1 Introduction

In Brazil, Law No. 9,394/96 establishes the Guidelines and Bases for National Education (LDBEN), which introduced Distance Education (EAD) as a teaching modality within the formal education system and as an alternative for offering educational services nationwide (Brazil, 1996). With the aim of expanding and decentralizing the provision of higher education courses and programs in Brazil, as well as stimulating teacher training in the country, the Ministry of Education (MEC), in collaboration with the National Association of Leaders of Federal Higher Education Institutions (ANDIFES) and state-owned enterprises, created the Open University of Brazil System (UAB) within the context of the Forum of State Enterprises for Education (^{Saldanha, 2018}).

The UAB System contributes to expanding access to public universities, even in the most remote and isolated areas of the country, by facilitating initiatives that encourage federal, state, and municipal government partnerships, involving 133 Higher Education Institutions (HEIs). The goal is to contribute to the National Teacher Training Policy, with priority admission opportunities directed at professionals working in basic education (Coordination for the Improvement of Higher Education Personnel [CAPES], ²⁰²¹).

The expansion of EAD and the quality of teacher education programs in Brazil deserve attention, as these programs are responsible for training professionals who will be in charge of the foundational and structural education of future generations (^{Bertolin, 2021}). According to the Higher Education Census, 93.7% of new enrollees in EAD teacher education programs are in private institutions, while in public institutions, this modality accounts for 22.2% of new enrollments (National Institute of Educational Studies and Research [Inep], ²⁰²³).

The democratization of access to HEIs through this modality must be accompanied by institutional policies, such as inclusion programs and affirmative actions. In addition to this expansion, there is a concern with ensuring the quality levels of higher education, adhering to the criteria established by the MEC. To this end, the HEI teaching evaluation system includes a mandatory triennial assessment known as the National Student Performance Exam (ENADE). Performance involves the dimension of action and assessment, being expressed through scores and ratings (^{Ferreira, 2015}).

Understanding the results of the educational system, through student performance, is important for the development and management of public policies, allowing for the efficient allocation of resources and diligent action. In this sense, research exploring factors associated with academic performance, which is one of the metrics related to the quality of education, becomes relevant (^{Araújo, 2021}). Furthermore, among educators, social scientists, and psychologists, there is unanimous agreement that the elements favoring academic performance need to be better understood (^{Dazzani; Faria, 2009}).

Studies aiming to identify factors associated with academic performance add socially relevant contributions, as they provide support for more effective policies (^{Araújo, 2021}). Identifying the factors that contribute to student performance can support more efficient resource allocation, thus contributing to the population's qualification. It can also assist in directing resources to public educational policies and contribute to the design of the EAD system in the country, given the ongoing debate about whether or not the provision of online classes influences student formation (^{Araújo, 2021}).

Evaluative studies on school effectiveness originated in the 1960s with the Coleman Reports conducted in the United States and the Plowden Report developed in England. Both revealed that the school and its resources had a limited effect on learning compared to factors such as family background, family size, and the family context (^{Broke; Soares, 2008}). Regarding higher education evaluation, the contributions of Hanushek's studies (1979) motivated various research efforts on academic performance, focusing on students' personal characteristics, their family backgrounds, and the resources of academic institutions.

Since the majority of evaluative studies on academic performance in higher education in Brazil focus on the in-person modality (^{Santos, 2012}; ^{Ferreira, 2015}; ^{Miranda et al., 2015}; ^{Santana, 2023}), there is a notable absence of studies on the Distance Education modality that address factors associated with student academic performance, comparing public and private institutions.

Thus, the objective of this study was to analyze the factors associated with the performance of students in EAD teacher education programs at public and private HEIs in Brazil, based on the Educational Production Function Theory (EPFT). Its contributions refer to the possibility of filling gaps in previous research by incorporating other variables that have yet to be explored in the literature into the analysis, with the potential for in-depth discussion to provide significant theoretical and practical contributions to the field.

2 Theoretical framework

3 Methodology

This article was developed with the objective of analyzing the factors associated with the performance of students in undergraduate EAD courses. To this end, microdata from the 2017 ENADE provided by INEP, part of the Ministry of Education (MEC), were used (^{Inep, 2022}).

In 2017, the total number of EAD students evaluated by ENADE was 114,607, of which more than 91% were in undergraduate teaching courses. Although the study sample consisted of 104,930 students, the final number of observations was 81,728 due to missing data for some variables, as shown in Table 1. The outcome variable, which represents the overall student performance on ENADE, had the fewest observations (83,914).

Regarding sample stratification, the percentage of students per course was as follows: 3.83% in Mathematics; 6.53% in Languages - Portuguese, English, and Spanish -; 0.45% in Physics; 0.58% in Chemistry; 3.29% in Biological Sciences; 65.92% in Pedagogy; 5.28% in History; 2.36% in Visual Arts; 2.65% in Geography; 1.96% in Philosophy; 5.10% in Physical Education; 0.46% in Computer Science; 1.05% in Music; and 0.58% in Social Sciences (INEP, 2017).

To fulfill the study's proposed objective, the dependent variable used was students' academic performance, measured by the total score achieved on the ENADE exam. The independent variables were divided into: i) students' personal characteristics (age, gender, self-declared race/ethnicity, weekly hours dedicated to the course/study); ii) students' family and socioeconomic factors (family income, whether enrolled in a professional or regular course, type of high school attended, father's education level, and mother's education level); iii) peer effect (marital status); iv) peculiarities of the educational system (administrative category of the institutions, whether private or public, and region of the course - 1: North / 2: Northeast / 3: Southeast / 4: South / 5: Midwest).

The selection of variables used in the study was based on the relevant literature on the subject, as well as the availability of data that allowed for the research's design. The details of these variables are presented in chart 1 below.

Multiple linear regression, estimated using Ordinary Least Squares (OLS), was employed to determine the explanatory factors for students' overall performance on the ENADE exam. The purpose of the model resulting from the use of this technique is to predict changes in the dependent variable in response to changes in the independent variables, based on the magnitude of the effect of the explanatory variables (^{Daniels; Minot, 2020}; ^{Fávero, 2015}; ^{Hair et al., 2005}). The software Excel© and STATA 17 were used as tools for data adjustment and for the statistical analyses.

To meet the assumptions of OLS, the following tests were performed: i) VIF test, which resulted in the elimination of the variables type of housing and financial situation due to high collinearity; ii) Breusch-Pagan test, which revealed the presence of heteroskedasticity, leading to the use of robust errors in the estimates (^{Daniels; Minot, 2020}); iii) Swilk test, which did not confirm that the residuals conformed to a normal distribution. This issue was mitigated by the robustness of the analysis, substantiated by the large sample size used in the study, as emphasized by ^{Hair et al. (2005)}, who noted that in large samples, the effects of nonconformity can be overlooked.

4 Discussion of results

In this section, Table 1 presents the results concerning the independent variables. Analyzing the variables employed in the model and their respective estimated coefficients, the personal characteristics of the students are variables that express characteristics inherent to the students themselves, whether internal or external (^{Ferreira, 2015}). According to the results presented, the higher the average age of the students, the lower the average performance. This finding corroborates the studies of Uyar and Güngörmus (²⁰¹¹), ^{Araújo (2021)}, and ^{Meurer and Pereira (2020)}, which indicate that a student's age has a negative influence on their performance; thus, the older the student, the lower the performance. ^{Santos (2012)} and ^{Ferreira (2015)} relate age to academic responsibility, an important factor in Distance Education. A possible justification for this may lie in the fact that older students tend to have more responsibilities than younger ones, as they may have a job and/or a family, thereby being unable to dedicate themselves as fully as they would like.

Regarding "gender," the findings of the research indicated that there are no significant differences in grades. This contrasts with the findings of ^{Santos (2012)}, ^{Caetano et al. (2015)}, ^{Ferreira (2015)}, ^{Meurer and Pereira (2020)}, and ^{Rodrigues et al. (2016)}, who found that male students performed better than female students, while ^{Campbell (2007)} demonstrated that female students exhibited better academic performance. Studies by ^{Monroe, Moreno, and Segall (2011)} and ^{Rocha, Leles, and Queiroz (2018)} found no significant differences between the genders. It is observed that empirical research on gender continues to diverge concerning the results obtained and whether this variable affects academic performance (^{Miranda et al., 2015}; ^{Ferreira, 2015}). The context in which the student is situated may influence the behavior of these variables (^{Seow, Pan, & Tay, 2014}). It is pertinent to state that further studies are needed to clarify these contradictions.

Concerning "color/ethnicity," it was identified that individuals self-declared as black, yellow, brown, and indigenous, on average, have lower grades than students self-declared as white. Similar results were found by ^{Santos (2012)}, ^{Ferreira (2015)}, ^{Rodrigues et al. (2016)}, and ^{Araújo (2021)}. When analyzing the effects of ethnicity, one must consider both the socioeconomic and personal issues of the students, given Brazil's historical process regarding social inequality and the disparities in opportunities that black, brown, and indigenous individuals have faced over the years and which still persist. ^{Soligo (2021)}, in her study aimed at tracing the socioeconomic profile of students and the characteristics of institutions in the context of EAD through the lens of ENADE, alerts that only 5.87% of students entered the educational system through public policy based on Ethnic-racial criteria. In other words, despite the increase in inclusion policies (such as quotas and affirmative action), much remains to be done to reduce racial inequality in the educational system. Courses of varying prestige carry different tuition costs, leading to segregation among students of lower socioeconomic status and affecting the class of black and brown students (^{Barbosa, 2019}). Finally, students who did not declare their color exhibited higher coefficients than white students.

With respect to the variable "study hours outside the classroom," the results indicated that students who dedicate 1 to 3 hours per week to studying outside the classroom tend to achieve better academic performance than students who do not allocate this additional study time. As expected, as study hours increase, the average student performance rises; that is, the more hours devoted to studies, the greater the likelihood of obtaining higher grades. It is observed that the difference between dedicating 8 to 12 hours and more than 12 hours weekly is not substantial, suggesting a saturation point. These results corroborate those found by ^{Santos (2012)}, ^{Ferreira (2015)}, and ^{Rodrigues et al. (2016)}. The personal effort of the student is one of the most significant variables influencing their performance in higher education (^{Ibrahim, 1989}; ^{Freitas, 2004}).

Concerning the family and socioeconomic factors of students, the family income of the student was initially analyzed. It is important to note that in 2017, the Minimum Wage (SM) was R$ 937.00. The results demonstrate a positive effect of income on student performance, such that as income increases, student performance also improves. ^{Santos (2012)}, ^{Ferreira (2015)}, and ^{Rodrigues et al. (2016)} found similar results.

Regarding the variable "employment," it was shown to be statistically significant for those working up to thirty-nine hours per week. Students who "work occasionally" and "those with a workload of up to twenty hours per week" had lower grades compared to those who "do not work." In turn, students with "a work schedule of 21 to 39 hours per week" demonstrated higher chances of achieving high performance on ENADE. This last result corroborates the studies of ^{Miranda et al. (2015)}, ^{Ferreira (2015)}, and ^{Meurer and Pereira (2020)}. ^{Masasi (2012)} found that working has a positive correlation with academic performance, and professional experience may provide students with prior knowledge, facilitating the learning process.

Concerning housing, distance education is a method that facilitates and enhances access to education for a broad range of individuals, allowing for simultaneous participation (^{Costa, 2019}). Nonetheless, the variable "number of people living with the student" indicates that the greater the number of individuals residing with the student, the lower the probability of achieving higher grades. According to ^{Soligo (2021)}, it is important to consider that there exists a profile of EAD students, characterized as a "young adult" who needs to carve out "space" in their daily life to dedicate some time to reading and completing assignments, and thus will have to "negotiate" with those closely tied to the family circle within the residential environment. (^{Litto & Formiga, 2012}).

Regarding the variable "high school," students who completed all of their secondary education in public schools tend to have lower academic performance than those who completed this level of education, entirely or in part, in private schools. This result corroborates the findings of ^{Rodrigues et al. (2016)} and ^{Ferreira (2015)}. There is a "close relationship between this variable and income, as those with more financial resources tend to study in private schools, thereby having greater opportunities to enter public higher education" (^{Ferreira, 2015}, p. 97). Conversely, low-income students, who generally attend high school in public schools, tend to enroll in private higher education institutions, which may represent a lower level of opportunity (^{Ferreira, 2015}).

The results obtained for the variable "type of high school" showed that students who attended traditional high school tend to perform better than those who attended high school in the Youth and Adult Education (EJA) and/or supplemental modalities. However, students who attended traditional high school tend to have lower academic performance compared to those who attended technical or teaching vocational high schools. This result confirms the findings of ^{Ferreira (2015)} and contradicts the results found by ^{Rodrigues et al. (2016)}, who identified the opposite, indicating that students who attended traditional high school tend to have superior academic performance compared to those who attended vocational or teaching high schools.

Regarding the "educational attainment of family members," in general, students with at least one family member who has completed higher education have a higher probability of achieving better performance than those students without any family members holding a higher education degree. Generally, studies on this topic show positive effects of parental education (^{Hanushek & Woessmann, 2011}) on student academic performance, and the literature indicates that parental education is directly related to income-related issues (Mendonça & Barros, 1997).

Also in Table 1, it is possible to observe the results regarding the variable "marital status," which aimed to capture the effects of peers on student performance. The results indicated that single students in EAD tend to perform better than widowed students, but exhibit lower academic performance compared to married and divorced students. These results were also found by ^{Ferreira (2015)}, ^{Santos (2012)}, and ^{Rodrigues et al. (2016)}, opposing the findings of ^{Masasi (2012)}, which demonstrated that marital status does not directly affect student academic performance. ^{Miranda et al. (2015)} warns of the divergences found in international literature regarding the variables of gender and marital status, hindering conclusive analysis.

Finally, addressing the particularities of the educational system, concerning the variable "administrative category," the results indicate that in the EAD modality, the average performance of students from public institutions of higher education tends to be superior to that of students from private institutions. This result contributes to those found by ^{Caetano et al. (2015)}, ^{Ferreira (2015)}, ^{Meurer and Pereira (2020)}, and ^{Araújo (2021)}. ^{Santos (2012)} found no significance for affiliation with public institutions in 2002, but found such significance in 2003 and 2006.

A close relationship can be observed among the variables "family income," "high school" (public or private school), and "administrative category" (graduation from public or private institutions). Students with higher family income tend to attend high school in private institutions and subsequently enroll in public higher education institutions. Consequently, they tend to perform better than those with lower income who did not have the same opportunities.

Furthermore, concerning the variable "region," students from the South and Southeast regions tend to demonstrate superior academic performance compared to students from other regions, while the North region is noted for the lowest academic performance. Similar findings were reported by ^{Santos (2012)}, ^{Ferreira (2015)}, and ^{Araújo (2021)}. A possible inference can be explained by ^{Soligo (2021)} in her study of the socioeconomic profile of students and the characteristics of institutions in the context of distance education. The author noted that in regions where it is understood that there are more needy students, paradoxically, there are fewer EAD students; that is, in the Northeast, Midwest, and North regions of Brazil, demonstrating the persistence of significant regional inequalities in the country.

Finally, it is observable in Table 1 that the R² (model fit) was 0.1500, indicating that the variables used in the study explain 15% of the variations in students' grades on ENADE. It must be acknowledged that this result does not reflect a high predictive adjustment. By incorporating some variables that have been less explored in the literature (Table 1), the study aims to provide relevant theoretical and practical contributions to the field and, in this aspect, makes a trade-off with lower predictability. These variables provide relevant information for educational policymakers and offer an overview of the performance of existing policies, revealing weaknesses and aspects that should be considered, even though they are not, strictly speaking, the ones offering the best predictions, which is not the primary focus of this study.

5 Final Considerations

In order to encourage academic and political debate regarding access to quality higher education and the increasing availability of distance learning, this study aimed to analyze the factors associated with the academic performance of students in teacher education courses offered in both public and private higher education institutions in Brazil, supported theoretically by the FPE model. To achieve this, multiple linear regression was employed, estimated by Ordinary Least Squares.

Regarding the results of this study, personal, familial, socioeconomic factors, and peculiarities of the educational system showed a significant relationship with academic performance, thereby confirming the study's hypothesis. It was concluded, based on the statistical tests conducted, that the grades from public HEIs tend to have a higher average performance compared to those from private HEIs.

In addition to the characteristics of the institution, other factors directly influenced student performance, among which the student’s age, family income, family background, geographic region of the HEI, the student’s work hours, and study hours are particularly noteworthy. These elements are relevant as they highlight that the characteristics of HEIs cannot be overlooked; however, they are insufficient to ensure effectiveness in the teaching-learning process.

The distance learning model was created for working individuals; nevertheless, the Brazilian educational model is built under the premise of exclusive dedication. Consequently, the greatest gap for theoretical and practical advancements in the sector is the confirmation of the influence of occupational workload on the quality of higher education. The results of the multiple regression analysis indicated that students who need to work more than 20 hours per week have higher chances of achieving high performance on ENADE in the EAD modality. The act of working (in the case of teacher education courses, having to teach, perform teaching internships, or work within the educational system) may have a positive relationship with academic performance, and professional experience can provide students with prior knowledge, facilitating the learning process.

Another finding pertains to the variable "number of people living with the student," which demonstrated that the greater the number of individuals residing with the student, the lower the likelihood of attaining higher grades. Lastly, some divergences were found that have already been noted in the international literature regarding the variables "gender" and "marital status," hindering conclusive analysis. Therefore, further studies are necessary concerning these variables.

EAD has been seen as a privileged modality for promoting democratization and expanding education, as well as for driving social transformation through education. However, it is essential to analyze the results of this policy concerning the quality of education and the promotion of equity in access to higher education, in order to foster social justice and contribute to the reduction of inequalities in their multiple forms.

For future research, it is suggested to include studies on variables such as: motivation, aptitude for the field, anxiety levels, sleep hours, learning styles, technological resources, classroom infrastructure at EAD support centers, digital teaching resources, materials provided to students, extension activities, research activities as learning strategies, recommendations for books, chapters and/or handouts, academic qualifications, pedagogical training, professional experience, and faculty work regimes, which, in some cases, are not addressed in the ENADE questionnaire but are highlighted in the literature as determinants of academic performance.

Additionally, it is crucial to conduct research investigating the relationship between receiving scholarships or funding, admission through affirmative action policies, and academic performance, as understanding the context of these students provides socially relevant contributions, supplying foundations for more effective public policies.