (0.28) (0.12) (0.18) Modern teaching 0.13 0.09 -0.04 -0.02 0.29∗0.20 (0.13) (0.15) (0.20) (0.18) (0.16) (0.15) Math dummy 0.00 -0.01 - - - - (0.01) (0.02) - - - - Students’ answers: [13590] [7934] [6795] [3967] [6795] [3967] Traditional teaching -0.29∗∗ -0.01 -0.26 -0.15 -0.32∗0.14 (0.15) (0.25) (0.20) (0.30) (0.18) (0.25) Modern teaching 0.40∗∗ 0.18 0.42∗∗ -0.03 0.37∗0.38 (0.16) (0.26) (0.19) (0.32) (0.21) (0.25) Math dummy -0.00 -0.01 - - - - (0.02) (0.02) - - - - C. Type of tutor (in 3rd and 4th grades; only in 4th grade) 4th grade 3rd-4th grades 4th grade 3rd-4th grades 4th grade 3rd-4th grades Tutor’s answers: [5666] [17826] [2833] [8913] [2833] [8913] Traditional teaching 0.06 0.07 -0.05 0.13 0.17 0.01 (0.27) (0.11) (0.35) (0.14) (0.25) (0.13) Modern teaching 0.47 0.24∗0.39 0.10 0.55 0.37∗∗∗ (0.43) (0.13) (0.49) (0.17) (0.47) (0.14) Math dummy -0.05 0.01 - - - - (0.03) (0.02) - - - - Students’ answers: [5222] [16302] [2611] [8151] [2611] [8151] Traditional teaching -0.98∗-0.28 -0.58 -0.37 -1.38∗∗ -0.19 (0.52) (0.19) (0.68) (0.25) (0.68) (0.20) Modern teaching 1.73∗∗∗ 0.44∗∗ 2.02∗∗∗ 0.40∗∗ 1.44∗0.48∗ (0.67) (0.19) (0.75) (0.19) (0.74) (0.26) Math dummy -0.05∗0.01 - - - - (0.03) (0.01) - - - - Observations in brackets. Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. All regressions control for teacher and student characteristics, and school fixed effects. 37 Table 18: Difference between the student’s modern and traditional indexes Math score -0.02 (0.01) Reading score 0.03∗∗ (0.02) Math score (class average)†-0.02∗∗∗ (0.00) Reading score (class average)†-0.03∗∗∗ (0.00) Public school 0.13∗∗∗ (0.05) Selected student characteristics††: Female -0.03∗∗∗ (0.01) Repeater 0.06∗∗∗ (0.01) Born in 4th quarter -0.01∗∗ (0.01) Age at starting school (ref: ≤2 years old): 3 years old -0.00 (0.01) 4 years old -0.02 (0.02) 5 years old 0.06∗∗ (0.03) 6 years old 0.00 (0.03) Mother’s education (ref: Primary or less) Compulsory -0.03∗∗ (0.01) High School -0.02 (0.01) Vocational training -0.02 (0.01) University -0.04∗∗∗ (0.01) Help with homework: Private tutor 0.04∗∗∗ (0.01) Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗p < 0.05,∗∗∗ p < 0.01.†Excluding student’s own value. ††The following characteristics are also included: siblings, single-parent household, country of origin, parents’ labor status, father’s education, experience, 5-years degree or more, person asking for meeting, meetings with parents, tutor in 3rd and 4th grades. For the sake of brevity we report characteristics with significant coefficients (the rest are available upon request). (Continued on next page) 38 Table 18: (continued) Family 0.01∗∗ (0.01) Selected tutor characteristics††: Female 0.02∗∗∗ (0.01) Instruction (ref: Math): Reading and Math 0.04∗∗ (0.02) Reading 0.03∗ (0.02) Constant -0.41∗∗∗ (0.10) School fixed effects Yes Class-average of student characteristics†Yes Observations 10762 R20.19 Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗p < 0.05,∗∗∗ p < 0.01.†Excluding student’s own value. ††The following characteristics are also included: siblings, single-parent household, country of origin, parents’ labor status, father’s education, experience, 5-years degree or more, person asking for meeting, meetings with parents, tutor in 3rd and 4th grades. For the sake of brevity we report characteristics with significant coefficients (the rest are available upon request). Table 19: Sensitivity to include each index separately Math-Reading Math Reading Baseline (1) (2) Baseline (3) (4) Baseline (5) (6) A. Tutor’s answers: Traditional teaching 0.00 0.01 0.08 0.08 -0.07 -0.06 (0.10) (0.10) (0.12) (0.12) (0.10) (0.10) Modern teaching 0.14 0.14 -0.03 -0.02 0.30∗∗∗ 0.29∗∗∗ (0.09) (0.09) (0.13) (0.13) (0.10) (0.10) Observations 23492 23492 23492 11746 11746 11746 11746 11746 11746 B. Students’ answers: Traditional teaching -0.26∗∗ -0.18 -0.26 -0.22 -0.26∗-0.15 (0.13) (0.12) (0.18) (0.17) (0.14) (0.12) Modern teaching 0.34∗∗ 0.27∗∗ 0.27∗0.19 0.41∗∗ 0.36∗∗ (0.13) (0.12) (0.15) (0.14) (0.16) (0.15) Observations 21524 22166 22022 10762 11083 11011 10762 11083 11011 Baseline columns report results from Tables 14 and 15. Each column in each Panel A and B represents a separate regression. All regressions control for student and teacher characteristics, class size and school fixed effects. Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. 39 Table 20: Sensitivity to include the teaching practices individually Math and Reading Math Reading Tutor Students Tutor Students Tutor Students A. Baseline estimates Traditional teaching 0.00 -0.26∗∗ 0.08 -0.07 -0.26 -0.26∗ (0.10) (0.13) (0.12) (0.10) (0.18) (0.14) Modern teaching 0.14 0.34∗∗ -0.03 0.30∗∗∗ 0.27∗0.41∗∗ (0.09) (0.13) (0.13) (0.10) (0.15) (0.16) Observations 23492 21524 11746 10762 11746 10762 B. Without aggregating individual practices Traditional practices Teach by telling 0.01 0.12 0.05 0.09 -0.02 0.14 (0.06) (0.12) (0.07) (0.15) (0.06) (0.14) Exercises proposed by teacher -0.14∗∗ -0.10 -0.14 -0.17 -0.15∗∗ -0.03 (0.07) (0.16) (0.09) (0.19) (0.07) (0.17) Students work individually 0.13∗∗ -0.18 0.16∗∗ -0.06 0.11 -0.31∗∗ (0.06) (0.14) (0.08) (0.19) (0.08) (0.13) Modern practices Student present works/topics -0.03 0.21∗∗ -0.06 0.15 0.01 0.27∗∗ (0.08) (0.10) (0.11) (0.13) (0.09) (0.12) Teacher promotes discussions 0.09∗∗ 0.02 0.06 -0.03 0.12∗∗ 0.07 (0.04) (0.10) (0.05) (0.13) (0.05) (0.10) Students work in small groups 0.07 0.09 -0.04 0.14 0.18∗∗ 0.04 (0.08) (0.10) (0.09) (0.14) (0.09) (0.12) Math -0.00 -0.01 (0.01) (0.01) School fixed effects Yes Yes Yes Yes Yes Yes Tutor characteristics Yes Yes Yes Yes Yes Yes Student characteristics Yes Yes Yes Yes Yes Yes Observations 23492 21524 11746 10762 11746 10762 R20.23 0.22 0.24 0.23 0.26 0.24 Each column in each Panel A and B represents a separate regression. Standard errors clustered at the class level in parentheses. ∗p < 0.10,∗∗ p < 0.05,∗∗∗ p < 0.01. 40