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Influence of algorithmic abstraction and mathematical knowledge on rates of dropout from Computing degree courses

Journal of the Brazilian Computer Society201824:10

https://doi.org/10.1186/s13173-018-0074-2

  • Received: 13 June 2017
  • Accepted: 20 July 2018
  • Published:

Abstract

This paper presents a study of rates of dropout from Brazilian degree courses, based on data provided by the National Institute for Educational Studies and Research “Anísio Teixeira” (INEP) and a case study carried out at the University of Brasilia (UnB). Dropout was calculated by tracking the status of each student between 2010 and 2014 in the eight major areas according to the classification of the Organisation for Economic Co-operation and Development (OECD), for the major area of Science, Mathematics, and Computing, and for the area of Computing. Data were analyzed in order to check for potential evidence regarding the influence on dropout of factors such as algorithmic abstraction, number of applicants per place, or the gender of students. A survey was also performed using online questionnaires for circumvented students from the courses of Bachelor of Computer Science, Degree in Computing, and Computer Engineering between 2005 and 2015. This survey revealed the influence on dropout of several factors and particularly institutional and vocational factors; it is clear that difficulties in algorithmic abstraction and mathematical knowledge influence rates of dropout from computing courses.

Keywords

  • Dropout
  • Computing
  • Algorithmic abstraction
  • Mathematical knowledge

Introduction

The number of enrolled students contributes to the budget matrix of an institution, and dropout generates a negative budget impact. “Student dropout in higher education is an international problem affecting the result of educational systems. Losses of students who begin but do not conclude their courses are social, academic, and economical wastes” [19]. In public institutions, for instance, an understanding of this phenomenon may contribute significantly to reducing wastage of resources. In private institutions, dropout and revenue loss are clearly interrelated. In Brazil, higher education in the area of Science, Mathematics, and Computing shows high dropout rates, as can be observed from the data from the National Institute for Educational Studies and Research “Anísio Teixeira” (INEP). Dropout also arises from the late diagnosis of several students at risk of circumvention, thus making it difficult to combat and reverse the problem. Dropout analysis is an important step in the search for subsidies for understanding this phenomenon in order to mitigate it. The following hypotheses were therefore investigated in the present study:
  1. i.

    The number of applicants per place in a course is related to student dropout.

     
  2. ii.

    Courses in the major areas of Science, Mathematics, and Computing requiring higher levels of mathematics and algorithmic abstraction show higher dropout rates.

     

The general purpose of the present study was to analyze dropout from Brazilian Computing degree courses, based on data provided by INEP and a case study carried out at the University of Brasilia (UnB), in which a student was considered circumvented when “disengage[d] from the course for any reason different from degree obtainment” [6] (except in the case of death).

Dropout rates were analyzed in order to check a possible correlation with the number of applicants per place, the influence of gender, and a possible relationship between the requirements of algorithmic abstraction and mathematical knowledge and rates of dropout from courses in the major areas of Science, Mathematics, and Computing (and particularly from Computing degree courses). Non-parametric statistical tests were performed in these analyses since some variables did not show a normal distribution. A case study was also carried out at the UnB through the application of questionnaires to circumvented students of Computing degree courses to investigate their reasons for dropping out. Non-parametric tests, a Cronbach’s alpha test, and an analysis of the content of spontaneous replies were used for data analysis.

This paper is organized as follows: The “Background” section presents the background providing the context for the development of this study. The “Methodology” section describes the methodology and the case study carried out at UnB. The “Analyses and results” section describes the analyses and results, and the “Conclusions” section presents the conclusions.

Background

In a study performed by the Special Commission for Studies of Dropout in Brazilian Public Universities [4], the concepts of course dropout (disengagement only from the course, with no disengagement from the institution), institutional dropout (disengagement from the institution in which the students were enrolled), and system dropout (disengagement from higher education) were presented. The commission recommended that the most suitable concept of dropout should be selected based on the purpose of each study.

Dropout from Computing courses is not restricted to the Brazilian education system. According to Kinnunen and Malmi [12], courses in the area of Computer Science at Helsinki University of Technology (Finland) have 500–600 entries every year, and dropout rates have ranged from 30 to 50%.

According to Barroso and Falcão [3], conditions leading to school dropout can be classified into three groups: (i) economic issues, i.e., the impossibility of continuing the course due to socioeconomic reasons; (ii) vocational issues, i.e., a lack of identification with the course; and (iii) institutional issues, i.e., disengagement due to failure in the initial courses, early disabilities of previous contents, a mismatch with the methods of study, and difficulties in the relationships with institutional colleagues or members. Xenos et al. [22] identified the reasons for dropout from Computer Science degree courses at the Hellenic Open University in Patras, Greece, as follows (the student may have indicated more than one reason): professional (62.1%), academic (46.2%), family (17.8%), personal (8.9%), and health-related (9.5%).

For courses in the major areas of Science, Mathematics, and Computing, the occurrence of students with difficulties in subjects requiring algorithmic abstraction has been reported by several authors; according to Piva and Freitas [18], “the difficulty shown by students as to algorithmic representation is due to their difficulty to extract details composing a problem situation”. Regarding Computing students, Paula et al. [17] state: “Students have difficulties to build mental representations in fact abstracting a problem completely, so it is necessary to seek means to stimulate them to develop such an ability.” A study carried out at the AL-AQSA University (Palestine) by Abu-Oda and El-Halees [1] involving 1290 student records between 2005 and 2011 and using data mining techniques showed that success in algorithm-related initial subjects reduces the probability of disengagement by students. Difficulties regarding algorithmic abstraction, i.e., difficulties in abstraction related to problem-solving translation in software, have therefore been identified by authors as being a particular problem for Computing students.

Several studies of the difficulties experienced by students of mathematical subjects have been published. Souza et al. [20] evaluated dropout from Brazilian degree courses over a period of 10 years, based on academic studies of this issue during this period, and observed that failures in subjects requiring mathematical knowledge are among the most frequently seen. In a study of African students of Computer Science, Gruner [8] detected a low percentage of students who wished to become researchers or scientists. This author also stated that Mathematics is becoming less fully covered in the curricula of such courses. Regarding the field of Computing, Barcelos and Silveira [2] found that “the lack of a proper domain of mathematical knowledge by students is a possible factor explaining the lack of interest and dropout in courses of this area.”

The studies described in the “Analyses and results” section of the current work required dropout values to be statistically tested, with parametric and non-parametric tests as options. Regarding non-parametric tests, Maroco [13] stated that “such tests do not require a known variable (normal).” Although parametric tests have often been considered more powerful than non-parametric tests, this effect is only observed for large samples and those with equivalent size; thus, non-parametric tests are suitable for small samples and those with changeable sizes [13]. According to Vieira [21], when data normality and homoscedasticity cannot be confirmed and the sample size is reduced, non-parametric testing becomes a viable option. Since data normality is the main assumption in parametric tests, non-parametric testing must be used when normality is not detected.

In studies involving the application of questionnaires, it is necessary to check whether the items used are suitable for the purpose of the study, thus ensuring the reliability of the questionnaire. In the “Analyses and results” section, a Cronbach’s alpha test was one of the mechanisms used to analyze the answers. According to Hora et al. [10], “alpha measures the correlation among answers in a questionnaire through their profile analysis. It refers to a mean correlation among questions.” According to Maroco and Garcia-Marques [14], “the α index estimates how evenly items contribute with the unweighted sum of the instrument, ranging from 0 to 1.”

Methodology

The methodologies adopted in the present study are described below. These consisted of an analysis of national data (the “National data” section) and a case study carried out at UnB (the “Case study—UnB” section).

National data

Quantitative analyses were performed using micro-data from the Higher Education Census between 2010 and 2014, provided by INEP (2017). INEP began to make the individual data of students from 2009 available, whereas the data were provided in aggregate prior to 2009. Changes in the methodology were made between 2009 and 2010, as observed in the technical summary of the Higher Education Census in 2010 [11]. Thus, data from 2010 were considered in the present study.

The micro-data information for each year was stored in ASCII (micro-data of 2010, 2011, and 2012) and CSV (micro-data of 2013 and 2014) files. These files contained information on students, courses, higher education institutions, professors, and places offered; files related to students and courses were used in the current work.

Before calculating dropout rates, the data were cleaned, retaining the information on the status of the students on the course (transferred, disengaged, died, attending, enrolment blocked, or graduated), the student code (unique to each student and provided by INEP), gender, the name of the course, its general area, its specific area according to the classification by the Organisation for Economic Co-operation and Development (OECD) [16], and the maintenance entity (public or private).

After cleaning, the data were transferred to a MySQL databank, from which dropout was calculated. Statistical tests were performed using SPSS Statistics version 22 software. Only non-parametric tests were used since data normality was not detected for some variables. The Spearman correlation coefficient was used to check for a possible correlation between dropout and competition. The p value (significance level) was set at 0.05, so that p < 0.05 was considered acceptable when evaluating the significance of the obtained results. A box plot diagram was used to compare dropout rates among knowledge areas.

The number of circumvented students per year was calculated as the number of enrolments of disengaged students plus the number of enrolments of transferred students in that year, for each course. Total enrolments were obtained from the sum of the number of enrolments of active, graduated, transferred, disengaged, and deceased students per year per course. Dropout rates were obtained from the ratio between the number of circumvented students and the total number of enrolments. In this study, transfers are considered as course dropouts, even in the absence of institutional dropout.

The analyzed data comprising the dropout between 2010 and 2014 were separated into tables according to the maintenance entity (public or private institutions) and gender (male and female).

Case study—UnB

A case study was carried out at UnB to investigate the causes of student dropout from Computing courses. The total number of circumvented students between 2005 and 2015 from the degree courses offered at the Darcy Ribeiro Campus (Bachelor of Computer Science degree in Computing and Computer Engineering) was obtained from the Secretariat of Academic Records.

Several items were included in the study in order to evaluate the influence of each of them on the decision of circumvented students to disengage from the course. The prevalence of dropout-related reasons was unknown. However, a prevalence of 50% was used for sample size calculation. The following criteria were used to define the minimum number of questionnaires to be answered: 10% error margin, 90% confidence level, and 50% prevalence. Equation 1 was used for sample size calculation:
$$ {n}_{0=\left[{Z}_{a/2}^2\times p\left(1-p\right)\right]/{E}^2} $$
(1)
where p = 50.0%, Za/2 = 1.645 represents the critical value corresponding to a 90% confidence level, and E = 10% represents the error margin used. After obtaining n0, a correction was made for a finite population according to Eq. 2, in which N corresponds to the total of circumvented students per course. The calculation below was made per course, thus defining the sample size for each course:
$$ n={n}_0\times \left\{N/\left[{n}_0+\left(N-1\right)\right]\right\} $$
(2)
Table 1 shows the number of circumvented students per course, the minimum sample size, and the number of questionnaires answered.
Table 1

Sample sizes

Course

Circumvented students (N)

Sample size (n)

Questionnaires answered

Computer Science

431

59

93

Degree in Computing

540

61

85

Computer Engineering

191

51

53

In order to contact students who circumvented between 2005 and 2015, their names and e-mail addresses were obtained from the Secretariat of Academic Records at UnB. Students were considered circumvented when they disengaged from the course before its conclusion, for any reason except death. Each student received an e-mail explaining the purposes of this study and a link to the questionnaire, which was available online via Google Forms. It must be emphasized that this questionnaire did not request the student’s identity.

To investigate reasons for dropout, 21 items were made available using a Likert scale questionnaire in which students were required to answer, on a scale from 0 to 5 (six levels), how strongly each item influenced their disengagement, where 0 indicated zero influence and 5 indicated a strong influence. Students could also report other reasons for their dropout if these were not mentioned in the scaled questionnaire. They could also report which subjects they considered the most difficult during the course and their reasons for choosing to attend a degree course in the field of Computing.

The Likert scale questionnaire contained items grouped into socioeconomic, vocational, and institutional issues, according to the classification proposed by Barroso and Falcão [3]. Other classifications were also used for items which did not fit into these categories, such as family, personal, health, or other issues.

The values obtained for each item of the scaled questionnaire were compared using the Kruskal-Wallis test, and the post-hoc Dunn test was used to obtain homogenous groups, with a 95% confidence interval. A non-parametric test was adopted since data normality was not detected according to the Kolmogorov-Smirnov test, in which the p value was < 0.05; thus, the null hypothesis in which the data originated from a normal distribution was rejected. Items belonging to the homogeneous group with the highest score per course were tested using Spearman’s rank correlation (Spearman’s rho). These tests were performed separately for each course and for all courses in general.

Other factors investigated were gender, mode of entry, period of disengagement, possible receipt of financial support, and whether the course was the first degree course of the student.

Analyses and results

This section describes the analyses, and the results of quantitative studies involving micro-data from INEP are shown (the “Analysis of micro-data from INEP” section) and the analyses and results of studies involving questionnaires applied to circumvented students of UnB (the “Analysis of questionnaires applied to circumvented students of UnB”).

Analysis of micro-data from INEP

Table 2 shows the dropout rates and competition (number of applicants per place) of Brazilian courses composing the eight major knowledge areas, according to the OECD [16]. Municipal, state, and federal public institutions were considered. Private institutions included both profit-seeking and non-profit establishments. In Table 3, N = number of tested samples.
Table 2

Dropout and competition in general areas of knowledge

Major area

Occurrence

Private institutions

Public institutions

Year

Year

2010

2011

2012

2013

2014

2010

2011

2012

2013

2014

Education

Competition

0.55

0.68

0.80

0.79

0.70

4.09

5.88

6.74

6.93

6.61

Dropout (%)

16.06

17.91

17.72

16.32

17.89

13.83

13.19

14.82

15.16

13.98

Humanities and Arts

Competition

0.92

1.18

1.16

1.09

1.00

6.13

7.29

9.97

8.87

7.95

Dropout (%)

16.07

18.00

16.76

17.40

18.29

14.64

13.46

12.47

14.91

12.47

Social Sciences, Business, and Law

Competition

0.94

1.20

1.22

1.16

1.06

7.29

10.61

13.93

13.61

13.87

Dropout (%)

15.60

17.44

17.76

16.76

17.55

10.43

10.09

10.35

10.86

10.59

Sciences, Mathematics, and Computing

Competition

0.74

1.09

1.07

1.00

0.87

6.37

8.95

12.39

9.78

9.58

Dropout (%)

18.72

20.22

19.65

20.22

20.53

14.97

14.40

15.46

15.28

16.01

Engineering, Production, and Construction

Competition

1.33

1.66

1.85

1.69

1.35

8.98

13.42

16.72

16.32

15.23

Dropout (%)

16.77

17.26

16.20

16.66

15.22

11.63

10.76

11.20

10.24

10.87

Agriculture and Veterinary Medicine

Competition

1.11

1.40

1.69

1.68

1.05

7.58

10.47

12.94

12.02

12.41

Dropout (%)

12.71

13.46

13.86

13.83

12.37

10.29

9.80

11.04

10.45

11.05

Health and Social Welfare

Competition

1.45

1.82

2.11

2.05

1.94

15.28

19.50

25.91

25.91

26.84

Dropout (%)

13.80

14.57

13.63

14.49

13.89

7.92

6.93

6.27

7.30

7.46

Services

Competition

0.88

1.17

1.03

1.24

0.85

8.51

13.19

16.46

15.39

15.01

Dropout (%)

17.12

20.77

18.97

18.84

21.50

13.57

13.07

14.41

15.44

16.07

Table 3

Correlation test (dropout and competition)

Spearman’s rho

Private institutions

Correlation coefficient

− 0.485**

Sig. (two-tailed)

0.002

N

40

Public institutions

Correlation coefficient

− 0.487**

Sig. (two-tailed)

0.001

N

40

**Significant correlation at 0.01 level (two-tailed)

Table 2 shows higher dropout rates in private institutions than in public ones, in all major areas. The competition (number of applicants per place) was higher in public institutions than in private ones.

Table 3 presents the Spearman correlation coefficient used to check for a possible statistical correlation between competition and dropout. Values were − 0.485 for private institutions and − 0.487 for public ones. Forty values (N = 40) were tested in each group, corresponding to the dropout rates and a number of applicants per place in each major area (eight in total) over 5 years (2010–2014). According to Dancey and Reidy [5], correlation coefficients can be classified as follows: 0.10–0.30 (weak), 0.40–0.6 (moderate), and 0.70–1 (strong). A negative value indicates an inverse correlation, and the values range from − 1 to 1. Thus, competition and dropout showed a moderate inverse correlation between 2010 and 2014 in private and public institutions. The Special Commission for Studies of Dropout from Brazilian Public Universities [4] found that “low remuneration in job market decreases the search for courses, affects the training quality of students, and increases the propensity to drop out.” Silva Filho et al. [19] evaluated the correlation between dropout and the number of applicants per place in general areas of knowledge in 2005 and observed that major areas showing larger numbers of applicants per place also experienced lower mean annual dropout rates than the national average (22%). These major areas were Health and Social Welfare, Agriculture and Veterinary Medicine, Engineering, Production, and Construction. The highest dropout rate between 2001 and 2005 (services) corresponded to the lowest number of applicants per place.

In Figs. 1 and 3, the x-axis of the box plot diagram shows the major knowledge areas according to OECD [16]. In Figs. 2 and 4, the x-axis shows the grouping of the areas or courses per gender. The y-axis shows dropout rates. In the boxes, the lower value is represented by the lower bar, while the upper value is represented by the upper bar. The black line inside the box represents the median value. Some boxes are larger than the others, indicating a higher variation in dropout rates than in the smaller boxes. Elements outside the box (represented by a circle or an asterisk) are referred to as outliers, which correspond to unusual values in relation to the other datasets. These boxes facilitate a comparison of dropout rates between areas, since those located in an upper position in the graph correspond to higher dropout rates in relation to those located in a lower position. In Figs. 1 and 2, the major areas of knowledge are represented as follows: 1—Education; 2—Humanities and Arts; 3—Social Sciences, Business, and Law; 4—Science, Mathematics, and Computing; 5—Engineering, Production, and Construction; 6—Agriculture and Veterinary Medicine; 7—Health and Social Welfare; 8—Services. Box plot diagrams were generated using SPSS Statistics software version 22.
Fig. 1
Fig. 1

Comparison of dropout rates among major knowledge areas

Fig. 2
Fig. 2

Comparison of dropout rates between male and female students in major knowledge areas

Figure 1 was generated from the data shown in Table 2. The highest dropout rate between 2010 and 2014 was observed for the areas of Science, Mathematics, and Computing and the area of Services, in public and private institutions. Dropout rates in these two areas were similar since their boxes are around the same height on the graph. The variability of dropout rates was higher for Services (larger box) than Science, Mathematics, and Computing. Thus, these major areas experienced higher dropout rates than others. Silva Filho et al. [19] also carried out a study of dropout from the general areas of knowledge between 2001 and 2005. The authors investigated the mean dropout from the public and private institutions during this period and observed higher values for Services (29%) and Science, Mathematics, and Computing (28%) than for those of other major areas and the national mean over the same period (22%). This result was similar to that observed in the present study, in which the abovementioned major areas also showed higher dropout rates between 2010 and 2014.

Table 4 shows the dropout rates for male and female students from private institutions between 2010 and 2014 in the major areas of knowledge, while Table 5 shows the dropout from public institutions.
Table 4

Dropout per gender in major knowledge areas (private institutions)

Area

Dropout (%)—private institutions

Male

Female

2010

2011

2012

2013

2014

2010

2011

2012

2013

2014

Education

20.15

21.47

20.94

19.67

21.28

14.78

16.84

16.76

15.32

16.83

Humanities and Arts

16.09

18.38

16.75

17.41

19.07

16.05

17.68

16.77

17.39

17.64

Social Sciences, Business, and Law

16.75

18.77

19.10

17.90

18.76

14.65

16.36

16.69

15.88

16.63

Science, Mathematics, and Computing

19.23

20.71

20.02

20.87

21.38

17.25

18.85

18.64

18.47

18.34

Engineering, Production, and Construction

17.52

17.97

16.89

17.27

15.81

14.61

15.33

14.42

15.21

13.85

Agriculture and Veterinary Medicine

13.06

13.44

14.07

14.01

12.89

12.19

13.48

13.56

13.61

11.75

Health and Social Welfare

14.38

15.88

14.82

15.43

14.98

13.62

14.18

13.28

14.21

13.57

Services

17.70

21.62

20.37

19.58

23.05

16.67

20.14

18.03

18.36

20.47

Table 5

Dropout per gender in major knowledge areas (public institutions)

Detailed area

Dropout (%)—public institutions

Male

Female

2010

2011

2012

2013

2014

2010

2011

2012

2013

2014

Education

16.66

15.67

17.66

17.89

16.22

12.07

11.67

13.10

13.49

12.62

Humanities and Arts

16.20

14.53

13.68

15.87

13.28

13.39

12.63

11.52

14.15

12.36

Social Sciences, Business, and Law

11.58

11.25

11.61

12.03

11.95

9.26

8.96

9.14

9.76

9.32

Science, Mathematics, and Computing

15.47

14.91

16.11

15.65

16.28

13.97

13.42

14.22

14.57

15.48

Engineering, Production, and Construction

12.42

11.29

11.82

10.69

11.34

9.79

9.61

9.90

9.32

9.94

Agriculture and Veterinary Medicine

10.79

10.27

11.54

10.86

11.63

9.63

9.20

10.45

9.98

10.42

Health and Social Welfare

8.70

7.68

7.67

8.20

8.54

7.61

6.64

5.73

6.94

7.01

Services

15.06

15.47

16.64

17.30

18.49

12.71

11.64

13.08

14.29

14.51

Figure 2 shows the box plot diagrams generated from the data in Tables 4 and 5 for private and public institutions, respectively. Each box is numbered with the identification of the major areas in Tables 4 and 5. The x-axis is divided into male and female students. Boxes related to male students are located in a higher position than those of the female ones, thus indicating a generally higher dropout rate for male students in the major areas of private and public institutions.

Table 6 shows the dropout rates for areas composing the major area of Science, Mathematics, and Computing, based on the classification of the OECD adopted by INEP. Thus, the area of Computing comprised the areas of Computer Science, Computer Use, and Information Processing. Degree courses were not included, since INEP classifies training courses of Computing professors in the major area of Education, according to the classification of the OECD [16].
Table 6

Dropout rates from courses in the major areas of Science, Mathematics, and Computing

Area

Dropout (%)

Private institutions

Public institutions

2010

2011

2012

2013

2014

2010

2011

2012

2013

2014

Life Sciences (general courses)

20.73

29.89

22.75

Biology and Biochemistry

16.38

18.76

18.25

17.18

16.74

13.86

12.72

11.59

11.81

14.52

Environmental Sciences

10.50

19.07

12.93

10.77

5.67

10.18

14.91

18.07

17.59

19.18

Physical Sciences (general courses)

11.02

19.03

15.17

16.09

13.88

16.15

Physics

21.26

35.52

18.91

17.56

18.05

21.16

25.97

20.65

24.09

21.74

Chemistry

13.44

15.08

14.59

18.14

14.26

15.24

12.65

14.64

16.21

14.08

Soil Sciences

12.31

17.61

20.02

18.46

13.86

10.75

11.15

11.47

12.54

13.13

Mathematics

5.60

29.01

26.32

22.06

19.55

28.39

27.49

24.23

26.90

26.53

Statistics

19.81

22.20

20.62

17.37

18.68

14.87

14.45

17.51

18.39

18.19

Computing

19.42

20.74

20.16

21.10

21.89

14.23

13.87

16.18

15.12

15.88

Figure 3 shows the box plot diagrams generated from the data in Tables 5 and 6 in order to compare the dropout from the courses composing the major area of Science, Mathematics, and Computing. The area of Life Sciences was excluded from Fig. 3 due to the low rates of enrolment between 2010 and 2014. The area of Physical Sciences was excluded from the graph of private institutions since enrolments were only detected in 2010. For private institutions, the boxes are located in a higher position, thus indicating higher dropout rates for Physics, Mathematics, Statistics, and Computing. Since these areas require greater mathematical and algorithmic abstraction knowledge than the other courses, the hypothesis was confirmed for private institutions, thus proving hypothesis ii (the “Introduction” section). For public institutions, higher dropout rates were detected in the areas of Physics and Mathematics, which also require a high level of mathematics knowledge. Dropout rates from Computing courses were similar to those of Physical Sciences, Statistics, Chemistry, and Environmental Sciences.
Fig. 3
Fig. 3

Comparison of dropout rates in courses of the major area of Sciences, Mathematics, and Computing

Table 7 shows the dropout from Computing courses at private institutions per gender, while Table 8 shows the dropout from public institutions. The courses presented in these tables were the same as those mentioned by Nunes [15] in statistical reports of the Brazilian Computer Society (SBC). Training courses of Computing professors were considered to be degree courses, according to the nomenclature provided by the OECD. Table 7 does not show the dropout from courses in Software Engineering in 2010, 2011, and 2012, since no enrolment was detected in the micro-data from INEP over this period.
Table 7

Dropout from Computing courses—male and female students (private institutions)

Course

Dropout (%)—private institutions

Male

Female

2010

2011

2012

2013

2014

2010

2011

2012

2013

2014

Computer Science

19.72

20.77

21.52

21.15

19.10

19.57

19.61

22.65

21.50

18.73

Computer Engineering

20.81

23.01

20.33

19.74

19.54

22.71

23.00

20.11

19.32

19.32

Software Engineering

13.64

4.40

41.67

4.35

Information Systems

17.81

18.68

17.72

19.31

19.37

17.95

17.60

18.11

19.03

19.73

Degree in Computing

22.12

23.99

14.25

23.12

28.13

19.76

20.99

13.87

20.34

23.15

Technology

20.63

22.48

21.10

22.27

24.21

20.83

23.26

22.56

23.35

26.17

Table 8

Dropout from Computing courses—male and female students (public institutions)

Course

Dropout (%)—public institutions

Male

Female

2010

2011

2012

2013

2014

2010

2011

2012

2013

2014

Computer Science

13.51

13.06

13.90

13.47

14.01

13.37

15.12

14.73

14.87

15.93

Computer Engineering

11.44

10.41

11.95

11.02

11.44

5.96

10.63

12.45

10.15

11.70

Software Engineering

9.22

10.05

13.53

9.17

13.45

15.63

10.71

10.53

8.51

14.75

Information Systems

16.35

13.51

13.88

16.34

15.12

16.49

12.82

13.26

17.09

17.08

Degree in Computing

13.48

17.70

17.98

20.71

18.19

10.05

18.43

17.75

17.23

16.68

Technology

13.75

14.46

17.42

14.76

16.68

15.81

16.09

19.10

17.00

18.13

Figure 4 shows the box plot diagrams generated from the data in Tables 7 and 8. The area of Software Engineering was excluded from the diagram of private institutions since no enrolment was detected in 2010, 2011, or 2012. One the x-axis, the boxes are separated per gender. Boxes for both genders are located at a similar height, which indicates no significant differences in dropout per gender, with some minor variations, e.g., in the course of Degree in Computing in private institutions, which shows a higher dropout of male students. Figure 4 does not indicate a relationship between dropout from Computing courses and the gender of students.
Fig. 4
Fig. 4

Comparison of dropout in Computing courses

Analysis of questionnaires applied to circumvented students of UnB

This section presents an analysis of the answers from circumvented students on the degree courses of Computer Science, Computer Engineering, and Degree in Computing, offered by UnB. Table 9 shows the sample demographics.
Table 9

Sample demographics

Respondents per course (%)

 

Computer Science

Computer Engineering

Degree in Computing

Gender

 Female

7.53

13.21

8.24

 Male

92.47

86.79

91.76

Shares

 Shareholders

16.13

18.87

9.41

 Non-shareholders

83.87

81.13

90.59

Entry

 ENEM/SISU1

5.38

5.66

12.94

 Entrance examination

70.97

79.25

67.06

 PAS2

16.13

15.09

16.47

 Others

7.53

0.00

3.53

Financial support

 Yes

5.38

15.09

8.24

 No

94.62

84.91

91.76

First higher education

 Yes

73.12

86.79

63.53

 No

26.88

13.21

36.47

ENEM/SISU National Secondary Education Examination/Unified Selection System, PAS Program of Serial Evaluation

As mentioned in the “Case study—UnB” section, the questionnaire applied to circumvented students of UnB to identify their reasons for dropout consisted of 21 items. The respondents were asked to indicate how far each item influenced their decision to circumvent the course. Each item ranged from 0 to 5 (where 0 indicated zero influence and 5 indicated a strong influence on dropout). Items were organized according to Table 10, which contains their classification and description, and the position of the question in the sequence in which they were answered by the respondent. Items were chosen according to those fitting into the reasons for student dropout presented by Barroso and Falcão [3] (socioeconomic, vocational, and institutional issues); options added were family/personal/health reasons and other issues.
Table 10

Reasons for dropout from Computing courses

Classification

Question number

Item

Socioeconomic issues

1

Impossibility of conciliating work and study

2

Financial difficulties

15

Non-receipt of financial support

Vocational issues

3

Change to a course in different field

4

Lack of affinity with the course

5

Dedication to other studies

6

Lack of identification with professionals in this area

Institutional issues

7

Criteria for the evaluation of students were unsuitable or very rigid

9

Difficulties in mathematics-related subjects

8

Difficulties in subjects related to programming and algorithms

10

Difficulties in other subjects

11

Lack of information on subjects covered by the course

12

Unsuitable physical infrastructure within the institution

13

Relationship difficulties with professors/staff

14

Difficulties in understanding lecturers

Family/personal/health issues

17

Family distance

18

Affective disorders

20

Relationship difficulties with colleagues

21

Health problems (yours or a relative’s)

Other issues

16

Transfer to another institution, while continuing the same course

19

Change of municipality

Cronbach’s alpha test was used to check for correlations between the classifications used in the present study. Table 11 shows the values of Cronbach’s alpha for each classification. A total of 231 cases were tested, corresponding to the number of respondents from Computer Science (93 cases), Degree in Computing (85 cases), and Computer Engineering (53 cases).
Table 11

Cronbach’s alpha for each classification evaluated in the present study

Classification

Cronbach’s alpha

No. of items

Socioeconomic

0.636

3

Vocational

0.717

4

Institutional

0.800

8

Family/personal/health

0.644

4

Other issues

0.457

2

According to Hair et al. [9] regarding the values of Cronbach’s alpha, 0.60 represents the lower limit of acceptability for exploratory studies, while 0.70 is the limit for other types of study. The higher the value, the higher the reliability of the indicator. The present study is considered to be exploratory. According to Godoy [7], a study is exploratory if it aims to improve the knowledge of the target object. Table 11 shows that all classifications except “Other issues” had values of Cronbach’s alpha higher than 0.60. Since the classification of “Other issues” includes several items not fitting into the other classifications, it is understandable that its value is low. However, the more specific classifications had suitable values for an exploratory study, thus indicating that, in the general analysis of all respondents, reasons for dropout can be classified according to the system presented in Table 10.

Table 12 shows the results of the Kruskal-Wallis test for subsets of homogenous items for the course of Computer Science. A total of 1953 values were tested (93 answers in each item, multiplied by 21 items). The chi-square value was 335.607, with 20 degrees of freedom and p value < 0.05, thus indicating statistically significant differences between the items. The largest homogeneous subset observed in Table 12 is subset 9, composed of items 3, 6, 12, 1, 11, 4, 5, 9, 14, and 7; of these, item 1 is classified as socioeconomic, while the others are classified as vocational or institutional. This shows that vocational, institutional, and socioeconomic issues were predominant among the reasons for dropout from the course of Bachelor of Computer Science at UnB.
Table 12

Kruskal-Wallis test (Computer Science)

Mean rank and homogenous subsets

Item1

Subset

1

2

3

4

5

6

7

8

9

3

622.586

        

17

632.72

        

15

696.758

696.758

       

16

710.823

710.823

710.823

      

2

 

790.887

790.887

790.887

     

20

 

818.048

818.048

818.048

818.048

    

21

 

819.301

819.301

819.301

819.301

    

18

  

869.726

869.726

869.726

    

10

   

912.613

912.613

912.613

   

8

   

937.242

937.242

937.242

937.242

  

13

    

984.285

984.285

984.285

984.285

 

3

     

1093.33

1093.33

1093.33

1093.33

6

      

1104.43

1104.43

1104.43

12

      

1113.15

1113.15

1113.15

1

      

1115.05

1115.05

1115.05

11

       

1165.84

1165.84

4

       

1174.51

1174.51

5

       

1215.00

1215.00

9

       

1225.69

1225.69

14

        

1253.26

7

        

1261.75

Chi-square value

7.599

9.011

7.836

8.886

10.661

6.689

10.969

13.817

9.247

Sig. (two-tailed test)

0.055

0.061

0.098

0.114

0.059

0.082

0.052

0.087

0.415

Homogenous subsets are based on asymptotic significances. The significance level was 0.05

1Each cell indicates the mean sample position for the variable item

Table 13 shows the results of the Spearman correlation test between item 9 (difficulties in mathematics-related subjects) and the other items in the largest homogenous subset. A significant correlation was detected between item 9 and items 7 (criteria for evaluation of students were unsuitable or very rigid), 11 (lack of information on subjects covered by the course), 12 (unsuitable physical infrastructure within the institution), and 14 (difficulties in understanding lecturers). According to Dancey and Reidy [5], the correlation coefficient can be classified as follows: 0.10–0.30 (weak), 0.40–0.6 (moderate), and 0.70–1 (strong). Based on this classification, a moderate correlation was detected for items 7, 11, and 14 (all of which are classified as institutional), thus indicating that mathematics-related difficulties were correlated to institutional factors, according to the respondents.
Table 13

Correlation test—item 9 (Computer Science)

 

I1

I3

I4

I5

I6

I7

I11

I12

I14

Spearman’s rho

Item 9

Correlation coefficient

0.029

0.019

0.151

−0.009

0.054

0.544*

0.504*

0.272*

0.527*

Sig. (two-tailed)

0.783

0.854

0.149

0.928

0.606

0.000

0.000

0.008

0.000

N

93

93

93

93

93

93

93

93

93

*Significant correlation at 0.01 (two-tailed)

Table 14 shows the results of the Kruskal-Wallis test for the subsets of homogenous items for the course of Degree in Computing. A total of 1785 values were tested (85 answers for each item multiplied by 21 items). The chi-square value was 278.360, with 20 degrees of freedom and p value < 0.05, thus indicating statistically significant differences between the items. Item 1 showed the highest score. It should be emphasized that the Degree in Computing is offered at UnB in the evenings, allowing students to work during the day. Thus, difficulty in reconciling work and study was a very important factor affecting the dropout of students. Since item 1 is alone in subset 10, subset 9 was also considered for analysis. Subset 9 was composed of items 4, 12, 11, 5, 14, 9, and 7, which were classified as vocational or institutional. This indicates that vocational, institutional, and socioeconomic (as described by item 1) issues were predominant among the reasons for dropout from the course of Degree in Computing at UnB, as for the course of Bachelor of Computer Science.
Table 14

Kruskal-Wallis test (Degree in Computing)

Mean rank and homogenous subsets

Item1

Subset

1

2

3

4

5

6

7

8

9

10

17

627.524

         

19

652.465

         

20

662.147

         

16

667.253

         

15

669.7

         

21

701.071

701.071

        

18

779.1

779.1

779.1

       

2

 

828.641

828.641

828.641

      

10

 

848

848

848

848

     

6

  

889.006

889.006

889.006

889.006

    

8

  

891.641

891.641

891.641

891.641

    

3

  

896.941

896.941

896.941

896.941

896.941

   

13

  

921.859

921.859

921.859

921.859

921.859

921.859

  

4

  

975.835

975.835

975.835

975.835

975.835

975.835

975.835

 

12

   

994.847

994.847

994.847

994.847

994.847

994.847

 

11

    

1041.87

1041.87

1041.87

1041.87

1041.87

 

5

     

1055.62

1055.62

1055.62

1055.62

 

14

      

1098.22

1098.22

1098.22

 

9

       

1116.47

1116.47

 

7

        

1159.87

 

1

         

1274.92

Chi-square value

9.958

7.623

10.692

10.077

12.778

12.491

10.928

11.304

10.897

.2

Sig. (two-tailed test)

0.126

0.054

0.153

0.184

0.078

0.086

0.091

0.079

0.092

.

Homogenous subsets are based on asymptotic significances. The significance level was 0.05

1Each cell indicates the mean sample position for the variable item

2This is impossible to calculate since the subset contains only one sample

Table 15 shows the results of the Spearman correlation test between item 9 (difficulties in mathematics-related subjects) and other items in the largest homogenous subset. Significant correlation was detected between item 9 and items 4 (lack of affinity with the course), 5 (dedication to other studies), 7 (criteria for the evaluation of students were unsuitable or very rigid), 11 (lack of information on subjects covered by the course), 12 (unsuitable physical infrastructure within the institution), and 14 (difficulties in understanding lecturers). According to the classification proposed by Dancey and Reidy [5], this correlation can be classified as moderate for items 7 and 11 and strong for item 14 (all of which are classified as institutional), as observed for the course in Bachelor of Computer Science, thus indicating that mathematics-related difficulties were correlated with institutional factors, according to the respondents.
Table 15

Correlation test—item 9 (Degree in Computing)

 

I1

I4

I5

I7

I11

I12

I14

Spearman’s rho

Item 9

Correlation coefficient

− 0.049

0.399**

0.239*

0.562**

0.533**

0.223*

0.716**

Sig. (two-tailed)

0.656

0.000

0.028

0.000

0.000

0.040

0.000

N

85

85

85

85

85

85

85

*Significant correlation at 0.05 (two-tailed)

**Significant correlation at 0.01 (two-tailed)

Table 16 shows the results of the Kruskal-Wallis test for the subsets of homogenous items in the course of Computer Engineering. A total of 1113 values were tested (53 answers for each item multiplied by 21 items). The chi-square value was 292.670, with 20 degrees of freedom and p value < 0.05, thus indicating statistically significant differences between the items. The largest homogenous subset observed in Table 16 was subset 9, composed of items 8, 13, 7, 3, 11, 14, 6, and 4, all of which are classified as vocational or institutional. This indicates that vocational and institutional issues were predominant among the reasons for dropout from the course in Computer Engineering at UnB.
Table 16

Kruskal-Wallis test (Computer Engineering)

Mean rank and homogenous subsets

Item1

Subset

1

2

3

4

5

6

7

8

9

17

317.43

        

19

349.17

349.17

       

15

361.32

361.32

       

16

371.66

371.66

       

2

388.76

388.76

       

21

409.90

409.90

409.90

      

18

428.38

428.38

428.38

      

1

 

440.53

440.53

440.53

     

20

  

522.20

522.20

522.20

    

10

   

536.20

536.20

    

9

    

608.79

608.79

   

12

    

614.11

614.11

614.11

  

5

    

630.68

630.68

630.68

630.68

 

8

    

638.31

638.31

638.31

638.31

638.31

13

    

644.93

644.93

644.93

644.93

644.93

7

     

711.60

711.60

711.60

711.60

3

     

714.02

714.02

714.02

714.02

11

     

732.93

732.93

732.93

732.93

14

      

741.77

741.77

741.77

6

       

765.51

765.51

4

        

768.80

Chi-square value

11.559

9.197

7.276

4.666

10.545

13.51

13.77

12.74

12.008

Sig. (two-tailed test)

0.073

0.163

0.064

0.097

0.104

0.061

0.055

0.079

0.1

Homogenous subsets are based on asymptotic significances. The significance level was 0.05

1Each cell indicates the mean sample position for the variable item

Table 17 shows the results of the Spearman correlation test between item 8 (difficulties in subjects related to programming and algorithms) and the other items in the largest homogenous subset. A significant correlation was detected between item 8 and items 3 (change to a course in different area), 4 (lack of affinity with the course), and 6 (lack of identification with professionals in this area). Based on the classification proposed by Dancey and Reidy [5], this correlation can be classified as moderate for item 3 (vocational), thus indicating that the difficulty with algorithms was correlated with vocational issues, according to the respondents.
Table 17

Correlation test—item 8 (Computer Engineering)

 

I3

I4

I6

I7

I11

I13

I14

Spearman’s rho

Item 8

Correlation coefficient

0.408**

0.321*

0.292*

0.255

0.210

− 0.021

0.015

Sig. (two-tailed)

0.003

0.021

0.038

0.071

0.139

0.882

0.918

N

53

53

53

53

53

53

53

*Significant correlation at 0.05 (two-tailed)

**Significant correlation at 0.01 (two-tailed)

Table 18 shows the results of the Kruskal-Wallis test for the subsets of homogenous items considering all results for the three evaluated courses. A total of 4851 values were tested (231 answers for each item multiplied by 21 items). The chi-square value was 787.352, with 20 degrees of freedom and p value < 0.05, thus indicating statistically significant differences between the items. The largest homogenous subset observed in Table 18 was subset 7, composed of items 6, 1, 5, 4, 11, 9, 14, and 7, which are classified as vocational (4, 5, 6), institutional (7, 9, 11, 14), and socioeconomic (item 1).
Table 18

Kruskal-Wallis test (all courses)

Mean rank and homogenous subsets

Item1

Subset

1

2

3

4

5

6

7

17

1576.63

      

19

1622.71

      

15

1723.75

      

16

1725.93

      

21

 

1926.15

     

20

 

2003.16

     

2

 

2005.52

     

18

 

2075.13

     

10

  

2299.44

    

8

  

2469.48

2469.48

   

13

  

2549.75

2549.75

2549.75

  

3

   

2705.96

2705.96

2705.96

 

12

   

2721.13

2721.13

2721.13

 

6

    

2762.74

2762.74

2762.74

1

    

2827.49

2827.49

2827.49

5

    

2896.88

2896.88

2896.88

4

     

2919.81

2919.81

11

     

2938.96

2938.96

9

     

2950.67

2950.67

14

     

3090.41

3090.41

7

      

3132.24

Chi-square value

7.027

2.586

5.466

6.876

10.008

15.318

11.554

Sig. (two-tailed test)

0.071

0.46

0.065

0.076

0.075

0.053

0.116

Homogenous subsets are based on asymptotic significances. The significance level was 0.05

1Each cell indicates the mean sample position for the variable item

Table 19 shows the results of the Spearman correlation test between item 9 (difficulties in mathematics-related subjects) and other items in the largest homogenous subset. Significant correlation was detected between item 9 and items 4 (lack of affinity with the course), 5 (dedication to other studies), 6 (lack of identification with professionals in this area), 7 (criteria for the evaluation of students were unsuitable or very rigid), 11 (lack of information on subjects covered by the course), and 14 (difficulty in understanding lecturers). Based on the classification proposed by Dancey and Reidy [5], this correlation can be classified as moderate for the institutional items 7, 11, and 14, thus indicating that the difficulties in mathematics are correlated with institutional factors, according to the respondents.
Table 19

Correlation test—item 9 (all courses)

 

I1

I4

I5

I6

I7

I11

I14

Spearman’s rho

Item 9

Correlation coefficient

0.033

0.173**

0.146*

0.131*

0.488**

0.404**

0.491**

Sig. (two-tailed)

0.618

0.008

0.026

0.047

0.000

0.000

0.000

N

231

231

231

231

231

231

231

*Significant correlation at 0.05 (two-tailed)

**Significant correlation at 0.01 (two-tailed)

Circumvented students also had the option to add other relevant reasons for their disengagement from the three courses at UnB, in the case where the elements described in the scale questionnaire did not reflect all their reasons for dropout. Of the 93 respondents for Computer Science, 26 added reasons for dropout; of the 85 respondents for the Degree in Computing, 27 added reasons for dropout; and of the 53 respondents for Computer Engineering, 20 added reasons for dropout. These answers were classified as institutional, vocational, socioeconomic, and other issues, and institutional issues were widely cited, as shown in Table 20. Widely cited issues included an outdated curriculum and an unsuitable choice of courses, lack of suitability of the course with respect to the job market, lack of educational background, and successive failures.
Table 20

Percentage of answers according to classification

Classification of issues

Course

Computer Science

Computer Engineering

Degree in Computing

Vocational issues

7.69

0.00

3.70

Socioeconomic issues

0.00

5.00

14.81

Family/personal/health issues

7.69

5.00

14.81

Institutional issues

42.31

60.00

62.96

Other issues

42.31

30.00

14.81

When giving reasons for choosing a Computing course, more than 50% of students from each course attributed their motivation as being mainly due to affinity, curiosity, and an interest in computers or the field of computing.

According to the answers from the respondents, most of these students disengaged from the course during the first four periods: 61.28% for Computer Science, 58.82% for Degree in Computing, and 64.14% for Computer Engineering.

Conclusions

The analysis of micro-data from INEP between 2010 and 2014 based on non-parametric tests gave the following results: the number of applicants per place was inversely proportional to dropout; rates of dropout were different for the major knowledge areas, with the highest values in the major areas of Services and Science, Mathematics, and Computing; for courses in the major area of Science, Mathematics, and Computing, those requiring a greater knowledge of mathematics and algorithmic abstraction had higher dropout rates in private institutions. On average over all the major areas, dropout was higher for male students than for females. For Computing, dropout rates were similar for both genders.

Based on the case study carried out at UnB, institutional, vocational, and socioeconomic issues were the reasons most cited as contributing significantly to dropout from the courses of Computer Science and Degree in Computing. For Computer Engineering, institutional and vocational factors were also often cited. For the courses of Computer Science and Degree in Computing, difficulty in mathematics-related subjects was one of the institutional factors most often cited. This factor was directly correlated with institutional factors (criteria for the evaluation of students were unsuitable or very rigid, lack of information subjects covered by the course, difficulty in understanding lecturers), thus indicating that in addition to a difficulty in mathematics representing a relevant factor for dropout, students see a relationship between their difficulties in these subjects and institutional issues. For the course of Computer Engineering, difficulty in subjects related to programming and algorithms was one of the most often cited institutional factors. This factor was significantly and moderately correlated with the vocational item 3 (change to a course in a different area). It must be noted that when giving their reasons for choosing a Computing degree course, most of the circumvented students attributed their main reasons as affinity, curiosity, and an interest in computers and in the field of computing. However, vocational aspects were widely cited by respondents as the reasons for dropout. Regarding this divergence, it should be emphasized that the item “Lack of information on subjects covered by the course: I expected to find different subjects and contents from those offered” was one of the most often cited in the questionnaires answered by students from all courses, thus indicating that many students had no idea of what the course covered, although they had already had some contact with computing. Family/personal/health and other issues were not cited as the strongest reasons for dropout from the evaluated courses.

Although the present study cannot reach the overall conclusions for such a complex and vast subject, it does provide some evidence for the influence of requirements regarding knowledge of mathematics and algorithmic abstraction on the dropout of students from Computing degree courses. It should be emphasized that the survey of circumvented students was performed in a public institution (UnB). Thus, the reasons for dropout are slightly different than for private institutions. For instance, it is reasonable that socioeconomic issues would have a higher impact on dropout in private institutions than in public ones. It can also be observed that students associate their difficulties in mathematics- and algorithm-related subjects with institutional factors such as classes taught by professors and evaluation criteria. Thus, the evidence points to a need for investment in teacher training.

An understanding of dropout from Computing degree courses has a great importance in the search for subsidies to mitigate this problem. Education managers can benefit from such information. In the face of the reasons highlighted in the present study, which mainly focus on institutional and vocational issues, measures can be suggested to decrease dropout rates from Computing degree courses: motivating students to form study groups with periodic meetings; stimulation of monitoring works with granting of benefits; teaching of reinforcement classes early in the course for students experiencing difficulties in algorithm-based and calculation subjects; with the aid of psychology professionals, students could be monitored in order to check their affinity with the course, since students often begin a degree course full of uncertainty, and professional guidance can help them to change courses (if applicable) within the same institution; encouraging students to participate as collaborators in scientific and extension projects, where possible associating theory and practice, and encouraging students to work in a team, which is an essential requirement in the job market.

Although difficulties in mathematics-related subjects and in algorithmic abstraction are not the only reasons for dropout from computing courses and are associated with other reasons, their relevance was observed in terms of dropout. An understanding of these difficulties within computing courses can contribute towards a decrease in dropout rates.

Abbreviations

CSV: 

Comma-separated values

ASCII: 

American Standard Code for Information Interchange

ENEM: 

National secondary education examination. The ENEM is a non-compulsory, standardized Brazilian national exam, managed by the Ministry of Education’s National Institute for Educational Studies and Research (INEP). The ENEM is used as an admission exam for enrollment in many public and private universities in Brazil

INEP: 

National Institute for Educational Studies and Research “Anísio Teixeira”

OECD: 

Organisation for Economic Co-operation and Development

PAS: 

Program of Serial Evaluation. PAS is a form of entrance into higher education in Brazil adopted by several universities, divided into three exams done at the end of each year of high school

SBC: 

Brazilian Computer Society

SISU: 

The Unified Selection System is a federal government program that uses students’ ENEM scores to classify candidates for openings in public universities without taking the Vestibular

UnB: 

University of Brasilia

Declarations

Acknowledgements

We thank the Secretariat of Academic Records at UnB, which kindly and rapidly provided student records, thus enabling them to be contacted for the present study.

Availability of data and materials

The data from INEP can be downloaded from http://portal.inep.gov.br/microdados.

Authors’ contributions

All authors have contributed equally to this work in terms of data sampling, writing, and reading. All authors read and approved the final manuscript.

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Not applicable.

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The authors declare that they have no competing interests.

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Authors’ Affiliations

(1)
Federal Institute of Education, Science and Technology of Northern Minas Gerais (IFNMG), Farm São Geraldo, Kilometer 06, Januária, MG, CEP 39480-000, Brazil
(2)
Department of Computer Science, University of Brasilia (UnB), CP 4466, Brasília, DF, CEP 70919-970, Brazil

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