Educational spaces: The relation between school infrastructure and learning outcomes

Abstract

This article examines the relationship between school infrastructure and academic performance in Ecuador. The objective of this research is to identify which types of infrastructure are associated with better student outcomes in elementary schools. The study employs data from the 2019 UNESCO standardized test, ERCE-2019, for Ecuadorian primary schools. The findings indicate a significant positive correlation between various types of school infrastructure and student achievement. Such infrastructure includes art and music installations, on-site nursing facilities, and basic service connections, especially in rural areas. Significant correlations between educational outcomes and large-scale infrastructure investments are either not observed or are inconsistently evidenced. These results challenge the heavy focus on prominent educational infrastructure projects in Ecuador, suggesting an opportunity to reorient educational spending to enhance outcomes cost-effectively. These research findings may apply not only to Ecuador but potentially to the broader Latin American context.

1. Introduction

The concept of education, like many studied within the social sciences, has evolved alongside the political, social, and economic changes experienced by society. The perception of education has shifted from reflecting a process of passive knowledge acquisition, where learners are considered "blank slates", to an active process where learners construct their understanding of the world. Education not only facilitates individual freedom but also cultivates functional contributors to the development of more secure, fair, and democratic societies [1,2]. Today, the importance of education in development and poverty alleviation is universally acknowledged.

In line with this critical role that education plays in social development, the United Nations Convention on the Rights of the Child established a child's right to education as a fundamental pillar of equal opportunity in 1989 [3]. Beyond the Convention, the right to education is also emphasized in the Sustainable Development Goals (SDGs) adopted by United Nations Member States in 2015 to end poverty, protect the planet, and improve the lives and prospects of all [4]. The Quality of Education goal (the fourth SDG) aims to "ensure inclusive and equitable quality education and promote lifelong learning opportunities for all", advocating holistic and lifelong learning [5]. A critical component of extending education to all is ensuring that educational spaces are safe and well-equipped to facilitate engagement in pedagogical activities [6,7].

In Ecuador, universal provision of education remains a significant challenge [8]. This persists despite substantial efforts to increase educational access over the past decades, particularly since 2007. Over the past fifteen years, government expenditure on educational infrastructure has increased exponentially. Despite this policy being a critical axis of the political discourse of the time, to the best of our knowledge, only one previous study has attempted to measure the impact of educational infrastructure on academic outcomes during this period [9]. This study, however, does not consider the full range of infrastructure types examined in the present study, nor does it consider results at the individual student level.

Accordingly, the present study aims to address this research gap and analyze the role of educational infrastructure investment in achieving educational outcomes in Ecuador. The main objective is to evaluate the relationship between various types of school infrastructure and the academic performance of primary school students in Ecuador. We use hierarchical linear models (HLM) to estimate the relationship, incorporating variables to control for student, family, and school-level characteristics. The data employed are taken from the Regional Comparative and Explanatory Study (henceforth ERCE) 2019 [10], which collects representative data on school achievement for third- and sixth-grade students across 16 countries in Latin America and the Caribbean. The study extends beyond that of Ponce and Drouet [9] by considering a more comprehensive range of infrastructure and incorporating student-specific information, thus controlling for student and family-level factors that may otherwise bias the results.

This paper begins by discussing the importance of education quality and UNESCO's approach to measuring academic performance in Latin America. Following this, a literature review will examine the relationship between school infrastructure and educational outcomes in both international and local contexts. Section 3 outlines the recent history of Ecuadorian education infrastructure investment and current educational outcomes in the country. The subsequent section details the methodology used to explore the relationship between academic performance and school infrastructure in Ecuador. Section 5 presents the main results and addresses the limitations of the study. A discussion of the findings is provided in Section 6, followed by concluding remarks in the final section.

2. Educational quality and school infrastructure

2.1. Measuring educational outcomes

According to UNICEF, educational quality is influenced by students’ learning conditions. Specifically, quality education requires a system where: a) learners are healthy and ready to participate and learn; b) environments are healthy, safe, protective, and gender-sensitive, offering adequate resources and facilities; c) curricula and materials reflect content relevant to the acquisition of basic skills; d) teaching approaches are child-centered in well-managed classrooms, and accompanied by skillful assessments employed to facilitate learning and reduce disparities; and e) outcomes that encompass knowledge, skills, and attitudes are assessed, linking them to national goals for education and positive participation in society [11]. The required conditions are fundamentally intertwined, interact with each other, and together reflect a comprehensive and multi-faceted view of quality education that encompasses political, cultural, and economic factors [11].

While there is broad agreement on the core components of quality education, measuring quality in outcomes remains challenging. The United Nations Educational, Scientific and Cultural Organization (UNESCO), tasked with monitoring progress towards Sustainable Development Goal 4, uses large-scale assessments to evaluate education system outputs and provide evidence of student achievement levels1 [11]. In Latin America, the Regional Comparative and Explanatory Study (ERCE), coordinated by the Latin American Laboratory for Assessment of the Quality of Education (LLECE), assesses student achievement in reading, mathematics, natural sciences, and global citizenship. The study also records related factors such as socioeconomic context, family life, and educational policies [12]. The latest evaluation was conducted in 2019 and assessed third- and sixth-grade students in sixteen Latin American countries, including Ecuador2 [12,13].

In Ecuador, the National Institute for Educational Evaluation (INEVAL) oversees the internal and external evaluation of the national education system, establishing quality indicators. Since 2013, INEVAL has conducted the Ser Estudiante and Ser Bachiller national evaluations and participated in three international ERCE studies (SERCE 2006, TERCE 2013, and ERCE 2019), the Program for the International Assessment of Adult Competencies (PIAAC) in 2017, and the Pisa-D study in 2018 [14]. The ERCE data are useful for mapping the relationship between educational outcomes and school infrastructure while controlling for other variables. This research thus utilizes ERCE data to investigate this relationship in Ecuador, where significant investments in school infrastructure have been made over the past 15 years. Before exploring the specifics of the Ecuadorian case, we review the existing literature on the role of school infrastructure in educational outcomes.

2.2. The relationship between school infrastructure and educational outcomes

While the value of human capital investment in personal well-being and broader economic development is well-recognized [15,16], there is less clarity regarding the specific investments that determine the quality of educational outcomes. Theoretically, improved school facilities are positively correlated with better student outcomes [17,18]. Several studies indicate that higher spending per student can enhance performance [[19], [20], [21]], and enrollment [22,23], yet not every dollar invested in education equally impacts school quality and student achievement.

Educational investment most often reflects school infrastructure and durable amenities. In empirical studies, educational infrastructure generally includes physical and organizational structures that support teaching and learning, such as buildings, classrooms, libraries, laboratories, and technology [24]. Common elements studied include classroom lighting, potable water access, toilet access, computer facilities, internet connectivity, and learning aids like whiteboards [7].

Over the past 40 years, a broad spectrum of individuals, ranging from politicians and physicians to researchers across various fields, has investigated whether and how the quality of school facilities may influence student achievement [[25], [26], [27], [28], [29]]. The results generally differ depending on the context or country of investigation [30]. Much of the research has, perhaps surprisingly, shown little to no effect of direct measures of facility quality on student learning [28,29,31].

Most of these studies have taken place in developed countries, and show some evidence that school capital spending can improve school grades [[32], [33], [34], [35], [36], [37], [38]] and increase earning outcomes later in life [15,[30], [31], [32], [33], [34], [35]]. In many developing countries, however, educational infrastructure is often inadequate and even largely absent [7]. In such contexts, investing in infrastructure may yield substantial benefits even at low levels of investment [7,19,39].

The empirical studies of the infrastructure-achievement nexus in developing and transition countries yield mixed results [20,21,24,[40], [41], [42], [43]]. A thorough meta-study examining the relationship between school resources and educational outcomes in developing countries from 1990 to 2010 was undertaken by Glewwe et al. [7]. The results suggest that school resources are not significantly related to student achievement. The exceptions are for largely obvious inputs such as desks, tables and chairs, electricity, blackboards, and adequate quality walls, roofs, and floors. Interestingly, the evidence is mixed for computers and related materials in developing countries. As Shmis et al. explain [43], this outcome could be related to a lack of knowledge concerning how best to incorporate information technology in the classroom.

More recent studies have found a relationship between educational infrastructure and school outcomes in specific cases. In the Philippines and parts of Latin America, overcrowded schools lacking basic facilities like toilets, clean drinking water, electricity, access roads, and adequate teaching materials suffer from poor enrollment, attendance, and high dropout rates, leading to lower educational achievement [21,44]. In Ghana and Pakistan, the absence of safe, hygienic facilities for female students results in gender-biased dropout rates, disadvantaging female achievements [23,45]. Comparisons of the association between school infrastructure investment and educational outcomes within particular countries have shown that the relationship is sensitive to in-country location and context. For instance, Figueroa et al. highlight the importance of facilities in remotely located elementary public schools in the Philippines [21].

Little research has been undertaken in Latin America on the relationship between school facilities and student achievement. An exception is a study by Murillo and Román [44] which used SERCE data (2005–2009) and a four-tiered, multilevel model to analyze the impact of facilities and resources on student achievement. They found an association between educational infrastructure and student achievement, with basic infrastructure (water, electricity, sewage) and capital investments (sports facilities, laboratories, libraries, computers) associated with better outcomes in mathematics and language courses.

Nevertheless, the effects of educational infrastructure on achievement are not uniform across countries, course types, or levels. In Ecuador, Murillo and Román [44] found that basic infrastructure correlated significantly with language achievement but not mathematics. Facilities like sports fields, laboratories, libraries, and computer rooms were linked to both mathematics and language achievement in sixth grade, but only to language achievement in third grade. While this study provides something of a benchmark, the findings are based on data from nearly two decades ago, when many Ecuadorian schools lacked basic amenities. Given substantial investments in public education over the last 15 years, the facility-achievement relationship is expected to have changed significantly.

The only recent study examining the relationship between school capital investment and education outcomes in Ecuador is a 2017 government report by Ponce and Drouet [9]. They investigated the Millennium Schools Program using a difference-in-differences strategy with propensity score matching to compare student performance before and after the program. Their methodology, using fixed effects, aimed to correct for biases by accounting for both observable and non-observable factors. The study found that the Millennium Program positively impacted mathematics achievement but did not affect other areas of achievement or enrollment. However, since the study was conducted at the school level, it did not account for individual student characteristics, likely resulting in significant selection bias.

Accordingly, the question of the relationship between specific school infrastructure investment and student achievement within Ecuador since the major education investment wave of the 2010s remains an open one. In the following section, we detail education infrastructure investments over recent decades and present student achievements on standardized international tests from the same period, providing an overview of the current state of education in the country.

3. Investment in educational infrastructure and student performance in Ecuador

Between 2007 and 2022, Ecuadorian educational policies reflected a significant infrastructure focus. Investment in educational infrastructure already increased markedly in 2006, but from 2007, under the government of President Rafael Correa, it further accelerated (see Table 1) [46].

Table 1.

Investment in educational infrastructure 1999–2013.

INVESTMENT IN EDUCATIONAL INFRASTRUCTURE 1999–2013
Year	Investment in nominal USD
1999	650,299
2000	858,269
2001	25,511,928
2002	7,585,635
2003	6,985,376
2004	6,855,191
2005	3,402,447
2006	73,505,845a
2007	116,230,845
2008	182,267,041
2009	27,975,112
2010	45,000,000
2011	57,141,461
2012	59,545,367
2013	103,345,442

^aIncluding investment of 22 million transferred on December 28th, 2005.

Data source: Minedu 2007 and Minedu 2014 [46,47].

In 2008, the government launched the 'Millennium Educational Units' (MEU) project to enhance educational infrastructure in underserved areas by providing modern learning facilities, including laboratories [9]. Other significant initiatives included the "Replica Schools", "New Educational Infrastructure", and the "Reorganization of the Educational Offer" plans presented in 2012 to increase the number and capacity of education centers. This reorganization involved defining "axis" education centers and the fusion, closure, or creation of other buildings, leading to the closing of rural schools and the integration of students into higher-capacity Millennium Educational Units [48].

In general, from 2007 to 2013, educational infrastructure investment increased substantially compared to 1999–2006. This investment included constructing new buildings, rehabilitating wet-season-affected buildings in the coastal region, furnishing and equipping facilities, and providing maintenance and consultancy services for infrastructure, furniture, and school equipment [46].

In 2015, the Ministry of Education's total investment budget was USD 130.86 million, with USD 54.7 million (41.80 %) allocated to educational infrastructure projects [49]. After a 7.8-magnitude earthquake in 2016, the government announced the construction of "21st-century schools" by China Railway Co [50,51]. By 2016, new educational units could enroll 600 to 2000 students, compared to 2007, when 75 % of facilities had maximum capacities of 100 or fewer students [52]. Over 10 years, the government invested USD 1.13 billion in educational infrastructure [53].

From 2017 to 2021, the new government continued investing in educational infrastructure, though with less consistency. In 2017, the investment was USD 119 million [54]. The New Educational Infrastructure project had an original budget of USD 32 million in 2018, with 61 % spent by December [55]. In 2019, the same project received USD 71,757,846 [56]. In 2020, the investment was USD 23,688,941, covering essential maintenance due to COVID-19, rehabilitation of schools, and new infrastructure [57]. In 2021, the Ministry of Education allocated USD 4.9 million to infrastructure [58,59]. In 2022, this amount was USD 55.3 million3 [60].

Despite substantial investments (principally during the period 2007–2017), educational infrastructure in Ecuador remains inadequate [8]. Many large projects are incomplete. A 2020 WASH diagnosis by the Ministry of Education and UNICEF found that nearly half of the over 16,000 educational institutions surveyed urgently need investment due to deficiencies in water, sanitation, and hygiene, affecting around 3.3 million students (77 % of the student population), especially in coastal and Amazonian areas [61]. In 2023, Ecuador had 4,322,138 students across all school levels, with 12,341 public schools (77 % of the total), 626 "fiscomisional" schools4 (4 %), 107 municipal schools (1 %), and 2923 private schools (18 %). Urban schools accounted for 53.7 %, while rural schools made up 46.3 % [62].

Despite significant infrastructure issues in many schools, Ecuador's public expenditure on education is comparable to the average in Latin American countries. International benchmarks recommend allocating 15–20 % of public expenditure, or 4–6% of GDP to education [5]. From 2010 to 2021, Ecuador's annual government expenditure on education fluctuated between 3.7 % and 5.3 % of GDP, peaking at 5.3 % in 2014 and reaching a low of 3.7 % in 2021 [63]. Notwithstanding a decline since 2018, Ecuador's education expenditure remains within the regional average for Latin America and the Caribbean [64].

3.1. Student achievement in Ecuador

Within this context, we review recent student performance. As shown in Fig. 1, the national promotion rate increased from 91.71 % in 2009 to 97.91 % in 2020, before slightly declining to 96.63 % in the 2021–2022 period [62].

Fig. 1.

Promotion rate 2009–2022.

Data source: Ministry of Education, Datos Abiertos 2023 [62]

According to UNICEF's 2023 report "The State of the World's Children 2023″, a major challenge in Ecuadorian education is the out-of-school rate in upper secondary education, which was 22 % for boys and 20 % for girls during 2013–2022 [65]. The report also shows that the completion rate is 98 % for both boys and girls in primary education, but drops to 89 % for boys and 92 % for girls in lower secondary education, and falls further to 78 % and 79 % in upper secondary education, respectively [65].

The decline in performance measures in recent years largely reflects the impact of the COVID-19 pandemic on Ecuador's education system. The pandemic significantly affected the country's economic and social landscape, with 30.70 % of households with children under 5 years old not enrolling their children in development courses [66]. Additionally, 80–90 % of children and adolescents in low and lower-middle-income households accessed education through a cell phone, which hindered their learning opportunities [66].

Adequate learning level achievement is a key component of educational system quality. In Ecuador, local assessments (Ser Estudiante and Ser Bachiller exams) and participation in three large-scale UNESCO tests (SERCE 2006, TERCE 2013, ERCE 2019) evaluate student comprehension and proficiency in reading and mathematics, placing them in performance levels [14].

The achievements measured by SERCE-2006, TERCE-2013, and ERCE-2019 tests are not directly comparable due to different scaling parameters. SERCE uses a mean of 500, while TERCE and ERCE 2019 use a mean of 700. However, two key reports have converted the tests to comparable measures: UNESCO 2014 [67] evaluates SERCE-2006 and TERCE-2013 based on scores and five achievement levels (−1 to IV) [68], and LLECE 2021 [69] compares TERCE-2013 and ERCE-2019, establishing a Minimum Performance Level. The two reports (see Table 2) allow Ecuadorian students' performances to be compared over time. In the SERCE-2006 Reading test, 86.29 % of students scored within levels -I, I, and II, the lowest performance levels [80]. In mathematics, 87.94 % fell into these levels. For sixth grade, 77.64 % were within the lowest levels in Reading, and 74.25 % in mathematics [67,68]. To summarize, most students in third and sixth grade failed to achieve basic knowledge and skills in mathematics and reading.5

Table 2.

Scores in SERCE-2006 and TERCE-2013 and percentage of students in levels -I, I and II.

	SERCE-2006 Score	SERCE-2006 % in levels -I,I,II	TERCE-2013 Score	TERCE-2013 % in levels -I,I,II
Third Grade Reading	452.41	86.29 %	508.43	71.34 %
Third Grade Mathematics	473.07	87.94 %	524,17	70.69 %
Sixth Grade Reading	447,44	77.64 %	490,70	62.06 %
Sixth Grade Mathematics	459.5	74.25 %	513.12	51.63 %

Data source: UNESCO, 2014 [67].

As shown in Table 2, TERCE-2013 results indicate a significant improvement in reading and mathematics scores compared to SERCE-2006. Despite this, the LLECE report (Table 3) reveals that 38 % of third-grade students did not reach the Minimum Performance Level (MPL) in reading, meaning they could not read or identify explicit information from age-appropriate texts [69]. In sixth grade 77 % of students did not attain the MPL, reflecting an inability to make inferences, integrate implicit ideas from complex texts, or establish relationships between verbal and visual information [69].

Table 3.

Percentage of students not reaching the minimum performance level in reading, mathematics, and science in the TERCE-2013 and ERCE-2019 tests.

	TERCE-2013	ERCE-2019
Third Grade Reading	38 %	41,9 %
Sixth Grade Reading	77 %	73,9 %
Third Grade Mathematics	48 %	43 %
Sixth Grade Mathematics	86 %	77,1 %
Sixth Grade Science	80 %	74 %

Data source: LLECE, 2021 [69].

In mathematics, 48 % of third-grade students did not reach the MPL, which includes writing and composing natural numbers up to 9,999, identifying elements of geometric figures, interpreting bar charts or graphs, and identifying measurement units and instruments. In sixth grade, this proportion reached 86 %, meaning that they were unable to solve problems requiring interpretation of information in various formats, including tables and graphs, and using multiple arithmetic operations [69].

The ERCE-2019 results are in close accordance with the preceding test (see Table 3). In the reading assessment, 41.9 % of third-grade students fell under the MPL. In sixth grade, this percentage was 73.9 %. The results in mathematics reveal that 43 % of third-grade students fall below the minimum level of competencies and in sixth grade, 77.1 % of the students do not reach the MPL [69]. The sixth-grade results in mathematics and science are the only results demonstrating a significant improvement compared with the 2013 results [69].6

In conclusion, the results of TERCE-2013 show a relevant increase in the domains of reading and mathematics compared to SERCE-2006. Nevertheless, when comparing TERCE-2013 to ERCE-2019 results, Ecuador maintained its average score in all areas except for the sixth-grade results in mathematics [69].

The percentage of students not achieving the MPL reflects the magnitude of the challenge faced. Given this, it is important to understand whether recent educational policies, which include substantial infrastructure investment, are the most effective in addressing this challenge. In the following section, we will explain the methodology utilized in the current study to investigate the relationship between infrastructure and academic performance in the Ecuadorian context.

4. Methodology

In this section, the econometric strategy used to estimate the relationship between infrastructure and educational outcomes is outlined. While the variable of interest is educational infrastructure, it is necessary to control for all other variables that can influence educational outcomes. This ensures that other determinants do not confound the measured relationship between educational outcomes and infrastructure.

According to Hanushek [70], the measurable or observable elements influencing cognitive and non-cognitive student achievement are a) the characteristics of the student's family; b) the influence of the classmate cohort; c) school resources; and d) the characteristics of the student. Thus, the Educational Production Function (EPF) is given by:

$$A_{it}=f\left(B_i^{\left(t\right)},P_i^{\left(t\right)},S_i^{\left(t\right)},I_i\right)$$ (1)

Where academic performance ($A_{it}$) —which is the score obtained by students on standardized tests to assess students' cognitive knowledge— is determined by: family factors $\left(B_i^{\left(t\right)}\right)\text{,}$ such as socioeconomic level, family composition, and household characteristics; peer effects $\left(P_i^{\left(t\right)}\right)\text{,}$ captured through variables such as peer academic performance, ethnicity, and socioeconomic status of classmates; innate ability factors $\left(I_i\right)$, such as IQ, biological abilities, and individual characteristics of students7; and a factor that integrates school resources ($S_i^{\left(t\right)}$) such as infrastructure, administrative and learning resources, and characteristics of the students' teachers.

The learning achievement results data include the assessment outcomes of mathematics and reading in third grade, and mathematics, reading, and science in sixth grade. In the ERCE 2019 sample design, the scores that represent student achievement for each subject use the plausible values methodology [71]. These plausible values comprise five different values per student and represent the expected degree of learning achievement in each assessed discipline. In addition, the properties of the plausible values methodology incorporate uncertainty and measurement error in the estimation of academic achievements [71,72]. For this reason, the ERCE 2019 user manuals recommend using all five plausible values together to make estimates, as omitting any component or using their average results in a loss of information and methodological properties [73].

In accordance with these database properties, the EPF estimated in this research incorporates vectors related to the determinants of educational performance, as represented in the following equation:

$$y_{ij}={\beta }_0+{\beta }_1{X}_{ij}^{\prime }+{\beta }_{2j}{X}_{ij}^{\prime }\ast {Rural}_j+{\beta }_{3j}{X}_{ij}^{\prime }\ast {Public}_j+{\beta }_{4j}{Z}_{ij}^{\prime }+{\beta }_{5j}{H}_{ij}^{\prime }+{\beta }_{6j}{D}_{ij}^{\prime }+e_{ij}$$ (2)

Academic performance (${\mathrm{y}}_{\text{ij}})$ corresponds to the five plausible values obtained by the student $i$ from school $j$ in the ERCE 2019 tests. The explanatory variables include a vector of the school's infrastructure (${\mathrm{X}}_{\text{ij}}^{\prime }$), an interaction ($X_{ij}^{\prime }\ast {Rural}_j$) between the infrastructure variables with a variable capturing schools located in rural zones, an interaction (${\beta }_{3j}{X}_{ij}^{\prime }\ast {Public}_j$) between the infrastructure variables and public schools, a vector of individual characteristics of the student ($Z_{ij}^{\prime }$), a vector of family characteristics ($H_{ij}^{\prime }$), and a vector of school characteristics ($D_{ij}^{\prime }$). ${\beta }_0$ is the intercept that reflects the global score obtained in the exam, and $e_{ij}$ is an error term that represents the unobserved characteristics.

It should be noted that if equation (2) is estimated using Ordinary Least Squares (OLS), this assumes that all students are randomly distributed across educational institutions. This is equivalent to assuming that all students in the sample belong to the same school. However, students are distributed across schools with varying characteristics and are not randomly distributed. Therefore, the error terms are not independent but are instead clustered by one or more grouping variables. Conventional analysis focused on individual data overlooks the interdependence arising from data grouping, whereas group-level analysis cannot make direct inferences or predictions for individual students. Consequently, traditional analysis fails to capture the true relationship between outcomes and predictors effectively [74].

There are several approaches to estimating this model. The first approach would be to estimate an ordinary least squares (OLS) model while ignoring the clustered nature of the data, treating the compound error term as if it consists solely of the error term. The second is to implement clustered standard errors. The third is to explicitly model the multilevel nature of the data [75].

In this research, we choose to estimate equation (2) using Linear Mixed Model (LMM) or Hierarchical Linear Model (HLM) methods to account for the multilevel nature of the data. These models are used to handle data where observations are not independent. They correct for the correlation between the errors of related observations (for example, students at the same school who may share similar learning influences) and were specifically developed to analyze hierarchical datasets [76]. These models can also be estimated using maximum likelihood [77]. Additionally, one of the main advantages of hierarchical linear models (HLM) is their ability to identify the factors driving the model's explanations by directly estimating variance components [75].

Effectively, the models comprise a two-level process whereby the first level includes estimations concerning the student, and the second level accounts for school-level effects, grouping the students by their school unit. By applying this second level, the model disaggregates unexplained variance into individual-level (student) and aggregate-level (school) components. Thus, the variation due to school-level effects (associated with peer influence and school selection bias), measured at the aggregate level $j$ (school) is separated from the remaining error term $e_{ij}$. This method ensures the independence of errors due to the nesting of observations within groups.

Additionally, the LMM (or HLM) model can be extended by allowing for Random Effects (RE). RE models allow the effects of covariates at the individual level (students) to vary between the grouping level (schools). In other words, each school will have its own intercept and slope (coefficient) to account for systematic differences. To apply a RE model, it is necessary to incorporate two equations for the second level (school); one equation for the general average of the academic result of each student (that is captured by the intercept), and another equation for the socioeconomic index of the students (that is incorporated in the slope):

$${\beta }_0={\gamma }_{00}+u_{0j}$$ (3)

$${\beta }_2=\left({\gamma }_{02}+u_{2j}\right){isec}_i$$ (4)

The intercept for the first level (student) is determined by the national average of the plausible values for each subject (${\gamma }_{00}$) and the deviation of the school average ($u_{0j}$) from this national average. The coefficient for the socioeconomic index (${isec}_i$) of the student is determined by the average of the socioeconomic level of the student at the national level (${\gamma }_{02}$) and the deviation of the school's socioeconomic level ($u_{2j}$) from the national isec. By incorporating these equations, the correlation of the residuals within the sample is corrected and the systematic differences between schools concerning average academic performance are identified. Thus, integrating equations (3), (4) of the second level in equation (5) results in a random-intercept and random-slope (coefficient) model [78]. The final model that incorporates the levels described is specified as:

$$y_{ij}={\gamma }_{00}+u_{0j}+{\beta }_1{X}_{ij}^{\prime }+{\beta }_{2j}{X}_{ij}^{\prime }\ast {Rural}_j+{\beta }_{3j}{X}_{ij}^{\prime }\ast {Public}_j+\left({\gamma }_{02}+u_{2j}\right){isec}_i+{\beta }_{4j}{Z}_{ij}^{\prime }+{\beta }_{5j}{H}_{ij}^{\prime }+{\beta }_{6j}{D}_{ij}^{\prime }+e_{ij}$$ (5)

RE models are widely used in the discipline of education and their main advantage is their ability to distinguish between the effects of school and individual characteristics on the outcome of interest [79]. Additionally, research has shown that omitting random slopes can lead to anticonservative standard errors, while including random intercepts improves the efficiency of estimators, even if they are not normally distributed [80]. Consequently, multilevel modeling offers advantages by generating statistically efficient regression coefficient estimates and accurate standard errors, confidence intervals, and significance tests. It also allows for the use of covariates measured at various levels within a hierarchy [74].

According to Lee [81], the appropriate method to analyze multilevel data and address multilevel research questions is the HLM model because educational contexts are inherently multilevel (i.e., individuals are nested in school contexts). In a similar context to the current research, the HLM method has been applied to cross-sectional data relating to 1653 students who took the secondary education State exam (Saber 11) in 2010, across 44 educational institutions in Medellín, Colombia [82]. Moreover, HLM has been used to investigate the how national level of Information and Communication Technology (ICT) development and individual ICT usage influence achievements in reading, mathematics, and science among fourth and eighth-grade students [83]. Alves and Candido [84] use a multilevel approach to evaluate the effect of Latin American schools on student performance and identify factors that contribute to their performance using three editions of the Program for International Student Assessment (PISA). The authors declare that using a multilevel approach is critical since a considerable part of student performance variation is explained by school differences (school effect). Konstantopoulos and Borman also used multilevel modeling techniques to partition the variance in students’ achievement into its individual-level and school-level components [85]. Finally, a study conducted in Latin America using the SERCE-2006 and applying HLM found that the factors most significantly associated with learning outcomes include the presence of spaces that support teaching (such as libraries, science, and computer laboratories); connection to electrical and telephone services; and access to drinking water, drainage, and bathrooms [86].

4.1. Data

To estimate the relationship between Ecuadorian students' achievements and school infrastructure, we will draw on the ERCE 2019 data that collected representative data of school achievement for 16 countries of Latin America and the Caribbean for third and sixth-grade students. The ERCE 2019 database comprises surveys from students (Student Questionnaire), parents (Family Questionnaire), teachers (Teacher Questionnaire), and principals (Principal Questionnaire). The Student Questionnaire provides information regarding learning achievement results, through five plausible values for each subject, (the subjects including mathematics and reading for third grade; and mathematics, reading, and science for sixth grade) as well as the general characteristics of the students. The Family Questionnaire gives information regarding family conditions, environment, and household characteristics. The Teacher and Principals Questionnaires consist of variables relating to teacher information and the general characteristics of schools, respectively. It should be noted that this latter survey includes categorical variables of the schools’ infrastructure. Table A1 (in the Appendix) details the name, code, type, measurement method, and questionnaire of each variable used in the ERCE-2019.

The nested nature of the ERCE-2019 survey data allows us to capture the student-specific factors determining their performance, as well as those that come from influences relating to the educational unit. In the context of the described methodology, the ‘student level’ variables (from the Student Questionnaire and the Family Questionnaire) correspond to the first level, while the ‘school level’ variables (those contained in the Teacher Questionnaire and the Principals Questionnaire) correspond to the second level. For the present investigation, only data available for Ecuador was used. In addition, the data is cross-sectional, observing n individuals during the survey year. Table 4, Table 5 present descriptive statistics for third and sixth grades, respectively.

Table 4.

Descriptive statistics and frequency table for third-grade.

Variable	Obs	Mean	Std. Dev	Min	Max	No	Yes
Director's office	6461	0.8251045	0.3799071	0	1	0.1749	0.8251
Additional offices	6461	0.5977403	0.4903917	0	1	0.4023	0.5977
Meeting room for teachers	6461	0.5270082	0.4993087	0	1	0.473	0.527
Sports field	6461	0.8189135	0.3851197	0	1	0.1811	0.8189
Gym	6461	0.0428726	0.2025856	0	1	0.9571	0.0429
Computer room	6461	0.6005262	0.4898281	0	1	0.3995	0.6005
Auditorium	6461	0.3148119	0.4644769	0	1	0.6852	0.3148
Arts and/or music room.	6461	0.1606562	0.367242	0	1	0.8393	0.1607
Nursing	6461	0.2332456	0.42293	0	1	0.7668	0.2332
Science labs	6461	0.2451633	0.4302173	0	1	0.7548	0.2452
Water	6461	0.8905742	0.3121968	0	1	0.1094	0.8906
Sewerage	6461	0.8720012	0.3341143	0	1	0.128	0.872
Phone	6461	0.7421452	0.4374875	0	1	0.2579	0.7421
Mobile computer lab	6461	0.1852654	0.3885428	0	1	0.8147	0.1853
Bathrooms in good condition	6461	0.8506423	0.3564683	0	1	0.1494	0.8506
Internet connection	6461	0.7908992	0.406698	0	1	0.2091	0.7909
Garbage collection	6461	0.9063612	0.291348	0	1	0.0936	0.9064
Rural location	6461	0.2121963	0.4088947	0	1	0.7878	0.2122
Public school	6461	0.7520508	0.4318556	0	1	0.2479	0.7521

Table 5.

Descriptive statistics and frequency table for sixth-grade.

Variable	Obs	Mean	Std. Dev.	Min	Max	No	Yes
Director's office	6758	0.8253921	0.3796594	0	1	0.1746	0.8254
Additional offices	6758	0.6037289	0.4891582	0	1	0.3963	0.6037
Meeting room for teachers	6758	0.5423202	0.4982426	0	1	0.4577	0.5423
Sports field	6758	0.8298313	0.3758087	0	1	0.1702	0.8298
Gym	6758	0.0417283	0.1999825	0	1	0.9583	0.0417
Computer room	6758	0.5986978	0.4901982	0	1	0.4013	0.5987
Auditorium	6758	0.3070435	0.4613017	0	1	0.693	0.307
Arts and/or music room.	6758	0.1569991	0.3638269	0	1	0.843	0.157
Nursing	6758	0.228322	0.4197822	0	1	0.7717	0.2283
Science labs	6758	0.2462267	0.430844	0	1	0.7538	0.2462
Water	6758	0.8937555	0.308173	0	1	0.1062	0.8938
Sewerage	6758	0.8715596	0.3346043	0	1	0.1284	0.8716
Phone	6758	0.7416395	0.4377656	0	1	0.2584	0.7416
Mobile computer lab	6758	0.1802308	0.384408	0	1	0.8198	0.1802
Bathrooms in good condition	6758	0.8617934	0.3451422	0	1	0.1382	0.8618
Internet connection	6758	0.8048239	0.3963655	0	1	0.1952	0.8048
Garbage collection	6758	0.9084049	0.2884749	0	1	0.0916	0.9084
Rural location	6758	0.2141166	0.4102385	0	1	0.7859	0.2141
Public school	6758	0.7598402	0.427212	0	1	0.2402	0.7598

5. Results

This section summarizes the most significant estimation results, which are grouped in Table 6, Table 7, Table 8, Table 9, Table 10, Table 11, Table 12. The estimates for third grade are grouped into three panels (see Table 6, Table 7, Table 8), which are divided into estimates for language (Table 6), mathematics (Table 7), and the joint estimate of the plausible values of language and mathematics (Table 8). The estimates for sixth grade are grouped into four panels (see Table 9, Table 10, Table 11, Table 12), which are divided into language (Table 9), mathematics (Table 10), science (Table 11), and joint estimates of the plausible values of language, mathematics, and science (Table 12).

Table 6.

Estimates for language third-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		−2.323	−0.755	−3.686	−3.661	1.945	36.805
Additional offices		0.065	−0.127	−4.553	−1.874	2.675	−16.902
Meeting room for teachers		13.968∗	8.973	9.545	4.003	2.374	−0.469
Sports field		−8.784	−14.442∗	−9.665	−10.505	−7.509	34.787
Gym		−8.863	0.372	−4.606	−14.905	−9.388	−15.288
Computer room		14.814∗	13.665∗∗	14.338∗∗	11.472∗	13.685∗∗	9.898
Auditorium		2.803	3.124	3.291	2.285	1.521	−17.164
Arts and/or music room.		37.905∗∗∗	32.339∗∗∗	23.520∗∗∗	18.356∗	14.498	12.732
Nursing		18.426∗	7.926	6.155	6.202	8.658	4.296
Science labs		16.243∗	19.386∗∗	13.809∗	9.541	7.324	19.431
Water		14.359	18.036∗	14.305	20.110∗	3.643	14.404
Sewerage		−14.879	−11.011	−18.142∗	−15.922	−17.675	−18.24
Phone		29.703∗∗∗	23.324∗∗∗	18.656∗∗	16.806∗	22.393∗∗	61.849
Mobile computer lab		−0.734	−2.262	−2.695	−1.082	−6.047	14.487
Bathrooms in good condition		6.477	10.015	11.386	8.094	1.488	7.635
Internet connection		−13.882	−6.563	−9.216	−11.127	−7.593	−96.944
Garbage collection		8.096	6.483	7.417	3.138	−8.499	26.008
Director's office ∗Rural						−26.662
Additional offices∗Rural						−16.42
Meeting room for teachers∗Rural						3.042
Sports field∗Rural						−1.343
Gym∗Rural						−0.159
Computer room∗Rural						−25.298
Auditorium∗Rural						−5.587
Arts and/or music room∗Rural						17.753
Nursing∗Rural						−19.402
Science labs∗Rural						0.736
Water∗Rural						45.583∗
Sewerage∗Rural						17.739
Phone∗Rural						−10.574
Mobile computer lab∗Rural						32.357∗
Bathrooms in good condition∗Rural						37.393
Internet connection∗Rural						−22.667
Garbage collection∗Rural						73.619∗∗∗
Director's office∗Public school							−40.383
Additional offices∗Public school							13.891
Meeting room for teachers∗Public school							7.794
Sports field∗Public school							−51.167∗
Gym∗Public school							20.015
Computer room∗Public school							6.052
Auditorium∗Public school							22.256
Arts and/or music room∗Public school							4.997
Nursing∗Public school							2.574
Science labs∗Public school							−12.109
Water∗Public school							5.235
Sewerage∗Public school							0
Phone∗Public school							−46.352
Mobile computer lab∗Public school							−23.802
Bathrooms in good condition∗Public school							0
Internet connection∗Public school							89.161
Garbage collection∗Public school							−26.378
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	698.276∗∗∗	658.351∗∗∗	614.723∗∗∗	617.276∗∗∗	640.289∗∗∗	658.126∗∗∗	609.208∗∗∗
Observations	6447	6447	4338	3361	3099	3099	3099

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Table 7.

Estimates for mathematics third-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		−9.809	−6.09	−8.659	−9.535	6.581	32.532
Additional offices		1.502	4.192	1.648	6.013	7.72	9.585
Meeting room for teachers		1.734	−2.606	−3.071	−9.354	−18.194∗∗	−41.860∗
Sports field		−1.814	−6.697	−5.386	−12.974	−15.556	5.636
Gym		10.35	20.178	20.787	6.722	25.194	−14.791
Computer room		13.081	12.141	10.291	4.171	8.905	13.468
Auditorium		2.663	3.481	2.67	1.284	6.787	−8.02
Arts and/or music room.		22.828∗	18.729∗	14.934	15.93	12.811	19.617
Nursing		28.693∗∗	22.468∗∗	20.733∗∗	25.438∗∗	22.828∗∗	26.66
Science labs		5.151	3.932	0.322	−1.689	1.077	1.046
Water		−6.597	−5.309	−4.946	2.34	−27.552∗	3.583
Sewerage		−2.43	−2.351	−3.196	0.34	5.105	1.384
Phone		18.968∗	13.611	10.5	4.283	17.819	72.171
Mobile computer lab		−8.3	−9.207	−4.869	−2.892	−7.958	6.023
Bathrooms in good condition		4.862	6.343	7.514	1.624	−4.227	1.298
Internet connection		−29.806∗∗∗	−22.409∗∗	−26.209∗∗∗	−26.227∗∗∗	−21.160∗∗	−96.058
Garbage collection		23.658∗	20.436	22.465∗	19.987	4.081	1.348
Director's office ∗Rural						−57.741∗∗∗
Additional offices∗Rural						2.5
Meeting room for teachers∗Rural						30.206
Sports field∗Rural						8.946
Gym∗Rural						−40.844
Computer room∗Rural						−36.582∗
Auditorium∗Rural						−28.769
Arts and/or music room∗Rural						20.638
Nursing∗Rural						11.976
Science labs∗Rural						−30.491
Water∗Rural						70.632∗∗∗
Sewerage∗Rural						10.566
Phone∗Rural						−46.933∗
Mobile computer lab∗Rural						34.936
Bathrooms in good condition∗Rural						57.533∗∗
Internet connection∗Rural						−7.196
Garbage collection∗Rural						94.995∗∗∗
Director's office∗Public school							−43.277
Additional offices∗Public school							−4.919
Meeting room for teachers∗Public school							37.962
Sports field∗Public school							−20.865
Gym∗Public school							72.307∗∗
Computer room∗Public school							−7.964
Auditorium∗Public school							9.908
Arts and/or music room∗Public school							−14.783
Nursing∗Public school							−3.878
Science labs∗Public school							−8.889
Water∗Public school							−4.943
Sewerage∗Public school							0
Phone∗Public school							−72.127
Mobile computer lab∗Public school							−11.263
Bathrooms in good condition∗Public school							0
Internet connection∗Public school							73.402
Garbage collection∗Public school							20.493
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	711.888∗∗∗	695.645∗∗∗	669.818∗∗∗	666.222∗∗∗	686.203∗∗∗	699.850∗∗∗	661.904∗∗∗
Observations	6447	6447	4338	3361	3099	3099	3099

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Table 8.

Estimates for language and mathematics third-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		−2.323	−0.755	−3.686	−3.661	1.945	36.805
Additional offices		0.065	−0.127	−4.553	−1.874	2.675	−16.902
Meeting room for teachers		13.968∗	8.973	9.545	4.003	2.374	−0.469
Sports field		−8.784	−14.442∗	−9.665	−10.505	−7.509	34.787
Gym		−8.863	0.372	−4.606	−14.905	−9.388	−15.288
Computer room		14.814∗∗	13.665∗∗	14.338∗∗	11.472∗	13.685∗∗	9.898
Auditorium		2.803	3.124	3.291	2.285	1.521	−17.164
Arts and/or music room.		37.905∗∗∗	32.339∗∗∗	23.520∗∗∗	18.356∗∗	14.498	12.732
Nursing		18.426∗	7.926	6.155	6.202	8.658	4.296
Science labs		16.243∗	19.386∗∗	13.809∗∗	9.541	7.324	19.431
Water		14.359	18.036∗	14.305	20.110∗	3.643	14.404
Sewerage		−14.879	−11.011	−18.142∗	−15.922	−17.675	−18.24
Phone		29.703∗∗∗	23.324∗∗∗	18.656∗∗	16.806∗∗	22.393∗∗	61.849
Mobile computer lab		−0.734	−2.262	−2.695	−1.082	−6.047	14.487
Bathrooms in good condition		6.477	10.015	11.386	8.094	1.488	7.635
Internet connection		−13.882	−6.563	−9.216	−11.127	−7.593	−96.944
Garbage collection		8.096	6.483	7.417	3.138	−8.499	26.008
Director's office ∗Rural						−26.662
Additional offices∗Rural						−16.42
Meeting room for teachers∗Rural						3.042
Sports field∗Rural						−1.343
Gym∗Rural						−0.159
Computer room∗Rural						−25.298
Auditorium∗Rural						−5.587
Arts and/or music room∗Rural						17.753
Nursing∗Rural						−19.402
Science labs∗Rural						0.736
Water∗Rural						45.583∗∗
Sewerage∗Rural						17.739
Phone∗Rural						−10.574
Mobile computer lab∗Rural						32.357∗
Bathrooms in good condition∗Rural						37.393
Internet connection∗Rural						−22.667
Garbage collection∗Rural						73.619∗∗∗
Director's office∗Public school							−40.383
Additional offices∗Public school							13.891
Meeting room for teachers∗Public school							7.794
Sports field∗Public school							−51.167∗
Gym∗Public school							20.015
Computer room∗Public school							6.052
Auditorium∗Public school							22.256
Arts and/or music room∗Public school							4.997
Nursing∗Public school							2.574
Science labs∗Public school							−12.109
Water∗Public school							5.235
Sewerage∗Public school							0
Phone∗Public school							−46.352
Mobile computer lab∗Public school							−23.802
Bathrooms in good condition∗Public school							0
Internet connection∗Public school							89.161
Garbage collection∗Public school							−26.378
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	698.276∗∗∗	658.351∗∗∗	614.723∗∗∗	617.276∗∗∗	640.289∗∗∗	658.126∗∗∗	609.208∗∗∗
Observations	6447	6447	4338	3361	3099	3099	3099

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Table 9.

Estimates for language sixth-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		7.887	5.462	1.027	−5.317	−6.704	−15.439
Additional offices		3.625	6.466	1.483	3.752	8.865	17.155
Meeting room for teachers		7.494	−3.372	−2.925	−3.691	−0.294	−1.097
Sports field		−12.041	−10.798	−1.992	3.294	4.45	18.158
Gym		−12.566	−3.675	−2.517	0.063	−1.981	21.911
Computer room		9.703	6.544	5.506	1.019	0.024	3.01
Auditorium		10.49	8.333	5.838	4.122	5.041	−11.683
Arts and/or music room.		44.853∗∗∗	39.813∗∗∗	27.836∗∗∗	13.161∗	16.229∗	−11.716
Nursing		16.555∗∗	15.856∗∗	10.838∗	0.855	−2.273	16.807
Science labs		6.638	12.050∗	4.948	−2.208	−3.168	6.36
Water		12.539	13.105	2.992	5.085	1.495	−16.589
Sewerage		1.937	0.011	−1.869	3.522	−7.192	3.867
Phone		9.85	3.841	−1.512	−0.472	−5.479	−0.314
Mobile computer lab		1.888	7.568	4.828	1.613	1.637	4.421
Bathrooms in good condition		5.578	3.602	0.676	2.686	2.244	27
Internet connection		−5.967	3.735	3.877	−1.524	0.837	−15.315
Garbage collection		4.621	−1.457	−1.756	3.058	3.501	−45.092
Director's office ∗Rural						9.71
Additional offices∗Rural						−18.328
Meeting room for teachers∗Rural						−13.475
Sports field∗Rural						−2.78
Gym∗Rural						−4.225
Computer room∗Rural						−3.369
Auditorium∗Rural						−4.425
Arts and/or music room∗Rural						−29.160∗
Nursing∗Rural						1.042
Science labs∗Rural						4.021
Water∗Rural						21.592
Sewerage∗Rural						33.198∗∗
Phone∗Rural						42.369∗∗∗
Mobile computer lab∗Rural						13.977
Bathrooms in good condition∗Rural						−21.051
Internet connection∗Rural						−43.274∗∗∗
Garbage collection∗Rural						−12.963
Director's office∗Public school							7.637
Additional offices∗Public school							−11.96
Meeting room for teachers∗Public school							−2.709
Sports field∗Public school							−14.423
Gym∗Public school							−32.963∗
Computer room∗Public school							−3.611
Auditorium∗Public school							20.396
Arts and/or music room∗Public school							47.983∗∗∗
Nursing∗Public school							−31.184∗∗
Science labs∗Public school							−16.234
Water∗Public school							24.759
Sewerage∗Public school							0
Phone∗Public school							1.928
Mobile computer lab∗Public school							3.488
Bathrooms in good condition∗Public school							−21.711
Internet connection∗Public school							11.749
Garbage collection∗Public school							53.478
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	683.830∗∗∗	640.427∗∗∗	584.620∗∗∗	564.444∗∗∗	601.707∗∗∗	614.843∗∗∗	644.020∗∗∗
Observations	6677	6677	4272	3607	3313	3313	3313

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Table 10.

Estimates for mathematics sixth-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		1.151	1.024	−4.263	0.503	2.646	132.010∗
Additional offices		2.999	1.926	−0.719	5.322	6.976	22.515
Meeting room for teachers		5.948	−1.134	−1.419	−6.065	−10.163	−44.787∗
Sports field		−11.818	−8.292	−3.186	−10.118	−11.591	31.7
Gym		−13.465	−7.476	−8.441	−14.525	0.54	−11.797
Computer room		8.501	3.215	2.611	3.076	6.418	23.59
Auditorium		2.148	1.833	−1.408	0.121	2.78	−12.775
Arts and/or music room.		48.681∗∗∗	45.643∗∗∗	36.429∗∗∗	25.237∗∗	31.914∗∗	−16.902
Nursing		26.346∗∗	26.689∗∗	25.031∗∗	23.022∗∗	15.227	46.044∗∗
Science labs		−4.274	0.554	−3.276	−3.124	2.136	1.678
Water		17.085	17.607	12.074	17.032	10.987	4.102
Sewerage		−4.433	−3.509	−7.033	−2.986	−8.024	−2.96
Phone		15.754	11.473	11.469	2.439	3.499	96.088
Mobile computer lab		3.267	5.676	5.863	5.234	−3.103	38.540∗∗
Bathrooms in good condition		3.454	1.846	3.86	10.584	10.01	106.617∗
Internet connection		−19.882∗	−15.555	−19.288∗	−26.715∗∗∗	−25.304∗∗	−138.136
Garbage collection		32.930∗∗	28.394∗∗	29.560∗∗	26.447∗∗	19.295	−6.886
Director's office ∗Rural						−17.577
Additional offices∗Rural						8.857
Meeting room for teachers∗Rural						24.6
Sports field∗Rural						−2.626
Gym∗Rural						−36.378
Computer room∗Rural						−25.601
Auditorium∗Rural						−44.895
Arts and/or music room∗Rural						−31.511
Nursing∗Rural						58.163∗
Science labs∗Rural						−28.024
Water∗Rural						21.196
Sewerage∗Rural						21.205
Phone∗Rural						6.987
Mobile computer lab∗Rural						60.030∗∗∗
Bathrooms in good condition∗Rural						10.074
Internet connection∗Rural						−12.854
Garbage collection∗Rural						43.433
Director's office∗Public school							−136.683∗∗
Additional offices∗Public school							−16.463
Meeting room for teachers∗Public school							42.234
Sports field∗Public school							−49.189
Gym∗Public school							7.977
Computer room∗Public school							−20.956
Auditorium∗Public school							12.753
Arts and/or music room∗Public school							76.385∗∗∗
Nursing∗Public school							−42.527∗
Science labs∗Public school							−12.388
Water∗Public school							16.12
Sewerage∗Public school							0
Phone∗Public school							−92.501
Mobile computer lab∗Public school							−36.675∗
Bathrooms in good condition∗Public school							−91.931
Internet connection∗Public school							110.187
Garbage collection∗Public school							40.104
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	719.341∗∗∗	667.893∗∗∗	638.739∗∗∗	619.947∗∗∗	626.960∗∗∗	635.870∗∗∗	430.495∗∗∗
Observations	6677	6677	4272	3607	3313	3313	3313

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Table 11.

Estimates for sciences sixth-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		0.454	−1.276	−5.452	−5.064	−6.672	−13.039
Additional offices		0.975	4.159	0.423	5.551	6.862	7.843
Meeting room for teachers		11.561	4.185	0.847	−2.064	−1.839	−18.919
Sports field		−14.107	−11.337	−3.969	−9.617	−10.345	35.634
Gym		−21.312	−13.547	−12.579	−17.022	−9.89	−1.326
Computer room		12.617	8.82	6.964	4.436	8.558	15.445
Auditorium		−0.448	−1.804	−3.885	−4.828	−3.222	−3.669
Arts and/or music room.		51.576∗∗∗	46.567∗∗∗	38.545∗∗∗	27.185∗∗∗	31.618∗∗∗	−0.05
Nursing		27.245∗∗	25.269∗∗∗	25.158∗∗∗	22.417∗∗	22.027∗∗	24.259
Science labs		2.163	5.985	2.363	−2.321	−1.706	−1.435
Water		12.541	12.626	7.687	10.867	7.321	−21.391
Sewerage		−2.354	−4.586	−9.654	−5.885	−5.091	−5.79
Phone		10.62	6.547	4.425	2.89	4.537	60.78
Mobile computer lab		0.94	3.898	2.816	−3.228	−11.126	8.784
Bathrooms in good condition		5.302	6.301	4.926	4.702	4.521	70.903
Internet connection		−15.029	−10.037	−12.496	−16.106∗	−13.469	−117.731
Garbage collection		18.051	11.021	11.503	5.668	−4.13	−22.924
Director's office ∗Rural						−4.565
Additional offices∗Rural						−0.049
Meeting room for teachers∗Rural						6.27
Sports field∗Rural						−0.929
Gym∗Rural						0.277
Computer room∗Rural						−28.166
Auditorium∗Rural						−23.738
Arts and/or music room∗Rural						−31.771
Nursing∗Rural						−21.563
Science labs∗Rural						−5.734
Water∗Rural						18.173
Sewerage∗Rural						3.91
Phone∗Rural						11.068
Mobile computer lab∗Rural						69.576∗∗∗
Bathrooms in good condition∗Rural						−6.177
Internet connection∗Rural						−17.906
Garbage collection∗Rural						50.667∗
Director's office∗Public school							6.53
Additional offices∗Public school							−2.032
Meeting room for teachers∗Public school							17.427
Sports field∗Public school							−50.331
Gym∗Public school							−23.426
Computer room∗Public school							−11.554
Auditorium∗Public school							−4.706
Arts and/or music room∗Public school							45.724∗∗
Nursing∗Public school							−9.378
Science labs∗Public school							−4.721
Water∗Public school							35.695
Sewerage∗Public school							0
Phone∗Public school							−55.236
Mobile computer lab∗Public school							−11.594
Bathrooms in good condition∗Public school							−65.269
Internet connection∗Public school							100.211
Garbage collection∗Public school							32.227
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	717.792∗∗∗	677.681∗∗∗	642.306∗∗∗	646.405∗∗∗	678.019∗∗∗	678.071∗∗∗	690.463∗∗∗
Observations	6677	6677	4272	3607	3313	3313	3313

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Table 12.

Estimates for language, mathematics, and science sixth-grade.

	(1)	(2)	(3)	(4)	(5)	(6)	(7)
Director's office		7.887	5.462	1.027	−5.317	−6.704	−15.439
Additional offices		3.625	6.466	1.483	3.752	8.865∗	17.155
Meeting room for teachers		7.494	−3.372	−2.925	−3.691	−0.294	−1.097
Sports field		−12.041∗	−10.798	−1.992	3.294	4.45	18.158
Gym		−12.566	−3.675	−2.517	0.063	−1.981	21.911
Computer room		9.703	6.544	5.506	1.019	0.024	3.01
Auditorium		10.49	8.333	5.838	4.122	5.041	−11.683
Arts and/or music room.		44.853∗∗∗	39.813∗∗∗	27.836∗∗∗	13.161∗	16.229∗∗	−11.716
Nursing		16.555∗∗	15.856∗∗	10.838∗	0.855	−2.273	16.807
Science labs		6.638	12.050∗	4.948	−2.208	−3.168	6.36
Water		12.539	13.105	2.992	5.085	1.495	−16.589
Sewerage		1.937	0.011	−1.869	3.522	−7.192	3.867
Phone		9.85	3.841	−1.512	−0.472	−5.479	−0.314
Mobile computer lab		1.888	7.568	4.828	1.613	1.637	4.421
Bathrooms in good condition		5.578	3.602	0.676	2.686	2.244	27
Internet connection		−5.967	3.735	3.877	−1.524	0.837	−15.315
Garbage collection		4.621	−1.457	−1.756	3.058	3.501	−45.092
Director's office ∗Rural						9.71
Additional offices∗Rural						−18.328
Meeting room for teachers∗Rural						−13.475
Sports field∗Rural						−2.78
Gym∗Rural						−4.225
Computer room∗Rural						−3.369
Auditorium∗Rural						−4.425
Arts and/or music room∗Rural						−29.160∗
Nursing∗Rural						1.042
Science labs∗Rural						4.021
Water∗Rural						21.592
Sewerage∗Rural						33.198∗∗
Phone∗Rural						42.369∗∗∗
Mobile computer lab∗Rural						13.977
Bathrooms in good condition∗Rural						−21.051
Internet connection∗Rural						−43.274∗∗∗
Garbage collection∗Rural						−12.963
Director's office∗Public school							7.637
Additional offices∗Public school							−11.96
Meeting room for teachers∗Public school							−2.709
Sports field∗Public school							−14.423
Gym∗Public school							−32.963∗
Computer room∗Public school							−3.611
Auditorium∗Public school							20.396
Arts and/or music room∗Public school							47.983∗∗∗
Nursing∗Public school							−31.184∗∗
Science labs∗Public school							−16.234
Water∗Public school							24.759
Sewerage∗Public school							0
Phone∗Public school							1.928
Mobile computer lab∗Public school							3.488
Bathrooms in good condition∗Public school							−21.711
Internet connection∗Public school							11.749
Garbage collection∗Public school							53.478
Student characteristics vector			X	X	X	X	X
Student family characteristics vector				X	X	X	X
Student school characteristics vector					X	X	X
Constant	683.830∗∗∗	640.427∗∗∗	584.620∗∗∗	564.444∗∗∗	601.707∗∗∗	614.843∗∗∗	644.020∗∗∗
Observations	6677	6677	4272	3607	3313	3313	3313

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.1.

Seven estimation specifications were generated for each grade and subject evaluated to verify the stability of the results. The first column includes student achievement estimations without the inclusion of control variables. The following estimations are made with the sequential incorporation of control variable vectors: school infrastructure (model 2 in column (2)), students’ characteristics (model 3), family characteristics (model 4), school characteristics (model 5), an interaction between the vector of school infrastructure with a rural school dummy (model 6), and an interaction between the vector of school infrastructure with the public school dummy (model 7). These interactions capture whether school infrastructure impacts differentially within rural (relative to urban) and public (relative to private) schools. All the models were estimated using maximum likelihood.

Interpreting the results, we can see that for both mathematics and language in third grade, there is a positive relationship between learning outcomes and the availability of a computer room, art/music room, science labs, water, sewerage, and telephone services. An association between internet connection and mathematics outcomes is also revealed. Rural schools reveal an important positive relationship between achievement and basic infrastructure provision, such as water, garbage collection, and computer labs. The exception is in the results obtained concerning mathematics: in rural locations, there is a negative relationship between the availability of computer rooms and the score obtained in mathematics. The negative relationship between a computer room with an internet connection and academic performance in mathematics could be explained by teachers lacking competence and digital skills, which could negatively influence the teaching-learning process [7,43].

In sixth grade, for the three areas of language, mathematics, and science, a positive relationship was found between the availability of art and/or music rooms as well as nursing facilities and learning outcomes. This corroborates the results from third grade. It is important to note that, as in the case of third grade, there is a negative relationship between internet connection and mathematics outcomes. Rural schools show a positive relationship between the availability of nursing facilities and learning outcomes in mathematics and science. This is also true for mobile computer laboratories. In the rural areas, the stand-out results are the positive relationships between language and basic infrastructure such as sewerage and telephone services. However, a negative relationship is observed between academic performance and the presence of an art and/or music room or an internet connection.

The commonalities between third and sixth grades are manifested in both language and mathematics; a significant and positive correlation exists between academic performance and art and/or music rooms as well as nursing facilities. In schools located in rural areas, basic infrastructure is shown to be essential for academic outcomes.

6. Discussion

As a key input into the education production function, it would be expected that school infrastructure shares a strong relationship with student academic outcomes. The regression results reveal, however, that not all school facilities influence learning outcomes. As several authors have shown, such results can be expected when studies cannot adequately account for the quality of infrastructure, as in the present case where the variables reflect only the presence, not the quality, of the infrastructure [[87], [88], [89], [90]]. Other research has emphasized that, particularly in developing countries, infrastructure quality may be substandard in many cases, muddying the measured empirical relationship between facilities and student results [[91], [92], [93]]. For instance, having a library with a limited selection of outdated books and housing a library with access to the latest resources across various subjects represent starkly different facilities. With categorical definitions of infrastructure, they are measured as equivalent in the database.

The present study's findings also suggest that the correlation between infrastructure and student performance is context-dependent. For example, investment in improving basic infrastructure such as water, sewage, and waste management systems is particularly important for rural student outcomes. This result corroborates research published by UNESCO and the World Bank manifesting that access to clean water and sanitation in educational settings is critical for attendance and health, considered necessary conditions for achieving learning outcomes [94,95].

The other consistent finding of this research is that infrastructure such as in-school nursing facilities and arts and/or music rooms yield a significant relationship with academic performance. The significance of nursing installations for educational performance has been emphasized by Bundy et al. [95] in their work, showing that school-based health services provide an extension of the necessary care for children in their early years, and ensure child health to enable optimal learning. The complementary relationship between health and education, particularly in developing countries, is echoed by Glewwe et al. [96].

Perhaps one of the most interesting revelations of the models’ estimations is the significant relationship between art and/or music rooms and student achievement. Given that less than a quarter of schools in our sample are reported as having such facilities, this finding reveals an important opportunity for school infrastructure planning and investment. Existing research finds the value of enhanced arts and music programs for academic achievement could be significant. Aprill [97] and Eisner [98] have stressed that there are positive connections between the arts and academic achievement. Along the same line, Gardner [99] demonstrates that multiple intelligences are steeped in the arts and notes the need for students to use the arts to communicate their knowledge.

Other researchers have examined the role of music in promoting academic achievement from a more lateral perspective. Through the exploration of the Mozart Effect, Hetland [100] demonstrates that, in a similar vein to the relationship between spatial and logical-mathematical intelligence, there is also a strong relationship between spatial and musical intelligence. In a study assessing a program to enhance mathematics achievement through musical interventions, which included exposure to classical music by Mozart and materials from School House Rock, Bryant-Jones et al. [101] find that students in both second and fourth grades exhibited a notable improvement, specifically in mathematical skills following the intervention. From a regional perspective, educational leaders in both Europe and Asia have effectively integrated the arts, particularly music, into their educational institutions [102,103]. According to Kelstrom [102,103], schools in these regions have also been positioned at the pinnacle of an international ranking of seventeen countries for secondary student scientific achievement.

However, despite the value of the arts to learning, because the arts are broadly understood as affective and expressive—not academic or cognitive—the arts often survive at the margins of education as curriculum enrichments; as rewards for good students, or electives for the talented [104]. Our study underscores the importance of incorporating subjects like music and art into the curriculum and ensuring that schools possess adequate infrastructure for teaching these specific subjects.

Thus, in summary, while the results of this study question the substantial investment and political importance given to large educational infrastructure projects, they also point to an opportunity to reorient educational policy spending and improve education outcomes at lower costs within the Ecuadorian context. Public policies should not only aim at broad infrastructure projects but at targeted improvements to address specific needs and contexts, ultimately leading to more equitable and effective educational outcomes.

6.1. Limitations

While the results obtained in Section 5 show consistency across several variables, it is important to interpret their implications with caution. Firstly, the data relating to infrastructure are taken from surveys requiring a binary response from school directors to the existence or absence of certain types of facilities. The responses do not allow for an indication of the installation quality. Accordingly, the estimations could underestimate the impact of quality amenities on learning outcomes by only considering the existence of a minimum standard of infrastructure within the categories in question.

Secondly, the obtained results cannot be interpreted as causal evidence but rather signify a correlation between infrastructure and educational outcomes. For instance, it cannot be said with certainty that the existence of a library causes better student achievement; rather there is an association between the two variables. Nevertheless, after controlling for clustered standard errors that can arise from cohort effects (which could otherwise generate selection bias), students’ and family characteristics, and other potential determinants of school achievement that may otherwise confound the results, the relationship found between educational outcomes and infrastructure is likely to be free from entanglement with other determining factors. Thus, while reverse causality is not impossible, the modeling strategy considering family socioeconomic status, geographic categorization, and school characteristics (such as whether the school is public or private) implicitly controls for factors that could otherwise conflate the estimated relationship between school achievement and infrastructure investment.

7. Conclusion

This research analyzed the relationship between school infrastructure and academic performance in Ecuador's primary schools. Empirical estimations showed that in urban schools, third-grade students had improved learning outcomes in mathematics and language with the availability of computer rooms, art/music rooms, science labs, water, sewerage, and telephone services. For sixth-grade students, positive correlations were found between learning outcomes and the availability of art/music rooms and nursing facilities. Consistently, significant positive correlations were observed between academic performance and the presence of art/music rooms and nursing facilities in urban schools.

Non-urban schools show different results. In rural areas, positive relationships are evidenced between basic infrastructure services (water, garbage collection, computer labs) and student outcomes. The exception is mathematics, where a negative relationship with computer rooms was observed. For sixth-grade rural students, positive relationships were found between learning outcomes in mathematics and science and the availability of nursing facilities and mobile computer labs. Language achievements were positively associated with sewerage and telephone services. Therefore, basic infrastructure is essential for academic outcomes in rural schools.

The results provide a better understanding of the correlation between school infrastructure investment and academic performance in Ecuador. The findings suggest that investing in basic infrastructure may yield greater benefits to student learning outcomes than complex infrastructure investments. Given the lower financial requirements, redirecting investment expenditure could produce substantial net benefits for a larger number of students. The recommendation for education policymakers is to reassess current infrastructure investment priorities and evaluate spending based on its potential to improve educational outcomes rather than its likelihood of being high-profile and socially popular.

While providing some insights, this research raises several questions for further investigation. Firstly, the negative relationship between technological infrastructure and academic performance may stem from factors such as teachers' lack of knowledge in using technology or restrictive school policies on facility use. Investigating these factors is essential for informing teacher training and investment allocation. Secondly, the significant relationship between art and music spaces and academic performance suggests potential positive spillover effects from strengthening these subjects in curricula. Lastly, the study indicates that the impact of educational infrastructure investment on performance may be limited without adequately trained teachers. A cost-benefit analysis of infrastructure quality and its use with trained teachers could offer valuable insights for optimizing education investment.

7.1. Biographical note Alejandra Espinosa

Alejandra Espinosa Andrade holds a Ph.D. in Cultural Analysis from the University of Amsterdam. She has worked as a researcher and lecturer in human rights, education, participative methodologies, project management, and territorial planning in national and international organizations. Currently, she works as a consultant for social and educational development programs and as a researcher affiliated with the Universidad de las Américas (Ecuador). Her approach is multidisciplinary and integrates sociocultural studies, urban studies, education, and politics.

7.2. Biographical note León Padilla

León Padilla is a research professor at Universidad de las Americas (UDLA). León obtained his Ph.D. in Economics and Business from Universidad Autónoma de Madrid. His research interests include topics related to macroeconomics, econometrics, monetary economics, and the macroeconomics of labor markets. His publications in specialized economics journals focus on productivity growth, monetary integration in the Eurozone and South America, and dollarization in Latin America.

7.3. Biographical note Sarah Carrington

Sarah Carrington is currently working as a researcher affiliated with the Universidad Espíritu Santo, in Samborondón, Ecuador. Sarah obtained her Ph.D. in Economics from Monash University. Her research interests include topics related to macroeconomics, finance, development economics, gender economics, and the macroeconomics of labor markets. Her publications in indexed journals focus on economic convergence, housing markets, credit cycles, corporate investment, gender economics, and the labor market.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Ethics declaration

Review and/or approval by an ethics committee was not needed for this study because this research involves information freely available in the public domain. Informed consent was not required for this study for the same reason. All the data used for this study are publicly available in the UNESCO's web page Estudio Regional Comparativo y Explicativo (ERCE 2019) at

https://www.unesco.org/es/articles/estudio-regional-comparativo-y-explicativo-erce-2019.

Geolocation information

https://goo.gl/maps/waY6T7RtfUaMEs6w5.

Declaration of Generative AI and AI assisted

During the preparation of this work the authors used Chat GPT3.5 to check grammar and to improve readability and language of a very limited number of paragraphs. After using this tool/service, the authors reviewed and edited the content as needed and take full responsibility for the content of the publication.

Data availability statement

The data that support the findings of this study are openly available in the UNESCO's web page Estudio Regional Comparativo y Explicativo (ERCE 2019) at

https://www.unesco.org/es/articles/estudio-regional-comparativo-y-explicativo-erce-2019.

CRediT authorship contribution statement

Alejandra Espinosa Andrade: Writing – review & editing, Writing – original draft, Supervision, Project administration, Methodology, Investigation, Formal analysis, Conceptualization. León Padilla: Writing – original draft, Software, Methodology, Investigation, Formal analysis, Data curation. Sarah J. Carrington: Writing – review & editing, Writing – original draft, Validation, Investigation, Formal analysis, Data curation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix.

Table A.1.

Dataset variables.

Variables	Code name in ERCE-2019	Type	Response Categories	Source in ERCE-2019
Plausible values for each subject
Language (plausible value 1)	LAN_1	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Language (plausible value 2)	LAN_2	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Language (plausible value 3)	LAN_3	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Language (plausible value 4)	LAN_4	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Language (plausible value 5)	LAN_5	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Mathematics (plausible value 1)	MAT_1	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Mathematics (plausible value 2)	MAT_2	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Mathematics (plausible value 3)	MAT_3	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Mathematics (plausible value 4)	MAT_4	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Mathematics (plausible value 5)	MAT_5	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Sciences (plausible value 1)	SCI_1	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Sciences (plausible value 2)	SCI_2	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Sciences (plausible value 3)	SCI_3	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Sciences (plausible value 4)	SCI_4	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Sciences (plausible value 5)	SCI_5	Escalar	Mean = 700, stand. dev = 100	Student Questionnaire
Infrastructure vector variables
Director's office	DDIT31_01	Categorical	1: Yes; 0: No	Principal Questionnaire
Additional offices	DDIT31_02	Categorical	1: Yes; 0: No	Principal Questionnaire
Meeting room for teachers	DDIT31_03	Categorical	1: Yes; 0: No	Principal Questionnaire
Sports field	DDIT31_04	Categorical	1: Yes; 0: No	Principal Questionnaire
Gym	DDIT31_05	Categorical	1: Yes; 0: No	Principal Questionnaire
Computer room	DDIT31_06	Categorical	1: Yes; 0: No	Principal Questionnaire
Auditorium	DDIT31_07	Categorical	1: Yes; 0: No	Principal Questionnaire
Arts and/or music room.	DDIT31_08	Categorical	1: Yes; 0: No	Principal Questionnaire
Nursing	DDIT31_09	Categorical	1: Yes; 0: No	Principal Questionnaire
Science labs	DDIT31_10	Categorical	1: Yes; 0: No	Principal Questionnaire
Water	DDIT33_02	Categorical	1: Yes; 0: No	Principal Questionnaire
Sewerage	DDIT33_03	Categorical	1: Yes; 0: No	Principal Questionnaire
Phone	DDIT33_04	Categorical	1: Yes; 0: No	Principal Questionnaire
Mobile computer lab	DDIT33_05	Categorical	1: Yes; 0: No	Principal Questionnaire
Bathrooms in good condition	DDIT33_06	Categorical	1: Yes; 0: No	Principal Questionnaire
Internet connection	DDIT33_07	Categorical	1: Yes; 0: No	Principal Questionnaire
Garbage collection	DDIT33_08	Categorical	1: Yes; 0: No	Principal Questionnaire
Student vector variables
Sex	SEX	Categorical	1: girl; 0: child	Student Questionnaire
Student attendance at preschool education	PREE	Categorical	1: Yes; 0: No	Student Questionnaire
Repetition	REPC	Categorical	1: Yes; 0: No	Student Questionnaire
Mathematics book	E3IT09_02	Categorical	1: Yes; 0: No	Student Questionnaire
Own computer	E3IT09_06	Categorical	1: Yes; 0: No	Student Questionnaire
Doesn't work	E3IT19	Categorical	1: Yes; 0: No	Student Questionnaire
Domestic work	E3IT19	Categorical	1: Yes; 0: No	Student Questionnaire
Sense of belonging to the school	SPESC	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Teaching attendance and punctuality	ASISP	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Disruption in the classroom	DISAU	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Self-efficacy in mathematics	EFMAT	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Parental involvement in learning	INVAP	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Absence from school	AUSE	Escalar	0: once a month; 1: 2 or more	Student Questionnaire
Tardiness in school attendance	ATRE	Escalar	0: no day; 1: almost every day	Student Questionnaire
Study days per week	TSTU	Escalar	0: none; 1 = almost every day	Student Questionnaire
Supporting student learning	AAEG3	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Interest in the well-being of students	CLBIE	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Violence inside the school	VIOES	Escalar	Mean = 0, stand. dev = 1	Student Questionnaire
Family vector variables
Maximum Parent Education	EDU	Categorical	1: Tertiary; 0: fewer than tertiary	Student Questionnaire
Parental involvement in learning	INVAH	Escalar	Mean = 0, stand. dev = 1	Family Questionnaire
Violence in the home neighborhood	VIOBF	Escalar	Mean = 0, stand. dev = 1	Family Questionnaire
Good relations in the neighborhood	RELBF	Escalar	Mean = 0, stand. dev = 1	Family Questionnaire
Family income (decile 1)	FFIT15	Categorical	1: decile 1; 0: other	Family Questionnaire
Family income (decile 2)	FFIT15	Categorical	1: decile 2; 0: other	Family Questionnaire
Family income (decile 3)	FFIT15	Categorical	1: decile 3; 0: other	Family Questionnaire
Family income (decile 4)	FFIT15	Categorical	1: decile 4; 0: other	Family Questionnaire
Family income (decile 5)	FFIT15	Categorical	1: decile 5; 0: other	Family Questionnaire
Family income (decile 6)	FFIT15	Categorical	1: decile 6; 0: other	Family Questionnaire
Family income (decile 7)	FFIT15	Categorical	1: decile 7; 0: other	Family Questionnaire
Family income (decile 8)	FFIT15	Categorical	1: decile 8; 0: other	Family Questionnaire
Family income (decile 9)	FFIT15	Categorical	1: decile 9; 0: other	Family Questionnaire
Electric light at home	FFIT17_01	Categorical	1: Yes; 0: No	Family Questionnaire
Water at home	FFIT17_02	Categorical	1: Yes; 0: No	Family Questionnaire
Sewerage at home	FFIT17_03	Categorical	1: Yes; 0: No	Family Questionnaire
Phone at home	FFIT17_04	Categorical	1: Yes; 0: No	Family Questionnaire
Cable or satellite television at home	FFIT17_05	Categorical	1: Yes; 0: No	Family Questionnaire
Internet connection at home	FFIT17_06	Categorical	1: Yes; 0: No	Family Questionnaire
Garbage collection at home	FFIT17_07	Categorical	1: Yes; 0: No	Family Questionnaire
Television at home	FFIT18_01	Categorical	1: Yes; 0: No	Family Questionnaire
Radio or music system at home	FFIT18_02	Categorical	1: Yes; 0: No	Family Questionnaire
Computer at home	FFIT18_03	Categorical	1: Yes; 0: No	Family Questionnaire
Refrigerator at home	FFIT18_04	Categorical	1: Yes; 0: No	Family Questionnaire
Washing machine at home	FFIT18_05	Categorical	1: Yes; 0: No	Family Questionnaire
Cell phone without Internet access	FFIT18_06	Categorical	1: Yes; 0: No	Family Questionnaire
Cell phone with Internet access	FFIT18_07	Categorical	1: Yes; 0: No	Family Questionnaire
Vehicle with motor	FFIT18_08	Categorical	1: Yes; 0: No	Family Questionnaire
Family socioeconomic index	ISECF	Escalar	Mean = 0, stand. dev = 1	Family Questionnaire
Has a mother	FFIT04_01	Categorical	1: Yes; 0: No	Family Questionnaire
Has a father	FFIT04_02	Categorical	1: Yes; 0: No	Family Questionnaire
Has a brothers	FFIT04_03	Categorical	1: Yes; 0: No	Family Questionnaire
Ecuadorian	FFIT07	Categorical	1: Yes; 0: No	Family Questionnaire
Speak Spanish	FFIT08	Categorical	1: Yes; 0: No	Family Questionnaire
School vector variables
Rural location	RURAL	Categorical	1: Rural; 0: Urban	Principal Questionnaire
Public school	DEP	Categorical	1: Public; 0: Other	Principal Questionnaire
Socioeconomic level of the school (low)	DDIT20	Categorical	1: low; 0: Other	Principal Questionnaire
Religious school	DDIT23_04	Categorical	1: Yes; 0: No	Principal Questionnaire
School deficiencies reported	DEFE3	Escalar	Mean = 0, stand. dev = 1	Principal Questionnaire
Violence in the school neighborhood	VIOB3	Escalar	Mean = 0, stand. dev = 1	Principal Questionnaire
Good relations in the school neighborhood	RELB3	Escalar	Mean = 0, stand. dev = 1	Principal Questionnaire
Violence inside the school	VIOE3	Escalar	Mean = 0, stand. dev = 1	Principal Questionnaire
Quality of interpersonal relationships	CLIM3	Escalar	Mean = 0, stand. dev = 1	Principal Questionnaire
School leadership	LIDE3	Escalar	Mean = 0, stand. dev = 1	Principal Questionnaire
Disruption in the classroom	DISPR	Escalar	Mean = 0, stand. dev = 1	Teacher Questionnaire
Challenging classroom composition	COMAU	Escalar	Mean = 0, stand. dev = 1	Teacher Questionnaire
Cognitive activation	ACCPP	Escalar	Mean = 0, stand. dev = 1	Teacher Questionnaire
Violence inside the school	VIOEP	Escalar	Mean = 0, stand. dev = 1	Teacher Questionnaire
Feedback from the management team	LIDRP	Escalar	Mean = 0, stand. dev = 1	Teacher Questionnaire
Director support	LIDAP	Escalar	Mean = 0, stand. dev = 1	Teacher Questionnaire