metadata: authors: 0: author: Lopez-Acevedo,Gladys C.
count: Mexico
docna: 0: docna: Professional development and incentives for
            teacher performance in schools in Mexico
docty: Policy Research Working Paper
subtopic: Primary Education,Educational Sciences,Educational Institutions & Facilities,Educational Populations,Education for Development (superceded),Educational Policy and Planning - Textbook,Effective Schools and Teachers,Education For All
teratopic: Gender
abstracts: cdata!: The quality of education is a
            determining factor in competitiveness. In order to globally
            compete, Mexico would have to raise its standards beyond its
            current low achievement. Several innovations at federal and
            state levels have been developed to raise the quality of
            basic education. One example is Carrera Magisterial (CM),
            which is a professional development program that was created
            as part of the National Agreement for the Modernization of
            Basic Education in 1992. This program is aimed at raising
            the quality of basic education through teachers'
            professional training, new learning presence in schools, and
            improving working and salary conditions this report
            evaluates the impact of CM. She shows several important
            results. First, teacher's enrollment in the CM program
            has a positive impact on learning achievement. Second,
            family characteristics are important in explaining
            students' achievement. Third, investment in primary
            school teachers is most effective when targeted toward
            increasing teachers' practical experience and
            developing content-specific knowledge. And fourth, students
            in schools with a high degree of supervision on the part of
            the school principal achieve better scores.
geo_reg_key: 119228,517191
repnme: repnme: Professional development and incentives for
            teacher performance in schools in Mexico
display_title: Professional development and
            incentives for teacher performance in schools in Mexico
listing_relative_url: /research/2004/03/3168055/professional-development-incentives-teacher-performance-schools-mexico
topicv3: Teachers Management m1326119 1523,Primary Education m1326139 480,Textbooks m1326802 2129,Education m1327048 470,Teacher Performance m1327509 1531
publishtoextweb_dt: 2010-07-01T00:00:00Z
historic_topic: Gender
no_of_pages: 49
author_keys: 0: author_key: 428192
model_extractions: WPS 3236

## **Professional Development and Incentives for Teacher Performance in Schools in Mexico**

Gladys Lopez-Acevedo (LCSPP)* Gacevedo@worldbank.org Latin America and the Caribbean Region Poverty Reduction and Economic Management Division The World Bank JEL Codes: D00

# <u>Abstract</u>

Quality of education is a determining factor in competitiveness. In order to globally compete, Mexico would have to raise its standards beyond its current low achievement. Several innovations at federal and state levels have been developed to raise the quality of basic education. One example is Carrera Magisterial (CM), which is a professional development program that was created as part of the National Agreement for the Modernization of Basic Education in 1992. This program is aimed at raising the quality of basic education through teachers’ professional training, new learning presence in schools and improving working and salary conditions. This paper evaluates the impact of CM. It shows several important results. First, teacher's enrollment in the CM program has a positive impact on learning achievement. Second, family characteristics are important in explaining students’ achievement. Third, investment in primary school teachers is most effective when targeted toward increasing teachers’ practical experience and developing content-specific knowledge. Fourth, students in schools with a high degree of supervision on the part of the school principal achieve better scores.

### World Bank Policy Research Working Paper 3236, March 2004

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the author. They do not necessarily represent the view of the government of Mexico, World Bank, its Executive Directors, or the countries they represent. Policy Research Working Papers are available online at http://econ.worldbank.org._

> * Please send your comments to <u>gacevedo@worldbank.org. Special thanks to Vicente Paqueo, Guilherme Sedlacek,</u> Eduardo Velez, Dulce Maria Nieto, Francisco Martinez, Daniel Lederman, Claudia Piras, William D. Savedoff, Marcelo Giugale, Kin Bing Wu, William Maloney and Laural Rawlings for valuable comments and discussion. Valuable comments were also received from the Impact and Evaluation Group, the Economic Policy Group in July 2000, the participants attending the CIDE seminar in September 2000 and the LACEA network in October 2000.

1
# **MAIN ABBREVIATIONS & ACRONYMS**

|**ANMEB**|**National Agreement for the Modernization of Basic Education**<br>**(Acuerdo Nacional para la Modernización de la Educación Básica)**|
|---|---|
|**EEEP**|**The Primary Education Assessment Survey, second round 1997**<br>**(Encuesta de Evaluación de Educación Primaria, segundo levantamiento 1997)**|
|**INEGI**|**National Institute of Statistics, Geography, and Information**<br>**(Instituto National de Estadística, Geografía e Informática)**|
|**SEP**|**Ministry of Education**<br>**(Secretaría de Educación Pública)**|
|**SNTE**|**National Union of Education Workers**<br>**(Sindicato Nacional de Trabajadores de la Educación)**|

2
# **1. INTRODUCTION**

Good quality of education is critical in the new era of global competition and technological change. Mexico’s future development depends on its ability to take advantage of new opportunities quickly and decisively. Good basic education that can be accessible to all is a necessary element for a sustainable, poverty-reducing development strategy.

This paper is part of a series that examines teachers’ incentives and professional development in Mexico, in pursuit of the long-term goal of improving student learning performance.<sup>1</sup> The paper is divided into the following sections: the background succinctly places the objectives in context. Section 3 describes the data and methodology used in this paper. Section 4 compares school factors and management that are correlated with learning achievement in highly effective and ineffective schools. Section 5 measures the impact of school factors on learning achievement, particularly _Carrera Magisterial_ , teachers' salaries and training. Section 6 offers conclusions.

# **2. BACKGROUND**

Mexico is a federal country with a population of almost 97.4 million people spread unevenly over nearly 2 million square kilometers. About three-fourths live in urban areas. The country is relatively young—24 percent of the population is between 5-14 years old. The share of this age group in the total population is the highest among OECD countries, which have an average of about 14 percent. The pace of demographic growth has been dropping dramatically in recent times. As a result, the population under 6 years old has been decreasing at the rate of 0.5 percent a year, while the 6-14 age group has been increasing by no more than 0.1 percent a year. By the end of the century, the total number of persons in this age group will have virtually stabilized.

The structure of Mexico’s educational system has the following main characteristics. Basic education is the Mexican government’s highest priority. The basic education system consists of: (a) early childhood education (or pre-school), which is optional for children 3 to 5 years old; (b) mandatory primary education,

> 1 Lopez-Acevedo and Salinas (2000a) Teacher’s Salaries and Professional Profile in Mexico. The World Bank Mimeo. Lopez-Acevedo and Salinas (2000b) Factors that Affect Learning Achievement in Mexico: The Case of Mexico D.F., Nuevo Leon and Tabasco. The World Bank. Mimeo.

3
ideally from ages 6 to 12, but due to late enrollment and grade repetition targeted to ages 6 to 14, and (c) mandatory lower secondary school, consisting of a 3-year cycle, and intended for children ages 12 to 16.

The Mexican educational system has become highly centralized in the hands of the federal government. This centralization is reflected by the growing share of federal schools in total enrollment, which rose from 64 percent in 1970 to 72 percent in 1990. In May 1992, however, the states, the federal government structures, and the National Union of Workers in Education ( _Sindicato Nacional de Trabajadores de la Educación_ , SNTE) signed the National Agreement for the Modernization of Basic Education ( _Acuerdo Nacional para la Modernización de la Educación Básica_ , ANMEB). This agreement was created in response to demand for a decentralized educational system. This agreement should allow states to have more participation. Previous attempts to decentralize the educational system have failed due to constraints on the states and federal government structures and to the opposition of the SNTE. ANMEB is part of a long process that yielded satisfactory results until May 1992, when the federal government, state governors, federal agencies and the SNTE signed the agreement.

This program had three main objectives. The first was associated with the reorganization of the educational system, which consisted in the transfer of the education sector, formerly administered by the federal government, to the States. The transfer included 513,974 teachers, 116,054 administrative posts, 3,954,000 hourly salaries, 1.8 million pre-school students, 9.2 million primary students, 2.4 million secondary students, and 22 million diverse materials.

The second objective was the reformulation of regional educational content, in which states received the authority and the right to propose changes. Proposals are evaluated by SEP and, if accepted, included in the Free Textbook System ( _Sistema Nacional de Libro de Texto Gratuito_ ). In this respect, the role of the states is to propose content, while the federal government decides and puts the proposal into practice.

The last objective, the revaluation of teaching activities, consisted in launching _Carrera Magisteria_ , for basic education teachers and union members. Overall, the objective was to improve teachers' welfare through better salaries and housing policies.<sup>2</sup> ́<sup>3</sup>

> 2  The Appendix presents a detailed review of the educational decentralization process in Mexico.

> 3 The ANMEB aimed at reorganizing the educational system through a process of administrative decentralization, as well as a revision of the basic educational program and the production of adequate textbooks. In accordance with this agreement, the federal government transferred the control and management of the basic education schools to the state governments. The 1992 agreement carried with it only a very limited idea of decentralization. Still, the federal government remains responsible for general policies and standards (normative and policy-making functions), teachers’

4
In this context, the federal government modified its educational discourse, placing more emphasis on the quality of educative content instead of the previous focus on educational coverage. As mentioned above, _Carrera Magisterial_ was created as part of the ANMEB in 1992. It was aimed at raising the quality of basic education through teachers’ professional training, new learning presence in schools, and improving working conditions. One component of this program is the training of teachers; another is a merit payment system in which professional staff is voluntarily evaluated and rewarded with salary increases for their performance as classroom teachers, school directors-supervisors and administrators ( _tecnico-pedagogicas_ ). The evaluation is based on experience (10 points), professional skills (28 points), educational school level (15 points) and completion of accredited courses (17 points). In the case of teachers' performance in school, 30 points are given to student’s learning achievement and professional performance.

As with principals and supervisors, 30 points are given to school performance and professional achievement. Teachers in the third area ( _tercera vertiente_ ) obtain 30 points for educational support. All the teachers in any one of the following modalities are considered as candidates for the program: initial education, basic education, indigenous schools and lower secondary education via television ( _telesecundaria)_ . There are five levels of promotion (“A”, “B”, “C”, “D”, “E”). The salary rewards allocated to each represent a salary increase but do not represent a change in the type of post assigned to the teacher. The amount assigned to each of these levels is a considerable increase with respect to the number of hours worked in the initial post. According to the General Direction of Evaluation (SEP), 21 percent of a teacher's total salary at Level "A" comes from _Carrera Magisterial_ program. _Carrera Magisterial_ contributes 38, 51, 61 and 68 percent to a teacher at Level "B", "C", "D" or "E," respectively. The promotion ladder attaches considerable importance to seniority within this program, posts or teaching jobs in under developed areas. Once a teacher gets the _Carrera Magisterial_ benefit, it is extremely rare that he/she looses it. If a teacher retires, she/he cannot be promoted within _Carrera Magisterial_ unless assigned to administrative tasks ( _tecnico-pedagogicas_ ).

The Mexican government is the predominant provider of basic educational services. It owns about 91 percent of primary and secondary schools, which account for 90 percent of the enrollment.<sup>4</sup> At university

> formation and allocation, textbook production, evaluation and monitoring, and the provision of financial resources needed to ensure proper coverage and quality of the educational system. Moreover, federal education transfers to the states remain earmarked for specific purposes. In 1998 the government passed the 1998 Law on Fiscal Coordination, which gave the states a greater discretion in the use of federal education and other transfers.

> 4 The enrollment rate for public schools is about 94 percent (primary), 93 percent (lower secondary) and 78 percent (upper secondary).

5
level, however, the private sector plays a much bigger role. It accounts for close to half of the enrollment (46 percent). The educational system in Mexico is now so extensive that there are over 483,000 schools (excluding preschool) staffed by over a million teachers, of which 84.3 percent are from public schools. Teachers represent 2.8 percent of the full time labor force from which only 20.1 percent are private school teachers.

In 1999, the public school teachers’ share<sup>5</sup> was 42.82 percent of the total number of government personnel. All teachers in public basic education are affiliated with SNTE. All teachers in upper secondary and tertiary education have a union of professors and administrative workers also affiliated with SNTE or are independent (Autonomous or State Universities).

# **3. DATA AND METHODOLOGY**

The Primary Education Assessment Survey, second round 1997 ( _Encuesta de Evaluación de Educación Primaria_ [EEEP] _, segundo levantamiento_ 1997) from the Ministry of Education is representative by state level and by stratum (urban — public and private — schools, public rural schools, indigenous schools<sup>6</sup> and community schools). Students were given standardized achievement tests at the beginning of sixth grade that covered the subjects studied in the 5<sup>th</sup> grade. EEEP also collected information on schools, parents, teachers, supervisors, socioeconomic and academic backgrounds. Non-categorical are students' scores, age, amenities or facilities in the house, the number of rooms in the house, the number of teachers' updating courses, didactic material available to the teacher and school equipment. The survey design was stratified and multistage. In each stage the sample size was chosen randomly. Importantly, the final sampling unit was the school and not the student. The sample included 53,209 students and 3,645 schools. In matching students with their parents, 8,450 students were lost because their parents did not respond to the questionnaire. Another 30 percent of the sample (number of students) was also lost when matching students with their corresponding 5<sup>th</sup> grade teachers. The distribution of the scores of those students that were matched successfully suggests that there was not truncation in the sample. The Appendix shows the sample sizes by state and stratum and the list of variables employed in the analysis.

> 5 Federal, state plus autonomous school teachers. 6 The indigenous schools refers to schools offering services to populations which mother tongue is not Spanish.

6
In order to avoid self-selection problems derived from non-response, the sample used in the subsequent analysis was corrected with the standard Heckman's methodology. It was assumed that the three nonresponding stages were independent.

Stage 1: Students' characteristics self-selection problem. The probit equation for computing the Mill's ratio was specified as follows: Define yi=1 if the ith student answered the questionnaire and yi=0 otherwise. State, stratum and classroom size variables explain this probability. In order to identify the model, we used a set of geographical dummy variables at state level (trigger variable) as a measure of the differences in willingness to answer the questionnaire. The Probit estimation results are shown in Section 1 in the Appendix.

Stage 2: Parents' characteristics Self-selection problem. The probit equation for computing the Mill's ratio was specified as follows: Define zi=1 if the ith student's parents answered the questionnaire and zi=0 otherwise. Geographical variables as state and stratum, as well as the classroom size and student's characteristics explain this probability. In order to identify the whole model, a set of geographical dummy variables is proposed at state level (trigger variable) as a measure of the differences in the willingness to answer the questionnaire. The probit estimation results are shown in section 1 in the annex Stage 3: Teachers' characteristics self-selection problem. The probit equation for computing the Mill's ratio was specified as follows: Defining xi=1 if the ith student's teacher answered the questionnaire and xi=0 otherwise. Geographical variables as state and stratum, as well as the classroom size, student characteristics, school characteristics, and director characteristics explain this probability. In order to identify the whole model, we propose a set of geographical dummy variables at state level (trigger variable) as a measure of the differences in the willingness to answer the questionnaire. The probit estimation results are shown in Section 1 of the Appendix.

In addition, it is possible that there is a _Carrera Magisterial_ self-selection problem. The relationship observed between a student's learning and her/his teacher being in a _Carrera Magisterial_ may occur because of the self-selection problem. That is, teachers who join _Carrera Magisterial_ are likely to see themselves as and be highly effective teachers, so have a high probability of being rewarded. In order to avoid a possible self-selection problem, the standard Heckman's methodology was applied.

7
_Carrera Magisterial_ self-selection problem. The probit equation for computing the Mill's ratio was specified as follows: Defining vj=1 if the jth teacher is in Carrera Magisterial and vj=0 otherwise. Geographical variables as state and stratum, as well as classroom size, teacher characteristics and school characteristics explain this probability. "Teacher's opinion about _Carrera Magisterial_ program" is proposed as the trigger variable for measuring the differences in the application of this program, which might affect the probability of participation. The probit estimation results are shown in Section 1 of the Appendix. Interestingly, the age, region, stratum, classroom size, gender, school level, experience in 5th grade, supervision and household size are important in explaining the probability of enrollment in _Carrera Magisterial_ . Being female increases this probability by 14% while age and experience increase it by 5% and 4.3% respectively. Selectivity bias is significant in urban areas but not in rural areas (see the Annex).

In Section 4, the EEEP is used in order to measure the effect of school variables on a student’s performance. An exploratory analysis was performed of the school variables, which are likely to constrain, empower and motivate teacher's performance. For this purpose, schools were grouped into learning achievement quintiles. In addition, compound indexes of some of these school variables were constructed. Examples of school variables used were teachers’ performance, school principal's supervision, schools' facilities, directorial supervision at classroom level, teacher's training, career opportunities available to the teacher ( _Carrera Magisterial_ ), experience, and school equipment, all by public/private institution and stratum. Section 5, which also uses the EEEP, presents the estimates of school and family effects on learning achievement by means of several multivariate models<sup>7</sup> . Section 6 offers conclusions.

# **4. THE EFFECT OF SCHOOL VARIABLES ON STUDENT PERFORMANCE: A DESCRIPTIVE ANALYSIS.**

Mexican education literature is rich in ethnographic studies of schools in various parts of the country. In contrast, there are hardly any econometric studies that quantify the effects of school factors on student learning. There are some econometric studies (World Bank 1998; Lopez-Acevedo 1999) analyzing _Programa para Abatir el Rezago Educativo_ (PARE) data, but they too are limited to a few states. This section presents a national/urban/rural and public/private analysis of the EEEP measuring students’ performance. The purpose

> 7 The methodology used for such a part is presented with more detail in section 5.

8
here is to test certain hypotheses regarding the determinants of student learning. These hypotheses relate to the effects of school quality, particularly the teachers’ quality, training, and teaching practices. Issues regarding teachers’ incentives, supervision, facilities, and specific students' characteristics and their parents' are also included in the analysis.

Based on the EEEP from SEP, Table 1 shows the distribution of Spanish and Mathematics test scores by school quintiles. The best 20% schools in the nation have a score of 57.7 on average in Mathematics (out of 100 points) and a relatively higher score in Spanish. The standard deviation is higher in this group compared to the rest of the learning achievement quintiles. The highest grade dispersions are concentrated at the tails of the distribution.

**Table 1.** **<u>5</u>**<sup>**th**</sup> **<u>Grade Test Scores by Learning Achievement quintile</u>**

|**Quintile**|**Mathe**|**matics**|**Span**|**ish**|
|---|---|---|---|---|
||**Mean**|**SD **|**Mean**|**SD **|
|1|40.7|2.9|46.5|2.7|
|2|45.6|0.8|51.5|1.0|
|3|48.4|0.7|54.5|0.7|
|4|51.5|1.0|57.8|1.3|
|5|57.7|4.2|65.5|5.0|
|Total|48.7|6.1|54.9|6.8|

Source: Primary Education Assessment Survey, second round 1997.

Table 2 shows the distribution of test scores nation-wide by stratum. Private urban schools perform relatively better than do other types of schools. Public urban schools rank second while indigenous schools are at the bottom of the distribution. Nonetheless, the grade differences between indigenous schools and community schools are small, particularly in Spanish scores. The highest dispersion of test scores is found in the learning of Spanish scores in private urban schools.

9
|**Tab**|**le 2. Test Sco**<br>**Mathem**|**res by Stra**<br>**atics**|**tum**<br>**Span**|**ish **|
|---|---|---|---|---|
|**Stratum **|**Mean**|**SD **|**Mean**|**SD **|
|Community School|47.3|5.7|52.0|5.2|
|Indigenous School|45.8|5.4|51.5|5.1|
|Public rural school|48.2|6.0|54.0|6.2|
|Public urban school|49.4|5.9|55.6|6.3|
|Private urban school|53.0|6.5|62.9|8.4|
|National|48.7|6.1|54.9|6.8|

Source: Primary Education Assessment Survey, second round 1997 Table 3 shows classroom size, which can be taken as a measure of relative school productivity among stratum. Surprisingly, indigenous schools perform better in this indicator than community schools given that the scoring difference between them is not significant. Classroom size does not differ significantly between private urban schools and public urban schools although variance is greater in the latter.

|**Table 3. Classroom size by Str**<br><br>|**atum**<br>|
|---|---|
|**Stratum **<br>**Mean**|**SD **|
|Community School<br>23.0|1.2|
|Indigenous School<br>22.5|8.0|
|Public rural school<br>21.5|7.1|
|Public urban school<br>24.6|3.5|
|Private urban school<br>24.3|4.5|
|National<br>22.6|6.6|

Source: Primary Education Assessment Survey, second round 1997.

Tables 4-5 below show the distribution of students by learning achievement quintiles. About 45% of students in private urban schools are enrolled in the top quintile of schools, compared to only 6.4 percent of the students from indigenous schools, which has the highest percentage of students enrolled in the bottom quintile of Mexican schools. These results are more pronounced in Spanish, since 61.4 percent of the students in private urban schools are enrolled in the best 20% schools, compared to only 4.0 percent of the students from indigenous schools, which also have the largest percentage of students enrolled in the lowest 20%. The distribution of students enrolled in public urban schools is evenly distributed across quintiles. The distribution of students in public rural schools is biased toward the lowest quintile.

10
**Table 4.** **<u>5</u>**<sup>**th**</sup> **<u>Grade Students Share by Mathematics Test Scores Quintiles within Stratum</u>**

|**Stratum **|**Quintile 1**|**Quintile 2**|**Quintile 3**|**Quintile 4**|**Quintile **|**5**<br>**Total**|
|---|---|---|---|---|---|---|
|Community School|26.0|23.4|20.2|18.2|12.2|100.0|
|Indigenous School|33.2|26.9|20.1|13.4|6.4|100.0|
|Public rural school|22.5|21.4|20.1|19.1|16.9|100.0|
|Public urban school|15.7|18.5|20.6|23.9|21.3|100.0|
|Private urban school|6.4|10.2|13.6|24.4|45.3|100.0|

Source: Primary Education Assessment Survey, second round 1997.

**Table** **<u>5. 5</u>**<sup>**th**</sup> **<u>Grade Students Share by Spanish Scores Quintile within Stratum</u>**

|**Stratum**|**Quintile 1**|**Quintile 2**|**Quintile 3**|**Quintile 4**|**Quintile 5**|**Total**|
|---|---|---|---|---|---|---|
|Community School|30.7|30.5|17.7|15.2|5.9|100.0|
|Indigenous School|34.8|28.8|16.7|15.7|4.0|100.0|
|Public rural school|22.5|24.9|18.9|20.8|12.9|100.0|
|Public urban school|15.4|20.8|17.5|25.6|20.8|100.0|
|Private urban school|4.9|6.9|6.9|19.9|61.4|100.0|

Source: Primary Education Assessment Survey, second round 1997.

Tables 3, 4a, and 4b in the Appendix show the distribution of the school variables across learning achievement quintiles. An exploratory analysis identifies different factors. Quintile 1 represents ineffective schools, while quintile 5 includes effective schools. For all the school strata considered, the results indicate a strong correlation between school effectiveness and teachers' pedagogical effort, family income and level of schooling. In public rural schools, parents’ expectation of a child’s scholastic achievement is positively and highly correlated with learning achievement. For all public schools, the quality of educational services as perceived by the parents has a positively strong effect on achievement. Other relevant variables in public schools were teaching experience, teachers' residence in the community, teachers' training, number of students in the classroom, enrollment in _Carrera Magisterial,_ parents' participation in the learning process; didactic material available to the teacher and supervision. All other variables show a weak correlation with school effectiveness.

# **5. TEACHERS’ INCENTIVES AT THE SCHOOL LEVEL IN MULTIVARIATE MODELS** .

As discussed above in the overall learning levels, the quality of basic Mexican education is low. According to the EEEP, 52.8 percent of 5<sup>th</sup> grade students are below the Spanish mean of 54.9. Just over half are also below the Mathematics mean of 48.7. Lopez-Acevedo and Salinas (2000b) show that these average 11
achievement rates mask disparities between states and regions. What primary school characteristics contribute the most to student learning in a multivariate model? How do these school variables impact on learning achievement? This section addresses these questions, indicating the factors that increase students' success in primary school.

The importance attributed to school factors is not unique, as school-level variables have a stronger effect on students' achievement in LDC's than in developed countries. It is clear that despite the strong contextual variables effect on primary level student achievement in Mexico, school variables are important. Thus, the identification of those school factors that lead to increase student learning is also important. Largely based on quantitative analysis of the EEEP, the impact of _Carrera Magisterial_ and other important school factors on learning achievement are examined using multivariate models.

The hierarchical structure of the data, with students nested within schools, requires a form of regression analysis that weighs the sources of learning achievement variation—students, school and teachers. To analyze the determinants of learning achievement, the models below were estimated. In each model, the school, socioeconomic and teachers ́ characteristics are the same. This estimation strategy allows us to measure the effect of these factors on learning achievement _._ The first model is the variance plus school fixed model, which is the starting point in every multilevel analysis.

The first model fully captures school effects through the use of a complete set of school dummies. The second model uses school variables (instead of dummies) to help analyze the determinants of school factors on learning achievement. Denoting child and household level variables by X, school dummies by D, and school variables by W, the models are: The two models are estimated separately for the urban and rural areas as well as nationally.

This attribute enables us to estimate the overall mean of achievement, and determine the deviations of student scores and school averages around that mean. The second model fully captures the students effects through adding student socioeconomic variables to the empty model. The third model uses school level 12
variables to help analyze the determinants of school effects on learning achievement. The fourth model drops the dummy variables from the third model and is estimated by ordinary least squares.

where,

- _Y_ Vector of individual student test scores, Mathematics or Spanish

- _X_ Matrix of student's socioeconomic background variables

- _Z_ Matrix of teacher's and school's variables

- _di_ The dummy variables that indicate schools in the sample

- `

- ε Vector of residual terms [ _E_ (ε) = 0 and _E_ (εε ) = 0 ].

- _(1) Model 1 (fixed effects model). The model is described by the following equation,_

where,

- _Y ij_ Vector of individual student test scores, Mathematics.

- γ00 Overall mean of achievement.

- _di_ The dummy variables that indicate schools in the sample.

- γk The deviations of achievement of the "k" school around the overall average.

- ε ij The deviations of students scores around the overall average.

Table 6 shows the estimates of the first model for public/private schools at national level, as well as for urban and rural areas. It can be seen in this table that the variation in mathematics test scores has an important school effect in urban/rural areas. At the national level, the total students’ scores variance is 48.35, of which 51% of the variance component ratio is attributed to school-level effects.

13
**Table** **<u>6.  The Empty Model Public and Private Schools</u>**

||**Pu**<br>|**blic Schools**<br>||**Public and Private Schools**<br>|
|---|---|---|---|---|
||**National**|**Urban**|**Rural**|**National**|
|Total students' scores variance|48.35|56.26|46.67|48.99|
|Variance within the schools|23.82|24.67|23.15|24.08|
|Variance between the schools|24.54|31.59|23.52|24.90|
|Variance component ratio of school effect|0.51|0.56|0.50|0.51|
|Number of students|19,419|11,256|8,163|23,955|
|Number of schools|1,586|744|842|1,909|

Source: Authors' estimates using the Primary Education Assessment, second round 1997, SEP.

# _(2) Model 2 with school dummies and students' characteristics:_

In order to have greater precision in the estimation of the students' effects on the learning achievement, several variables were introduced at the student level, including student's gender, age, pre-school education, repetition of 5th grade, blurred vision, teacher performance, student attitude towards learning, household size, household income, household utilities, number of books in house, number of rooms in house, parent schooling level, parent expectations of student educational achievement and parent opinion of educational services in the school. The variables were entered individually to test whether the coefficients remained robust. The model is described by the following equation: where,

- _Yij_ Vector of individual student test scores, Mathematics.

γ00 Overall mean of achievement.

- _Bh_ Vector of parameters to estimate ; 1, .., H .

- _X ij_ Matrix of student's socioeconomic background variables.

- _dk_ The dummy variables that indicate schools in the sample.

- γk The deviations of achievement of the "k" school around the overall average conditioned on students’ characteristics.

- ε ij The deviations of students scores around the overall average.

14
**Table** **<u>7.  Model 2. Students' Characteristics</u>**

|||**Nationa**|**l**<br>||**Urban**|||**Rural**|<br>|
|---|---|---|---|---|---|---|---|---|---|
||Coeff.|S.E.|Level of<br>Sig.|Coeff.|S.E.|Level<br>of Sig.|<sup>Coeff.</sup>|S.E.|Level of<br>Sig.|
|Student's gender (Male)|0.211|0.309|0.495|0.985|0.489|0.044|0.034|0.503|0.946|
|Student's age|-0.358|0.150|0.017|-0.484|0.179|0.007|-0.204|0.224|0.363|
|Pre-school education (Yes)|-0.069|0.279|0.805|-0.046|0.455|0.919|-0.259|0.434|0.551|
|Repetition in 5th grade (Yes)|-0.652|0.323|0.044|-0.204|0.370|0.581|-0.743|0.430|0.084|
|Blurred Vision (Yes)|-1.281|0.366|0.000|-1.301|0.560|0.020|-1.286|0.580|0.027|
|Teacher's performance|0.244|0.070|0.000|0.382|0.084|0.000|0.227|0.107|0.034|
|Student's attitude towards learning|-0.111|0.063|0.079|-0.105|0.076|0.166|-0.101|0.103|0.326|
|Household income|0.152|0.054|0.005|0.135|0.053|0.012|0.115|0.089|0.194|
|House services|0.023|0.017|0.188|0.023|0.022|0.296|-0.002|0.027|0.944|
|Father's schooling level|0.105|0.073|0.151|0.097|0.067|0.144|0.210|0.099|0.034|
|Mother's schooling level|0.121|0.065|0.062|0.127|0.065|0.052|0.081|0.111|0.466|
|Parent's opinion of educational services in school|0.309|0.101|0.002|0.265|0.110|0.016|0.288|0.167|0.085|
|Correction of self-selection bias at stage 2|8.441|13.094|0.519|-4.276|19.114|0.823|9.487|25.695|0.712|
|Correction of self-selection bias at stage 3|-3.689|13.007|0.777|12.644|19.728|0.522|-12.356|21.904|0.573|
|Constant|50.832|2.948|0.000|48.597|3.872|0.000|53.011|4.893|0.000|
|Total Variance|34.958|||39.105|||39.228|||
|Variance within the schools|23.408|||23.479|||22.563|||
|Variance among the schools|11.550|||15.626|||16.665|||
|Variance component ratio of school effect|0.330|||0.400|||0.425|||
|R squared( explained variance)|0.277|||0.305|||0.159|||
|Students' R squared(explained variance)|0.017|||0.048|||0.025|||
|Schools' R squared(explained variance)|0.529|||0.505|||0.291|||
|Number of Students|13,439|||7,721|||5,718|||
|Number of Schools|1,553|||740|||813|||

Source: Authors' estimates using the Primary Education Assessment, second round 1997, SEP.

The advantage of this model is that it provides extensive information about the sources of variation that constitute the R-squared. At the national level, the student socioeconomic variables explain 27.7 percent of the total variation. This is understandable, because almost all explanatory variables are categorical. Notice that this set of socioeconomic student variables explains more than 52 percent of the variation among schools but only explains 1.7 percent of the students’ variance. In urban areas, the explanatory power of the socioeconomic variables is similar to that of the national level. The introduction of these variables has several effects. It reduces in absolute terms the variance among schools (from 24.54 in model 1 to 11.55 in model 2) because individuals are less heterogeneous. The variance component ratio of school effect from model 1 to model 2 dropped by 18% percent, implying that the variance component ratio of student effect increased by 69%. Thus, schools appear to be more similar (homogenous) considering students’ characteristics, but the differences among schools (heterogeneity) remain relatively important. The explanatory power of the student 15
variables is much lower for rural areas than for urban areas. These variables explain only 29.1 percent of the total school variance and 2.5 percent of the student variance.

This analysis also weighed student socioeconomic profile. Males and females achieve equally in mathematics. Age and grade repetition have a significantly negative impact on mathematics achievement. These students achieve lower grades than do others. Repetition has been associated with low achievement and school dropout (Lopez-Acevedo, 1997). Pre-primary school level is not significant for mathematics test scores, possibly because parents infrequently participate in their children’s learning achievement. Additional work is needed to establish the links between initial education, parents’ participation and learning achievement. Nonetheless, the results show that the development of self-driven and studious students who seek information beyond textbooks is a key factor in increased learning achievement. How to develop good learning habits and motivation among students should be a challenge not only to teachers but also to parents. Blurred vision has a large negative impact on achievement, which has been consistently strong thorough all estimations. Vision problems increase rapidly with age.

Teacher's pedagogical behavior (efforts and performance in the classroom) is of great importance in grading learning achievement. The impact of this variable is many times larger than the impact of other school factors, such as didactic material available to the teacher. Students learn better when they are taught by teachers who teach clearly (that is, explain concepts clearly), who have a thorough knowledge of the subject matter and who are able to intelligently handle students’ questions and doubts. Although some individual teachers have introduced more interactive practices, the majority continue to use traditional, instructorcentered approaches. No general tradition exists in Mexico for encouraging active learning, managing group work, developing locally relevant materials, or adapting lessons to teach problem-solving. The quality of teachers’ assessments of student progress appears inadequate, and teacher responses to students’ questions are also.

Students in households with higher per capita income or family assets achieve higher scores. In addition, there is a strong positive relationship between mother’s schooling level and children learning achievement in urban areas and, conversely, father's schooling level and student achievement in rural areas. The quality of educational services, as perceived by the parents, has a considerable positive impact on learning achievement.

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_(3) Model 3 (with student's socioeconomic index, and school and dummy variables)._ To estimate the impact of school variables on student achievement scores, conditional upon the socioeconomic student's profile, a socioeconomic student index was constructed by means of principal component analysis. In order to do this, we assumed (as suspected) that student's age, repetition in 5<sup>th</sup> grade, blurred vision, student's household income, mother's schooling level, and father's schooling level were related to each other. Once this index is estimated, we introduce it into the regression model as an additional explanatory variable. Accordingly, model 3 is described by the following equation: where,

- _Yij_ Vector of individual student test scores, Mathematics.

- γ00 Overall mean of achievement.

_B_ Parameter to estimate

- αm Vector of parameters to estimate; 1, ..., M.

- _Ii_ Vector of student's socioeconomic index.

- _Z_ j   Matrix of schools variables.

- _dk_ The dummy variables that indicate schools in the sample.

- ε ij   The deviations of students scores around the overall average.

Table 8 presents estimation of model 3 at the national level. Table 5 in the Appendix presents the estimations for rural and urban areas<sup>8</sup> . As in model 2, the variables were entered individually to test whether the coefficients remained robust.

> 8 In order to measure the academic achievement of students, socioeconomic variables, teacher and school variables have to be taken into account, since students are grouped in classrooms, which are grouped in a particular school. Within a school, this provides different educational experiences and determines specific characteristics for students as a group, depending on the class they are in. At the school level, differences can be even more striking. For example, the environment in a private school is different from that of a state owned school. This variable grouping limits the usefulness of traditional statistical analysis, Ordinary Least Square analysis gives equal weight to each observation and, as shown in various studies in which observations are grouped in levels, the assumption gives us biased estimates.

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**Table** **<u>8. Determinants of Mathematics Achievement Scores in 5</u>**<sup>**th**</sup> **<u>grade at National Level</u>**

||**Public**|**and Privat**<br>**Ll f**|**e Schools**||**Public Sch**<br>**Ll f**|**ools**|
|---|---|---|---|---|---|---|
||**Coeff.**|**eve o**<br>**Sig.**|**Elasticity **|**Coeff.**|**eve o**<br>**Sig.**|**Elasticity**|
|Student Socioeconomic Index|0.485|0.000||0.485|0.000||
|Teacher's gender (Male)|-0.675|0.023|-0.0072|-0.916|0.015|-0.0103|
|Teacher's age|0.190|0.095|0.0183|0.280|0.070|0.0270|
|Attendance to updating courses (Yes)|-0.931|0.074|-0.0171|0.416|0.476|0.0077|
|Teacher's residence within the community (Yes)|-0.052|0.890|-0.0004|-0.102|0.801|-0.0008|
|Teacher's years of residence in the community|0.240|0.027|0.0261|0.135|0.261|0.0148|
|Teacher's schooling level|0.139|0.294|0.0103|0.219|0.183|0.0163|
|Teacher's pedagogical behavior|0.053|0.034|0.0052|0.194|0.015|0.0041|
|Teacher's interest in students' learning|0.288|0.023|0.0098|0.092|0.003|0.0031|
|Number of updating courses|0.028|0.584|0.0030|0.021|0.709|0.0023|
|Type of post. Short term (Yes)|-1.210|0.030|-0.0013|-1.177|0.014|-0.0013|
|More than one post (Yes)|-0.004|0.990|0.0000|0.304|0.395|0.0014|
|Teacher's income|0.135|0.225|0.0097|0.094|0.475|0.0069|
|Didactic material available to the teacher|0.011|0.608|0.0033|-0.004|0.878|-0.0011|
|Number of supervisor visits (as Director's answer)|5.523|0.000|0.0754|5.484|0.000|0.0780|
|Teacher's enrollment in Carrera Magisterial (Yes)||||1.436|0.003|0.0187|
|Carrera Magisterial level||||-0.413|0.056|-0.0072|
|Correction of self-selection bias at stage 2|6.886|0.222||8.146|0.154||
|Correction of self-selection bias at stage 3|-9.769|0.054||-12.472|0.014||
|Correction of self-selection bias in Carrera Magisterial||||1.674|0.182||
|Constant|45.854|0.000||44.873|0.000||
|R^2|||0.388|||0.377|
|Number of Students|||14847|||13,767|
|Number of Schools|||1718|||1602|

Source: Authors' estimates using the Primary Education Assessment, second round 1997, SEP. n.a. Not applicable.

# **_General Results_**

In general, students with teachers that have more years of experience (using age as a proxy) achieve higher scores in Mathematics. It is clear that teacher experience and seniority improve student achievement growth rates, suggesting that teacher proficiency is enhanced by practical experience and training. The marginal productivity of time spent in formal education of teachers on teacher effectiveness is statistically insignificant. But the potential of training to contribute to the improvement of teaching effectiveness appears high. The following findings show: the importance of teachers’ experience and practice; teacher ability to deal with children’s questions and doubts intelligently (implying the importance of teachers’ subject matter knowledge), and teacher effectiveness in monitoring students' performance or difficulties and talking to students.

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Female teachers increase learning achievement. Interestingly, training (measured by the number of courses taken by the teacher) has not impacted student achievement. Moreover, each one of these courses separately failed to have an impact on learning achievement. Thus, investment in primary school teachers seems most effective when targeted towards increasing practical experience and developing content-specific knowledge.

Teacher’s years of residence in the community increases student’s achievement, possibly because of the teacher’s involvement with the community. Type of post (permanent or short-term) negatively impacts learning achievement. A possible explanation is that in public schools, a temporary post has almost the same benefits as a regular or permanent post. It is extremely rare to find a case where an individual had to leave his job because his “short-term post” was not renewed or because it was not changed to a long-term post. For practical purposes, “short-term post” does not mean that the teacher has to go through a probation period. This system of posting and assignments generates a conflict within learning.

Teacher’s years of schooling failed to demonstrate significant effects on student learning, which is expected since there is little variance in the level of schooling. A teacher's income has no significant effect on learning achievement, but many studies have found that teacher's salary is a poor predictor of a student's achievement.

Frontline educators feel that problems relating to school infrastructure and facilities negatively affect teaching effectiveness and student learning achievement. Their foremost recommendation for raising school quality is to address this inadequacy. To what extent this recommendation will actually lead to student learning achievement is questionable. Some studies in other countries show that improvement in school infrastructure can have a significant positive impact on student learning. Mexican data do not appear to support this hypothesis.

Teacher’s pedagogical efforts show a positive and significant marginal effect on learning achievement. Pedagogical effort and teacher answers to student questions are highly correlated with greater learning achievement. Other work or secondary activity does not effect a student’s test scores, possibly because only a small proportion of 5<sup>th</sup> grade teachers have a secondary occupation. A large number of public school teachers, however, have two or more posts. As part of ANMEB, teachers have at least two posts, one at the primary school level and another at the lower secondary school level. Didactic materials available to the teacher and school facilities failed to demonstrate a significant effect on learning achievement.

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An additional important variable to explain learning achievement in public schools was school supervision by the principal and supervisor. The frequency of supervisors’ school visits has a significant and positive correlation with student learning. It is also consistent with the PARE experience, which indicates that the quality of supervisors and their frequency of school visits had significant and positive effects on student test scores (World Bank 1998). The type of post assigned to the teacher (short and long term) has a negative impact on learning achievement (mathematics test scores), particularly in urban areas. Students in schools with a high degree of supervision on the part of the school principal achieve better scores. Thus, differences in school organization and management could be important for student achievement. In this study it was found that the availability and maintenance of school facilities have a very modest impact on learning achievement.

Additionally, the impacts of each explanatory variable in elasticity terms were computed in order to compare the quantitative effects among all explanatory variables. As can be seen in Table 8, variables with the highest elasticity values include supervision, teacher's enrollment in _Carrera Magisterial_ and teacher's interest in students' learning.

# **_Carrera Magisterial_**

_Carrera Magisterial_ was aimed at raising the quality of basic education through teachers’ career development, presence in schools, and working conditions. This program represents an effort on the part of the government to provide better support for and recognition of the valuable work of teachers.<sup>9</sup> Results from the multivariate regression model show that at the national level and particularly in rural areas, enrollment in _Carrera Magisterial_ positively impacts learning achievement. Notice that being in the _Carrera Magisterial_ program increases a students achievement in mathematics by 1.87 percent (3.31 percent in rural areas—see Table 5 in annex). However, the level in _Carrera Magisterial_ is negatively correlated with learning achievement. Ultimately, the program may have good components that promote better teaching practices, but there is a pervasive incentive affecting teacher promotion. Results show that a large share of the teachers in basic education are relatively old and work in administrative tasks.

> 9 The _Carrera Magisterial_ Program, which contains several parts, is governed by the Comisión Nacional Mixta consisting of officials of the SEP and SNTE.

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The EEEP shows that 62.8 percent of the teachers in the sample are enrolled in _Carrera Magisterial_ . In addition, there is no significant difference in test score distribution between students with a teacher in _Carrera Magisterial_ and students without such a teacher.

**Table** **<u>9. Teachers' Share in</u>** **_<u>Carrera Magisterial</u>_ in 5**<sup>**th**</sup> **<u>grade</u>**

|**_Carrera Magisterial_**|**Number of Teachers**|**Share**|
|---|---|---|
|Yes|2420|62.8|
|Not|1139|29.6|
|No answer|292|7.6|
|Total|3851|100.0|

Source: Primary Education Assessment Survey, second round. 1997 Non-weighted data Tables 10 and 11 present the distribution of test scores for those students in _Carrera Magisterial_ and those with a teacher not enrolled in _Carrera Magisterial_ , nationally and by stratum. Since there is no significant difference, one might infer that there is no selection bias with teachers in _Carrera Magisterial_ getting the best students and other teachers getting worse students.

**Table 10.  Test Scores of Students with a Teacher in** **_Carrera Magisterial_**

||**Num**<br>|**ber of st**<br>|**udents in the sample**<br>**Share of students with**<br>|**Ma**<br>|**themati**<br>|**Test**<br>**cs**<br>|**Scores**<br>|**Spanish**<br>||
|---|---|---|---|---|---|---|---|---|---|
||**Number**|**Share**|**Identified Teachers**|**Mean**|**Median**|**SD **|**Mean**|**Median**|**SD**|
|In_Carrera Magisterial_|19029|35.8|70.9|49.0|48.6|6.1|55.1|54.4|6.3|
|Not in_Carrera Magisterial_|7804|14.7|29.1|48.5|47.8|6.5|55.1|54.1|7.4|
|Not Identified*|26376|49.6||48.6|48.1|6.0|54.8|54.1|6.8|
|Total|53209|100.0|100.0|||||||

Source: Primary Education Assessment Survey, second round 1997. * "Not Identified" refers to those teachers who could not be matched to their respective students.

**Table 11. Test** **<u>Scores by Teacher's</u>** **_<u>Carrera Magisterial</u>_** **<u>Status by stratum</u>**

|**Stratum**|<br>|**Teacher is enrolled in**<br> **_Carrera Magisterial_**|**Teacher is not enrolled**<br>**In****_Carrera Magisterial_**|**Teacher**<br>**not identified**|
|---|---|---|---|---|
|Community School|Mean|||47.3|
||Median|||47.2|
||SD|||5.7|
|Indigenous School|Mean|45.6|45.7|46.0|
||Median|45.5|45.5|46.3|
||SD|5.4|5.6|5.3|
|Public rural school|Mean|48.4|47.9|48.1|
||Median|47.8|47.8|47.8|
||SD|6.2|6.2|5.8|
|Public urban school|Mean|49.7|49.9|49.0|
||Median|49.2|49.2|49.2|
||SD|5.9|6.9|5.6|

Source: Primary Education Assessment Survey, second round 1997.

* "Teacher not identified" refers to those teachers who could not be matched to their respective students.

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Students in rural schools with a teacher in _Carrera Magisterial_ achieve slightly better scores than their peers (Table 11). In public urban schools, there is no significant difference as there is in the case of indigenous schools. Few teachers in private urban schools report being enrolled in _Carrera Magisterial_ . This could be a result of a sampling error, or because a teacher works at both public and private schools.

# **5. CONCLUSIONS**

This study is the first to link family background, teacher profile, and schools characteristics to student achievement. In the analysis of comparing high effective schools versus low effective schools, the main findings were: Private urban schools have a relatively better performance than do other types of schools. Public urban schools rank second, while indigenous schools are at the bottom of the distribution. Student enrollment in public urban schools is evenly distributed across quintiles. The distribution of students in public rural schools is biased towards the lowest 20 percent of schools. For all school strata, the results indicate a strong correlation between school effectiveness and teachers' pedagogical effort, family income and level of schooling. Other relevant variables in public schools were teaching experience; teachers' residence in the community; teachers' training as measured by content of the course taken; the number of students in the classroom; enrollment in _Carrera Magisterial_ ; parents' participation in the learning process; didactic material available to the teacher and supervision. All other variables show a weak correlation with school effectiveness.

Multilevel analysis showed that variation in mathematics test scores has a significant effect for all geographical levels. Additionally, national level student socioeconomic variables explain 27.7 percent of the total variation. Whereas this set of variables explains more than 52 percent of the variation among schools, it explains only 1.7 percent of the student-level variation. For urban areas, the power of explanation of these variables is similar to the power for national level areas. On the other hand, the predictive power of these variables is much lower for rural areas. The school level variation in the outcome scores reflects the socioeconomic student variables to an important extent. However, some of the remaining within-school variation might be explained by other explanatory variables. Another remarkable result is that although the 22
inclusion of student variables significantly reduces the variance component ratio of schooling, this ratio remains relatively important.

As expected, family background factors are important in student achievement. The quality of educational services, as perceived by the parents, has a considerably positive impact on learning achievement. Another important result is that blurred vision has a large negative impact on achievement, which is consistently strong throughout all estimations.

In the third model, type of post (permanent or short-term) has a negative impact on learning achievement. Teacher’s years of schooling and income failed to demonstrate significant effects on student learning. Teacher's pedagogical efforts show a positive and significant marginal effect on learning achievement. Pedagogical effort and teacher answers to student questions are highly correlated with greater learning achievement. Didactic materials available to the teachers and school facilities failed to demonstrate a significant effect on learning achievement. Another striking result is that the teacher’s enrollment in _Carrera Magisterial_ has a positive relationship with learning achievement; however, the higher the level reached by the teacher in this program, the lower the student's learning achievement becomes, particularly in rural areas. In addition, students in schools with a high degree of supervision on the part of the school principal achieve better scores.

# **_Policy implications_**

- The family background factors are not merely important in explaining student enrollment, but are also important in determining the student's achievement. **The importance of these demand factors brings out the relevance of targeted social programs such as PROGRESA, which not only may have an impact on enrollment but may also influence students' achievement through affecting the family**

## **socioeconomic level.**

- Blurred vision has a very significant negative impact on students' achievement. **Accordingly, it will be very important to expand the eyeglasses program throughout basic educational system and to make this program permanent.**

23
- Training, as measured by the number of courses taken by the teacher, does not significantly impact student achievement. Moreover, each one of these courses separately failed to have an impact on learning achievement. **Thus, investment in primary school teachers seems most effective when it is targeted to increasing practical experience and developing content-specific knowledge.**

- The type of post (permanent or short-term) has a negative impact on learning achievement. A possible explanation is that in public schools a temporary post (short-term) has almost the same benefits as a regular or permanent post. For practical purposes, “short-term post” does not mean that the teacher has to go through a probation period. Thus, it creates a pervasive relationship in the system of posts and assignments that have a conflict with learning. **Therefore, a review of the rules for defining this kind of post needs to be done in order to provide the right signals to the short-term teachers.**

- Teacher’s enrollment in _Carrera Magisterial_ has a positive relation with learning achievement; however, the level in _Carrera Magisterial_ is negatively correlated with the student's learning achievement. The bottom line is that the program might have some good aspects that possibly promote better teaching practices but there is a pervasive incentive as to how the teacher is promoted. Additionally, the results show that a large share of the teachers in basic education are relatively old and working in administrative tasks **. Accordingly,** **_Carrera Magisterial’s_ criteria for assignment to a level must be revised in order to avoid perverse incentives. Another important issue in this regard is to eliminate the** **_Carrera Magisterial_ option, namely** **_Tercera Vertiente_ (Pedagogical Technician,** **_Técnico pedagogico_ ), which is likely to increase such perverse incentives.**

- Students in schools with a high degree of supervision on the part of the school principal achieve better scores. **Indicators of organizational and management differences among schools need to be implemented in order to evaluate how those schools' organization (with a high degree of supervision) affects students achievement.**

# **_Future research_**

- Pre-primary school level is not significant for mathematics test scores. However, additional work is needed to establish the linkage between initial education, parent participation and learning achievement. Nonetheless, results show that the development of self-driven and studious students, who seek

24
information beyond their textbooks, is a key factor in increased learning achievement. How to develop good learning habits and motivation among students should be a challenge not only to teachers but also to parents.

- CM's assessment should not be made only on the basis of whether it helps to provide better pay for good teachers and retain them, but also on whether it pushes bad teachers to improve.  Testing this assessment will require a panel data of teachers.

- Linking teachers' pay to the rate of growth (not the level) in their students' grades in standardized tests would require a panel of students. Lopez-Acevedo (1997) shows that teachers’ salary is weakly correlated to changes in learning achievement.

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