1.1 Retention: concept, legal background and statistical data

School retention means the student will stay in the same school year for an additional period, instead of moving on to a higher level together with his/her age peers (^{Brophy, 2006}). In Portugal, the legal framework related to school year transition is like most European countries, which have lower retention rates. Therefore, the conclusion is that high retention rates are not a consequence of the legal framework (^{Perdigão, Rute & Ferreira, Antonieta & Félix, Paula,2015}). Portuguese legislation (^{Decree 98-A/1992 of 20 June 1992}) defines that in secondary education, in the scientific-humanistic courses, the student's approval in each subject depends on obtaining a final score equal or superior to 10. In the last year of multi-annual subjects, attendance score cannot be less than eight. Student’s transition to the next school year happens whenever the final grade is not less than 10 for more than two subjects. In vocational courses (labor market-oriented), a student does not move forward, if he/she has more than ten modules in arrears. Although the evolution of retention and dropout rates have shown an improvement in the last decade in all school years, Portugal is among the three OECD countries with the highest retention rate (31.2%), only surpassed by Belgium (34%) and Spain (31.3%), with the OECD average rate being 12 (Graph 1)% . In cycle transitions, the retention values increased in the 7th and 10th grades, critical moments in a school career. In Portugal, this percentage is higher than 50% for young people aged 15 with a problematic socio-economical situation, compared with the OECD average of 20%. ( Source: ^{OECD, PISA, 2015}). According to ^{Duarte et al. (2008}), a cycle transition can be a difficult phase in terms of students' adaptation and lead to a decrease in their academic performance.

Source: ^{OECD, PISA, 2015}

Graph 1 Percentage of 15-year-old students who have failed at least once. 

Portugal has participated in all PISA cycles to date - 2000, 2003, 2006, 2009, 2012 and 2015. In 2015 the sample was 7325 students with 15-year-old from 246 school clusters throughout the country. Since 2000, Portugal's average results have consistently improved in three areas (Portuguese, Mathematics and Reading), approaching the OECD average scores. Between 2009 and 2012 there was some stagnation in the results, improving again in 2015. PISA 2015 edition showed that Portuguese students improved their grades in all areas (Mathematics, Reading and Science). Considering the 35 countries/economies included in the OECD, Portugal now reaches the following positions: 17th in Science with 501 points, 18th in Reading with 498 points and 22nd in Mathematics with 492 points, being above the OECD average in all areas. Despite the improvement, Portugal is in the top 3 of the percentage of 15-year-old students who have failed at least once. Retention and dropout rates (2012-2016) in secondary education (humanistic, scientific courses) tend to reduce, albeit small, in 11th/12th grades and remain stable in the 10th grade. (Source :^{OECD, PISA, 2015})

The average data on school retention (2003/04 to 2015/16), provided by the Ministry of Education (Table 1) shows that humanistic and scientific courses have a higher percentage than technological and vocational courses in the 11th grade (difference of 3.7%) and 12th grade (8.2%). In both, the retention rate is higher in the last year of high school 38.7% in humanistic science courses and 30.5% in technological and professional courses. Source: http://infoescolas.mec.pt

Table 1 Average Retention Rate per Curriculum Orientation 2003-2016 

Source: http://infoescolas.mec.pt

A comparative analysis between women and men revealed a higher retention rate among boys compared to girls in primary and secondary Portuguese schools (Source: http://www.dgeec.mec.pt) . "The advantage of girls over boys in their environment is greater the more deprived that environment is" (^{Grácio & Sérgio, 1997}, p.70). Statistical data proved that the differences in achievement between boys and girls are more significant in low-class families and lower in middle-class and high-class families.

Male retention rate is higher than the female retention rate in all cycles and worsens after the 2nd cycle: in the 1st cycle the difference between boys and girls is 1.4%, in the 2nd cycle 5.9%, in the 3rd cycle 6.3% and in secondary education 7.6%. (table 2) Source: http://infoescolas.mec.pt

Table 2 Average Retention Rate for Girls and Boys 2003-2016 

Source: http://www.dgeec.mec.pt

The students’ percentage who moved forward until the 9th grade in 2016/2017 47% were girls, while 37% were boys. In the 9th grade, the success rate (zero retention in the 7th and 8th year and positive in the 9th year exams) was 51% for girls and 41% for boys.

In secondary education, the difference between boys and girls rose from seven percentage points in 2015/2016 to ten points in 2016/2017. In the 3rd cycle, the gap rose slightly in one year, from nine percentage points to ten (Source: http://www.dgeec.mec.pt).

1.2 Students’ engagement with school and its connection with school performance

Many studies show that student engagement is an indicator of school performance (^{Connell, Spencer, & Aber 1994}, ^{DiPerna, Volpe, & Elliot, 2005}, ^{Skinner & Belmont, 1993}; Veiga et al. 2009). It can be defined by the degree of students’ commitment to the school and their motivation to learn (^{Simons-Morton & Chen, 2009}; Veiga et al., 2012). The multidimensionality of this engagement is recognized, regarding the following dimensions: behavioral, emotional/affective, cognitive, academic (^{Appleton, Christenson, & Furlong, 2008}; ^{Fredricks et al. 2004}). Even though it is not consensual, which component is more critical, the behavioral and emotional appeared in many studies as the most vital. The transition between educational levels can affect engagement and learning as it implies changes in the level of requirement and often forces the student to change school, which involves adaptation and new relationships with teachers and peers (^{Reschly & Christenson, 2006}). ^{Klem and Connell (2004}) realized that students’ involvement diminished as they progressed from primary school to junior high school and from junior high school to high school, while ^{Anderson and Havsy, (2001}) show a decline in attendance when changing school years. Some studies also point out the increase on substance use (^{Henry, Knight, & Thornberry, 2011}; ^{Li & Lerner, 2011}; ^{Simons-Morton, 2004}) and mental health problems (^{Elias, Gara, & Ubriaco, 1985}; ^{Li & Lerner, 2011}). In the international study PISA "Program for International Student Assessment", sponsored by the OECD in 2015, the results regarding the feeling of belonging to school showed that 17.7% of students do not feel integrated and 12.9% feel as "outsiders". Regarding the ease of making friends at school, 22.2% reported that they do not have this ability. Besides, 11.8% stated having already suffered some act of bullying, 6.7% said that other students mock them, and 2.3% were already hit or pushed by other students. Interest towards school is measured by delays and absences, especially interim absence. PISA 2015 data showed Portugal and Sweden are the countries where students are later to school: 21% in Sweden and 16% in Portugal showed occasional delays or even frequently. As for intermediate absences Portugal and Spain are where it happened the most, although the percentage of students who admit to frequent or occasional absences is residual. Another yardstick to measure students' interest in the school is disruptive behavior. OECD 2015 study found out that Portugal is one of the three countries where teachers spend the most time keeping the order in class (15.7%), alongside Iceland and behind Brazil (19.8%). A large percentage of teachers (38%) admit having more than 10% of undisciplined students in a class; this percentage is above the OECD average (32%). OECD 2015 study also found out an impact of the variable sense of belonging on academic results in sciences as well as on total life satisfaction. The higher the sense of belonging, the better sciences results and overall life satisfaction. They also compared students who feel outsiders and students who do not feel outsiders in the sciences scores with those who feel outsiders showing worse results (minus 29 points on average without controlling the socio-economic variable and - 23 points controlling that variable). In an ethnographic study (Finne, 1991) on school dropout, one of the main reasons was that students did not feel emotionally involved. Lee (2014) noticed that emotional engagement measured as a sense of belonging is a significant value of reading performance, i.e., students with higher levels of engagement achieved better reading outcomes than students with less. In the same study, the author found out that the effect of this variable on reading performance is partially mediated by behavioral involvement, i.e. students with high levels of emotional involvement show high levels of behavioral involvement and this leads to higher reading scores. The study by Lee (2014) thus verified a direct and indirect effect of the emotional dimension on school performance. Baumesteir and Leary (1995) state that the need to belong is an essential human motivation. Hence, it is natural that when students have a high sense of belonging to the school, this can translate into a more considerable effort in academic activities. Veiga (2016) studied the criteria validity of the EAE four-dimensional scale, comparing two types of students, students with one or more retentions and students without retentions. Both groups expressed a moderate level of agency and cognitive involvement. However, the group with one or more retentions revealed a considerable lower involvement in all dimensions; the most significant differences are in the behavioral and affective dimensions. ^{Nobre and Janeiro (2010)}, in a study of 134 students from the 9th grade, discovered a positive and significant correlation between achievement and adaptation to school. They also showed a negative correlation between the number of failures and welfare at school. The authors concluded: "students involved feel more motivated, influencing their academic performance positively. Consequently, there is an adaptation in a cognitive, behavioral and emotional level" (p. 3027). In addition to the impact on school performance, there is also an impact on disruptive behavior. Henry, Knight and Thornberry (2011) studied the relationship between involvement and variables such as dropout, delinquency, offence and substance use and it was shown an inverse relationship between involvement and problematic behaviors both in early adolescence and early adulthood. Li and Lerner (2011) analysed the effects of school involvement (behavioral and emotional) on risk behaviors (delinquency and substance use), noting that high levels of involvement, both emotional and behavioral, projected a lower risk of disruptive behaviors and substance use. ^{Hirschfield and Gasper (2011}) considered that cognitive, in addition to emotional and behavioral involvement, also predicts a delinquency decrease, both in school and in general. ^{Borowsky et al. (2002}) also discovered that retention, the occurrence of school problems, absenteeism and low connection to school are predictors of violence one year after evaluation. ^{Wentzel (2012}) considers that learning takes place in a social context, so positive interactions influence students' emotionally and psychologically.

Juvoven, Espinoza & Knifsend (2012) stress the importance of having at least one friend at school in a transition between cycles. Several authors highlight the role of the teacher in promoting student involvement at school (^{Wang and Holcombe 2010}; ^{Birch & Ladd, 1997}; ^{Furrer & Skinner, 2003}; ^{Ryan & Patrick, 2001}), and can be preventive of disruptive behavior (^{Ryan & Patrick, 2001}; ^{Veiga, 2012}).

2.1 Sample

The sample contains 330 students in the 10 ^th grade of a Secondary School of the Lisbon district. The sampling technique was a non-probability sampleofconvenience because of the easy access to the institution where it was done. There is a balance in the sample related to gender, 44.2% - 146 male individuals, and 55.8% - 184 female individuals. Students were from humanistic, scientific courses (80.6%) and professional courses (19.4%).

2.2 Data collection instruments and procedures

Instrument: the Four-dimensional scale about Student’s Engagement in School (EAE-E4D)

The four-dimensional scale about Student’s Engagement in School (EAE-E4D) written by ^{Veiga (2013}, ²⁰¹⁴, ²⁰¹⁶) is a survey of 20 items with the following dimensions: cognitive, affective, behavioral and agency. The response scale is from 1 to 6 (1 being Total Disagreement and 6 being Total Agreement). The author studied the validity of the scale withconfirmatoryandexploratory factor analysis, proving the existence of a structure of 4 factors related to cognitive, affective, behavioral and agency dimensions. Another study of the psychometric qualities of the scale (^{Silva, Ribas, & Veiga 2017}), a confirmatory factor analysis using the AMOS software, confirmed the four-dimensional structure (X ² /df= 1.758; CFI =.941; TLI = 0,930; RMSEA =.051; PCFI = 0,797). The author also studied the accuracy of the scale related to internal consistency and obtained Cronbach alphas ranging from 0.701 to 0.870. The Cronbach alpha values found in the study (^{Silva, Ribas, & Veiga 2017}) were like those found by the author, with the total alpha being 0.828, revealing a good internal consistency. The Cognitive Dimension evaluates the information process, related subjects, information management, drawing up work plans. The Affective Dimension evaluates the connection to the school, friendship received and practised, sense of inclusion and belonging to a school. The Behavioral Dimension analyses intentionally disrupting classes, being incorrect with teachers, being distracted in class and absent from class. Finally, the Agency Dimension evaluates the student as an agent of action, initiative of students, intervention in class, dialogue with the teacher (Table 3). In this study, the affective dimension was the only one used, with the same items to the questions posed in the PISA 2015 study which assess the sense of belonging and ease in making friends.

Table 3 Scale of Students’ Engagement (EAE-E4D) - Dimensions and their Items 

* The asterisk indicates that the item is reversed.

2.3 Ethical procedures

We asked the permission to the scale's author (EAE-E4D) who, in addition to giving the authorization, agreed to collaborate in this study. We asked permission to the school's management to carry out the study and to pass over the scale (EAE-E4D) to all classes of the 10th grade at the end of the first term. The information was also requested at the end of the school year for those students who did not pass. After the favorable opinion of the school's management, we requested to the student's parents for informed consent and guaranteed the anonymity and confidentiality of individual results. The scale was applied with the collaboration of the Psychology and Guidance Service (SPO) and it was done in group, in a classroom context, by the psychologist of the SPO at the end of the first period.

2.4 Statistical analysis

The statistical analysis was performed through IBM SPSS Statistics software version 24.0.

To analyze whether there were significant differences between the group that did not carry over from year to year (81 individuals) and the group that carried over from year to year (249 individuals) Chi-square was used in the in the four dimensions and in the five items of the affective dimension and the answers were polarized.

The Chi-square test was used when no more than 20% of cells with expected frequencies ("expected count less than five") below 5 were found, when this happened Fisher's test was used as an alternative.