“That Wasn’t the Math I Wanted to do!”—Students’ Beliefs During the Transition from School to University Mathematics

It is a well-known fact that many students struggle during the transition from school to university mathematics. The aim of our quantitative study was to clarify the role of students’ beliefs concerning the nature of mathematics for a successful transition. We distinguish between static beliefs (mathematics as a finished system of rules, facts and formula) and dynamic beliefs (mathematics as a dynamic discipline with applications in everyday life). In particular, we examined whether first year students’ beliefs are suitable to predict students’ exam achievement and their satisfaction (as criteria for a successful transition) and how students’ beliefs develop during the transition. Therefore, we used questionnaires at the beginning and in the middle of the first term at university. Our results indicate that dynamic beliefs decrease during transition, whereas static beliefs remain rather stable. This seems problematic since dynamic beliefs turned out to negatively predict students’ dropout intention, while static beliefs are a negative predictor of students’ achievement in real analysis. Furthermore, the beliefs assessed in the middle of the term had a stronger predictive power than those at the beginning of the term. Based on these results, we discuss implications for the teaching of mathematics during the transition.

Introduction
The transition from school to university is a challenging process for many students, likewise in mathematics. This is illustrated by high dropout and subject change rates. In Germany-where our study took place-up to 80% of students quit their studies of mathematics without graduation, 35% of them during their first year at university (Dieter & Törner, 2012) while attending courses in linear algebra and real analysis. Chen (2013) reported similar numbers for the USA. Furthermore, many students fail their first exams or do not even attend them (Geisler & Rolka, 2018). These findings underline the necessity to understand students' problems during the transition phase. In this contribution, we focus on the development and influence of students' beliefs concerning the nature of mathematics during the transition. In particular, we are interested in the relation between students' beliefs and different criteria of success (achievement in real analysis and dropout intention) as well as in the development of students' beliefs over time. In order to better understand the role that students' beliefs play in this transition process, we first give an overview about major differences between mathematics at school and university and second discuss theories of person-environment fit (Lubinski & Benbow, 2000;Nagy, 2006;Swanson & Fouad, 1999), which have already been used in the context of transition from school to university mathematics (e.g. Rach & Heinze, 2017).

Differences Between Mathematics at School and University and Related Students' Difficulties
The starting point for most research concerning the transition from school to university mathematics is students' difficulties during this process. Researchers have investigated those difficulties through various lenses (Gueudet, 2008). Most of them refer to the differences between mathematics at school and at university. These differences involve firstly institutional changes within the new learning environment at university and secondly changes of the learning content, meaning changes in the nature of mathematics and the related tasks as well as required skills. The institutional changes involve a new didactical contract with more autonomy and self-regulated learning for the students (Gueudet, 2008). With regard to the nature of mathematics, two major changes can be identified: the way in which new concepts are presented and the kind of tasks that have to be performed.
In this context, Tall (2008) mentioned three mathematical worlds, which build on one another. The conceptual-embodied world is based on experiences with real-world objects, whereas the proceptual-symbolic world additionally involves thinkable concepts (e.g. numbers). The axiomatic-formal world is based on definitions and proofs. Following Tall (2008), school mathematics is usually located within the conceptualembodied and the proceptual-symbolic worlds, while university mathematics belongs to the axiomatic-formal world. Accordingly, in school, new concepts are based on intuitive understandings and experiences with examples as well as real objects, whereas at university, concepts 1 are introduced through formal and precise definitions. and this new environment, which is very different from school-as illustrated above. In particular, the fit between students' cognitive prerequisites, learning behaviour and the learning environment (especially the requirements of university) determines the students' achievement. The achievement, in turn, determines whether the students meet the university's demands and therefore affects the so-called satisfactoriness. Students' satisfaction is the result of sufficient fit between their interests as well as their attitudes and the learning environment (Lubinski & Benbow, 2000;Swanson & Fouad, 1999). Whereas satisfactoriness reflects the viewpoint of the university (e.g. is he or she a satisfying student, does he or she meet the university's demands), satisfaction reflects the experiences of the student (e.g. is he or she satisfied with his or her studies). Both dimensions, satisfactoriness and satisfaction, are important for a successful transition. In the case of low satisfactoriness, usually indicated by low achievement, the students may have to quit their studies due to university restrictions. This is the case, for example, if a student has finally failed a necessary exam. Low satisfaction can lead to a voluntary decision to drop out. We are aware of the fact that satisfaction and satisfactoriness are not independent in the sense that low satisfaction might influence students' learning and therefore their success in exams as a criterion of satisfactoriness. Furthermore, low achievement can lead to less satisfaction and might lead students to voluntarily drop out.
According to Haak (2017), incongruences between personal characteristics and the environment lead to a personal crisis. For Clark and Lovric (2008), this crisis is even an integral part of the transition from school to university mathematics. Swanson and Fouad (1999) pointed out that this crisis leads to adjustment behaviour, but they did not describe this behaviour in detail. Haak (2017) proposed two possibilities to overcome the crisis: students can either adapt the environment's characteristics or their personal characteristics (e.g. attitudes, learning behaviour). The first means to leave the learning environment by changing the subject or dropping out (Haak, 2017), since students have only little influence on the characteristics of mathematics courses at university. Regarding a possible adaption of personal characteristics, the development of these characteristics during the transition can be even more important for students' success than their characteristics at the beginning of their studies. Indeed, with regard to engineering students, Bengmark, Thunberg and Winberg (2017) found that beliefs measured close to exams are better predictors of success than those measured at the beginning of one's studies. Moreover, Schiefele, Streblow and Brinkmann (2007) reported that students who drop out differ from those who continue their studies, more concerning interest and learning behaviour at the time of the dropout than at the beginning of their studies.

Beliefs
The notion of mathematical beliefs has been of growing interest in mathematics education during the last decades. However, beliefs are not easy to conceptualise which leads to what Pajares (1992) called "a messy construct". We refer to beliefs as "psychologically held understandings, premises, or propositions about the world that are thought to be true" (Philipp, 2007, p. 259). Like many authors, we locate beliefs within the affective domain (Hannula, 2012;McLeod, 1992;Philipp, 2007). This is reasonable since beliefs are crucial for the development of attitudes and emotions towards mathematics (McLeod, 1992). However, beliefs are more cognitive in nature than attitudes and emotions (McLeod, 1992) and can be seen as subjective knowledge (Pehkonen & Pietilä, 2003). The relevance of studying beliefs lies not only in their affective effects but also in their influence on learning behaviour. Schoenfeld (1985) stated that one's beliefs determine how one works on mathematical tasks and how much effort is put into them. Furthermore, beliefs influence which information are learned since they function as a regulation system (Pehkonen & Törner, 1996). Thus, students' beliefs seem to be related to their achievement. Stylianou et al. (2015) found that high-performing students hold more elaborated beliefs about proofs (e.g. "Proofs serve the purpose of not only validating mathematical conjectures, but also of communicating and explaining new ideas" (Stylianou et al., 2015, p. 110)) than lowperforming students.
In this contribution, we will focus on students' beliefs concerning the nature of mathematics. Following Grigutsch and Törner (1998), we distinguish between rather static beliefs and dynamic beliefs. The static beliefs are characterised by the formal and exact structure of mathematics. Mathematics is seen as a coherent system of rules, facts and formulas. Sometimes, these rules and formulas are even experienced as unconnected and mathematics is reduced to a toolbox, while doing mathematics primarily means calculating and using such rules and formulas (e.g. Grigutsch & Törner, 1998;Liljedahl, Rolka & Rösken, 2007). The dynamic beliefs focus more on the development of new mathematical knowledge. This development involves processes which include experimental and inductive activities. Here, mathematics is seen as a creative field of research with applications in other sciences and everyday life. These dynamic beliefs also stress relations between different mathematical objects and statements (Grigutsch & Törner, 1998;Liljedahl et al., 2007).

Beliefs During the Transition from School to University Mathematics
Since the nature of mathematics changes during the transition from school to university, it is not surprising that many students experience a big gap between school and university mathematics (Di Martino & Gregorio, 2019;Hernandez-Martinez, 2016). The experience of this gap can be the result of unfulfilled expectations (Hirst, Meacock & Ralha, 2004) and incongruences between students' established beliefs and the reality they face at university (Andrà, Magnano & Morselli, 2011;Witzke, 2015). Daskalogianni and Simpson (2001) introduced the notion of beliefs overhang, describing students' beliefs that have evolved for a long time during school but are not fitting to university mathematics. In this case, the beliefs are "inappropriate for students' adjustment to advanced mathematics, and result in a problematic move from school to university" (Daskalogianni & Simpson, 2001, p. 99). This leads to the question, which beliefs actually fit to university mathematics and therefore are beneficial during the transition.
From a theoretical point of view, both static and dynamic beliefs can fit to the mathematics students' encounter at German universities. On the one hand, students usually have to work on weekly so-called "task sheets" to gain extra points or the admission for the exams. These sheets mainly include tasks with a focus on proving. Many of these proofs cannot be performed using well-known schemes and algorithms. New ideas (at least from the viewpoint of the students) and creative thinking are necessary. One can argue that students have to undergo a process of proving, which involves failure and dead ends, to solve their tasks and that dynamic beliefs should be beneficial in this case. On the other hand, during lectures, mathematics is presented in a rather static way and appears as a coherent system. Proofs are usually presented in their final version, while the process that lies behind often remains invisible. This is exactly what Hersh (1991) referred to in his distinction between the front and the back of mathematics where "the 'front' of mathematics is mathematics in 'finished' form, as it is presented to the public in classrooms, textbooks, and journals. The 'back' would be mathematics as it appears among working mathematicians, in informal settings, told to one another in an office behind closed doors" (p. 128).
In line with these theoretical considerations, university teachers hold static beliefs as well as dynamic beliefs (Grigutsch & Törner, 1998)-which could be another indicator that both kinds of beliefs fit to university mathematics. Nevertheless, some university teachers clearly articulate that they want their students to hold dynamic rather than static beliefs (Kuklinski et al., 2018), indicating that they consider dynamic beliefs to be advantageous. Furthermore, many supporting programmes and bridging courses aim to increase students' dynamic beliefs (Biehler et al., 2018).
Indeed, dynamic beliefs seem to have a positive influence during the transition, since they positively correlate with interest in mathematics during the first year at university (Kolter, Liebendörfer & Schukajlow, 2016;Liebendörfer & Schukajlow, 2017). Qualitative approaches have raised the hypothesis that static beliefs seem to result in less interest in university mathematics (e.g. Daskalogianni & Simpson, 2002;Liebendörfer & Hochmuth, 2013) and can lead to typical mistakes like not checking the conditions of a theorem before using it for a proof (Liebendörfer & Ostsieker, 2014).
Dynamic beliefs concerning the nature of mathematics often go hand in hand with constructivist beliefs concerning the learning of mathematics, whereas static beliefs correlate with transmissive beliefs of learning (Manderfeld & Siller, 2018), which are considered to be less useful for university mathematics. In addition, students with a rather fragmented (and therefore static) view on mathematics tend to take a surface approach to mathematics learning, which mainly involves memorising and reproduction (Liston & O'Dnoghue, 2009). These students are less successful in exams at university than students with a deep-learning approach (Crawford, Gordon, Nicholas & Prosser, 1994). Geisler and Rolka (2018) found significant differences concerning dynamic beliefs between students who succeeded in their first university exam, those who failed and students who did not even attend their exam. The latter showed the lowest acceptance of dynamic beliefs, while the successful students indicated the highest consent to dynamic beliefs. A similar relation could not be found for static beliefs. According to Baars and Arnold (2014), not attending exams is a useful indicator for dropout.
On the basis of these findings, dynamic beliefs seem to be more beneficial for a successful transition than static beliefs. This seems problematic because most upper secondary students hold static rather than dynamic beliefs concerning the nature of mathematics (Baumert et al., 2000). Geisler and Rolka (2018) found that even mathematics university students as a whole agree more with static beliefs than with dynamic ones. In contrast, Törner and Grigutsch (1994) identified predominantly dynamic beliefs among mathematics freshmen.

Changing Beliefs
Since beliefs are considered to evolve over a long time and remain rather stable (McLeod, 1992;Philipp, 2007), there is a debate between researchers whether and how beliefs can be changed. Assuming that beliefs which do not fit to university mathematics (in the sense of person-environment fit) lead to a personal crisis as well as adjustment behaviour and that this crisis can be overcome by either dropping out or adjusting personal characteristics (Haak, 2017), the question whether beliefs can be changed becomes crucial. Recent studies showed that beliefs can be changed and that the learning environment can play a substantial role for this change. Liljedahl et al. (2007) have used a specially designed university course to shift pre-service elementary school teachers' beliefs from static towards more dynamic ones. Furthermore, changes in attitudes and beliefs of secondary school students have been observed, when entering specially designed learning environments (Liljedahl, 2018). We argue that the changes in the nature of mathematics and the learning environment during the transition may induce change in students' beliefs as well.
Indeed, Kolter et al. (2016) showed that dynamic beliefs held by elementary preservice teachers decreased during the first term at university while their static beliefs increased slightly. In a mathematics course with secondary pre-service teachers, Kuklinski et al. (2018) found no changes in students' dynamic beliefs during the first term at university and only a weak decrease of their consent to static beliefs, but here, increasing students' dynamic beliefs was a clearly stated goal of the university teacher. However, it remains uncertain whether these results can be transferred to a traditional mathematics course with pre-service upper secondary teachers and mathematics majors.

Research Questions and Hypothesis
Our guiding research interest lies in the question which beliefs "fit" to the mathematics and learning environment that students encounter when entering university and which beliefs are therefore beneficial during the transition. In particular, we are looking at: i. the connection between students' beliefs and different criteria of success and ii. the change of students' beliefs during the transition. This leads to the following sets of research questions:

Connection Between Beliefs and Success
In which way can beliefs concerning the nature of mathematics predict students' dropout-intention and their achievement in the exam at the end of the semester? Are students' beliefs in the middle of the term better predictors of the dropoutintention and the achievement than the beliefs at the beginning of the term?
In line with theories of person-environment fit, we expect students' beliefs to predict both, dropout intention (as a criterion for low satisfaction) and the achievement in the exam (as a criterion for satisfactoriness). Since dynamic beliefs appear to be more beneficial during the transition (e.g. Crawford et al., 1994;Geisler & Rolka, 2018), we believe that static beliefs will be a negative predictor of the achievement in the exam (H1) while dynamic beliefs will positively predict the exam outcome (H2). Regarding dropout intention, we assume the opposite relations: static beliefs will be a positive predictor of dropout intention (H3) while dynamic beliefs will be negatively related to dropout intention (H4).
As described before, an insufficient fit between students' personal characteristics-in our case, their beliefs-and the learning environment will lead to adjustment behaviour (Swanson & Fouad, 1999). Students can react by changing the environment (which means to change subject or drop out from university) or they can adapt their own characteristics (in our case, their beliefs) (Haak, 2017). We argue that the outcome of this adjustment process is more relevant for students' achievement and dropout intention than their beliefs at the beginning of their studies. This leads to the hypothesis that students' beliefs in the middle of the term will be stronger predictors of the achievement in the exam and the dropout intention than their beliefs at the beginning of the term (H5). This hypothesis is supported by recent studies (e.g. Bengmark et al., 2017;Schiefele et al., 2007).

Change of Beliefs During the Transition
Recent studies have shown that students' beliefs can change within the first year at university (Kolter et al., 2016). However, we argue that in order to better understand students' problems during the transition, it is of great interest to find out whether there are differences in this development between rather successful and unsuccessful students. This leads to the questions: How do students' beliefs concerning the nature of mathematics change during the first weeks at university? Are there differences in this change between students who succeed in their exam at the end of the semester and those who fail or between students with and without dropout-intention?
Due to the fact that recent studies provided inconsistent results (e.g. Kuklinski et al., 2018;Kolter et al., 2016), we have no special hypothesis concerning the overall development of students' beliefs during the first term, but since beliefs are rather stable, we expect only small or medium effects. To the best of our knowledge, there is currently no quantitative study examining differences in the development of beliefs between different groups of university students during the transition from school to university. Therefore, the research questions posed under ii) are rather explorative. However, we assume that beliefs of successful students will undergo changes in a more beneficial way (e.g. increasing dynamic beliefs, decreasing static beliefs) than beliefs of unsuccessful students.

Design and Instruments
We used paper and pencil questionnaires during the real analysis lecture in the first week of the winter term (T1) and 8 weeks later (T2) to access students' beliefs concerning the nature of mathematics. Demographic data (gender, age, school leaving marks) was also included at T1. Since students can rarely be aware of their intention to drop out during the first week at university, their dropout intention was only captured by the second questionnaire (T2). The timing was carefully chosen: on the one hand, we did not want to measure dropout intention too early since we wanted the students to give a realistic assessment. On the other hand, our experiences over the past years show that many students decide to drop out during the winter break around Christmas. That is why we decided to hand out the second questionnaire in mid-December, which falls within the middle of the term. The instruments used in the questionnaires can be found in Table 1.

Sample
Our sample consists of freshmen at a large public university in Germany. The students are enrolled in the bachelor (pure mathematics) or teacher education programme for upper secondary school and attended the course real analysis. A total of 226 students participated in the first questionnaire in the first week of the term. One hundred thirtyone students filled out the second questionnaire in the middle of the term. We could match N = 104 students (54.7% male, M(age) = 19.5, SD = 2.2) who participated in both questionnaires. We only used data of those for our analysis. Sixty-two of these students (60%) also attended the real analysis exam at the end of the term.

Preliminary Analysis
Only the data from students who participated in both questionnaires were used to assess the reliabilities and factorial structures of the used instruments. All instruments have at least sufficient reliabilities, except the static beliefs scale. We eliminated the item "Fundamental to All items had to be answered on a 5-point Likert scale, where 1 indicated totally disagree and 5 totally agree mathematics is its logical rigor and preciseness" which increased reliability from 0.55 to 0.66 (T1) or, respectively from 0.69 to 0.72 (T2). An explorative factor analysis (varimax rotation) with the number of factors set to two confirmed the factorial structure of the beliefs scale. All items have factor loadings > 0.5 with cross-loadings < 0.3 except the previously mentioned item "Fundamental to mathematics is its logical rigor and preciseness", which has no high loadings on either factor (0.36 and − 0.08).
Since we only used the data from those students who participated in both questionnaires (T1 and T2), we wanted to know whether those students differ from the group which only participated in the first questionnaire. We therefore used a multivariate analysis of variance (MANOVA) to compare the students' school leaving marks (German Abiturnote) and their beliefs at the beginning of the term (T1). The results can be found in Table 2.
School leaving marks between 1 (very good) and 4 (sufficient); answers to beliefs scales between 1 (totally disagree) and 5 (totally agree) The MANOVA revealed significant differences between students who participated only in the first questionnaire and those who filled out both questionnaires (F(3, 209) = 4.78, p < 0.01, η 2 = 0.06). In particular, students who participated in both questionnaires have better school leaving marks (F(1, 211) = 3.61, p < 0.01, η 2 = 0.05) and show a higher acceptance of dynamic beliefs (F(1, 211) = 1.98, p < 0.01, η 2 = 0.03) than those who participated only in the first one. We therefore assume that students who were included in our analysis have to be seen as positively selected. However, according to Cohen (1988), these effects are rather small. Furthermore, we checked whether students enrolled in a teacher education programme and bachelor students differ concerning their beliefs and school examination marks. We conducted a MANOVA including all students who participated in both questionnaires. The results can be found in Table 3. Students enrolled in a teacher education programme reported slightly higher acceptance of static beliefs and lower acceptance of dynamic beliefs than bachelor students at the beginning of their studies. However, only the differences concerning static beliefs are significant (F(1, 96) = 6.02, p < 0.05, η 2 = 0.06). In the middle of the term, no relevant differences between both groups of students can be identified.
School leaving marks between 1 (very good) and 4 (sufficient); answers to beliefs scales between 1 (totally disagree) and 5 (totally agree)

Connection Between Beliefs and Success
We used hierarchical linear regressions (method inclusion) to assess the connection between students' beliefs and their achievement in the exam as well as their dropout intention. Model 1 only consists of students' school leaving marks. Model 2 consists of the beliefs at T1, while the school leaving marks are still controlled. In model 3, the beliefs at T2 were added. Since we expected significant correlations between students' beliefs at the beginning and the middle of the term, we screened for multicollinearity of the independent variables included in the models. For all performed regressions, multicollinearity was no problem (VIF > 0.4; tolerance < 2.2). Table 4 summarises the results of the linear regression to predict students' achievement in the analysis exam (method inclusion). All four models significantly explain the achievement (p < 0.001). Model 1 shows that students' school leaving marks can explain 26% of the variance in the exam achievement (R 2 = 0.26; β = − 0.51; p < 0.001)-they remain a significant predictor in all four models. The inclusion of the beliefs at T1 (model 2) increases the explained variance significantly (ΔR 2 = 0.08; p < 0.05), indicating that the static beliefs are a negative predictor of the exam outcome (β = − 0.24; p < 0.05). In model 3, the beliefs at T2 are added (ΔR 2 = 0.13; p < 0.01). The static beliefs at T2 turn out to be a negative predictor (β = − 0.51; p < 0.01), while the static beliefs at T1 have no predictive power anymore. Model 3 can explain 47% of the variance in the exam outcome. However, dynamic beliefs do not significantly predict the exam achievement. Thus, (H1) can be confirmed and (H2) has to be refuted. The results of the hierarchical linear regression (method: inclusion) to predict students' dropout intention can be found in Table 5. The first two models, consisting of the school leaving marks (model 1) and additionally the beliefs assessed at T1 (model 2), cannot significantly explain students' dropout intention (R 2 = 0.02 respectively 0.06). In line with this global analysis of the two models, neither the school leaving marks nor the beliefs at T1 are significant predictors. Adding students' beliefs in the middle of the term increases the explained variance significantly to 24% (ΔR 2 = 0.18; p < 0.001) (H5) and reveals that the dynamic beliefs are a negative predictor of dropout intention (β = − 0.53; p < 0.001), confirming H4. We find no significant effect of the static beliefs, which refutes H3. Table 6 shows means and standard deviations of students' beliefs at both measurement points T1 and T2:

Change of Beliefs During the Transition
We used independent t tests to compare all students' beliefs at the beginning of the winter term and in the middle of the term. The t tests reveal a significant decrease of dynamic beliefs (t = 7.8, p < 0.001, d = 0.77), while the static beliefs remain nearly constant (t = − 1.83, p = 0.07). To enable more differentiated insights into the development of the beliefs, we distinguished between students who succeeded in their real analysis exam (more than 50 out of 100 points) and those who failed. Furthermore, we distinguished between students without dropout intention (M < 3) and with dropout intention (M ≥ 3). ANOVAs with repeated measures were used to check whether the development of beliefs differs between students who succeeded in the real analysis exam and those who failed. Concerning the static beliefs (Diagram 1(left side)), the ANOVA reveals a significant mean effect of the time (F(1, 60) = 5.87; p < 0.05; η 2 = 0.09) and the exam achievement (F(1, 60) = 10.08; p < 0.01; η 2 = 0.14) as well as a significant interaction time*exam achievement (F(1, 60) = 5.39; p < 0.05; η 2 = 0.08). The acceptance of static beliefs increases for students who failed in their exam, while students who succeeded show no change.
With regard to dynamic beliefs, we find no differences in the development between students who were successful in the exam and those who failed (Diagram 1(right side)). Both groups of students report decreasing consent to dynamic beliefs. Consequently, the ANOVA only shows a significant main effect of the time (F(1, 60) = 42.55; p < 0.001; η 2 = 0.42) but neither a significant mean effect of the exam achievement (F(1, 60) = 2.7; p > 0.1; η 2 = 0.04) nor a significant interaction time*exam achievement (F(1, 60) = 0.4; p > 0.5; η 2 = 0.01). We compared the development of beliefs between students with and without dropout intention by using ANOVAs. For static beliefs (Diagram 2(left side)), we see a significant main effect of the dropout intention (F(1, 102) = 5.77; p < 0.05; η 2 = 0.05). The main effect of the time (F(1, 102) = 3.01; p > 0.1; η 2 = 0.03) and the interaction time*dropout intention are not significant (F(1, 102) = 0.04; p > 0.5; η 2 = 0.00). Thus, there is no significant difference in the development of static beliefs in both groups.
The development of the dynamic beliefs differs between students with dropout intention and those who did not think about quitting their studies of mathematics (Diagram 2(right side)) with a significant main effect of the time (F(1, 101) = 92.38; p < 0.001; η 2 = 0.48) and dropout intention (F(1, 101) = 18.23; p < 0.001; η 2 = 0.15) as well as a significant interaction time*dropout intention (F(1, 101) = 20.15; p < 0.001; η 2 = 0.17). Both groups of students report decreasing consent to dynamic beliefs, but this decrease is considerably stronger for students with dropout intention.

Discussion
According to theories of person-environment fit, the fit of students' personal characteristics and the characteristics of the university influences satisfaction and satisfactoriness. In this study, we focused on students' beliefs concerning the nature of mathematics. As expected, students' beliefs are related to their exam achievement (as a criterion for satisfactoriness) and their dropout intention (as a criterion for low satisfaction).
Static beliefs go along with lower exam achievement, which is in line with the results of Crawford et al. (1994). Liebendörfer and Ostsieker (2014) have hypothesised that static beliefs can lead to typical mistakes in exams (e.g. using theorems without checking the necessary conditions). Moreover, static beliefs are often connected with a surface approach to mathematics learning (Crawford et al., 1994). Even if-theoretically-static beliefs fit to the way mathematics is presented during lectures, it seems that static beliefs are not beneficial during the transition. Therefore, keeping ones' static beliefs can be viewed as a form of beliefs overhang (in the sense of Daskalogianni & Simpson, 2001). While many previous quantitative studies focused on students' achievement (e.g. Crawford et al., 1994;Rach & Heinze, 2017), we took into account students' dropout intention as well. We found a strong negative relation between students' dynamic beliefs and dropout intention. This is in line with our previous findings that students who do not attend their exams-according to Baars and Arnold (2014) an indicator for dropout-show lower acceptance of dynamic beliefs (Geisler & Rolka, 2018).
The beliefs measured in the middle of the term turn out to be stronger predictors than those measured at the beginning of the term, which supports our hypothesis that the outcome of the development during the transition is more important than students' personal characteristics at the beginning of their studies.
In line with previous studies (Burton & Ramist, 2001;Rach & Heinze, 2017), the school leaving marks are a strong predictor of the exam achievement-in this case the most significant one in all models we tested. In contrast, the school leaving marks have no significant effect on students' dropout intention. This is clearly in line with theories of person-environment fit, which suggest that cognitive prerequisites mainly affect satisfactoriness but not satisfaction.
With regard to the development of students' beliefs, previous studies have reported inconsistent results (e.g. Kolter et al., 2016;Kuklinski et al., 2018). Our results show that dynamic beliefs decrease during the first term at university, which supports the findings of Kolter et al. (2016). Overall, the static beliefs remain rather stable in the whole sample. One might expect that students enrolled in the teacher education programme and those enrolled in the bachelor programme differ concerning their beliefs. We found only small differences with regard to static beliefs. Bachelor students start their studies with slightly less consent to static beliefs and report a moderate growth of their consent. However, decreasing dynamic beliefs are prevalent in both groups of students.
In contrast to previous studies that only examined the development of beliefs in a whole sample, our results enable a more differentiated perspective by comparing the development of successful and rather unsuccessful students: The decrease of dynamic beliefs is significantly smaller for students without dropout intention than for those who thought about quitting their studies. Students who succeeded in their exam report nearly constant static beliefs, whereas unsuccessful students indicated even increasing consent to static beliefs. It seems that successful students start their studies of mathematics with rather beneficial beliefs and do not undergo substantial changes concerning their beliefs, whereas less successful students already begin their studies with rather disadvantageous beliefs and undergo changes to even less beneficial ones. This conclusion holds for both criteria of a successful transition: the exam achievement and the dropout intention. In both cases, unsuccessful students change their beliefs into a direction that turned out to be disadvantageous. With respect to Haak (2017)-who supposed that students can overcome the crisis which emerges from incongruences between characteristics of themselves and the learning environment by adjusting their characteristicswe find no hints of functional adjustments. Instead, the changes in students' beliefs have to be seen as dysfunctional. The question remains in which way a functional adjustment is possible.

Limitations and Strengths
As stated above, students whose data we analysed seem to be positively selected. We therefore argue that those students, who were excluded from the analysis because they only participated in the first questionnaire, might have undergone an even less beneficial development of beliefs during the transition than those who failed their exam and/ or indicated that they thought about dropping out. However, further investigations are necessary to confirm this hypothesis. Besides, our results rely on self-reports and the questionnaires had to be filled in during lectures. Students who do not regularly attend the lectures are not captured by our study.
Another limitation of the study lies in the small sample that only consists of students from one university. Our findings might therefore reflect local peculiarities: all students in our sample attended real analysis and linear algebra during their first term. At some other German universities, students enrolled in a teacher education programme attend only linear algebra during the first term. Moreover, in some other countries (e.g. the USA), linear algebra and real analysis are advanced courses, while freshmen usually attend calculus courses at the beginning of their university studies.
A strength of our study lies in the distinction between successful and unsuccessful students while investigating the changes in their beliefs during the transition from school to university. We found clear evidence that the changes differ between these groups of students and that unsuccessful students undergo a less beneficial change of beliefs. In line with theories of person-environment fit, we focused on objective criteria (exam achievement) and subjective criteria (dropout intention) of success in the transition to gain a more comprehensive picture of the role that students' beliefs play in this phase.

Conclusion and Outlook
All in all, we found evidence that dynamic beliefs are beneficial for a successful transition from school to university mathematics while static beliefs seem to be disadvantageous. Furthermore, our results indicate that dynamic beliefs decrease during the first term at university whereas static beliefs remain rather stable.
These results have some implications for teaching at university. When planning undergraduate courses, especially for freshmen, lecturers should try to foster students' dynamic beliefs. Since traditional lectures tend to draw a rather static picture of mathematics, the way in which mathematics is presented in the lectures could be reconsidered. Instead of showing the front of mathematics (in the sense of Hersh, 1991), students should be invited to the back: For example, some shorter proofs could be developed together with the students during lectures in order to highlight the dynamic character of mathematics and to strengthen students' dynamic beliefs. In order to structure this collaborative proving process, lecturers might build on Pólya's (1957) four steps to mathematical problem solving: understanding the problem, devising a plan, carrying out the plan and looking back. Especially understanding the problem and devising a plan-those steps that carry students to the front of mathematics-but also looking back are usually absent in traditional German mathematics lectures (Rach, Siebert & Heinze, 2016). However, some universities have introduced lectures with collaborative proving and problem solving activities as well as bridging courses that try to foster students' dynamic beliefs (Biehler et al., 2018;Kuklinski et al., 2018).
Furthermore, tasks should be created in a way that allows insightful experiences of success. Such moments of "illumination," how Liljedahl (2005) calls it, can shift students' beliefs towards more dynamic ones.
Finally, further investigations are required to clarify why even dynamic beliefs of successful students decrease during the transition. Using a qualitative approach may gain deeper insights.
Funding Information Open access funding provided by Projekt DEAL.
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.


extfieldsofstudy: Psychology Medicine

text:
RISK AND PREVENTIVE FACTORS FOR TRAFFIC ACCIDENTS: ANALYSIS OF CHILDREN’S PERCEPTION USING THE EDUTHERAPEUTIC METHOD

ABSTRACT Objective: To describe children’s perception of risk and preventive factors related to traffic accidents using the Edutherapeutic Method. Methods: This is a qualitative descriptive study carried out with 173 students from public schools aged seven to 14 years in Lagarto, Sergipe, Brazil. Data were collected in the second half of 2014. The first stage consisted of an activity with drawing/writing sheets in all classes selected by the Nursing undergraduate students. Next, the children answered a questionnaire on sociodemographic data. The qualitative analysis of the expressive language of the children’s drawings generated two categories: positive and negative factors for the prevention of traffic accidents and their subcategories. Results: The children’s perception regarding preventive and risk factors for traffic accidents was considered adequate according to other studies found in the literature on the same subject. The drawings and descriptions were used later to provide the students with a better understanding of these factors. Conclusions: The study lends support to educational activities and interventions about prevention with schoolchildren. This is one of the main goals proposed by Brazil in the National Plan of Action for Road Traffic Safety for the decade 2011-2020.

INTRODUCTION
Traffic accidents are responsible for a high number of victims and represent a major public health problem. However, this topic is neglected by governments and the general population. 1 According to the Global Status Report on Road Safety, traffic accidents cause more than 1.3 million deaths and 20-50 million injuries each year, resulting in a huge impact on the health and development of the country. 2 Faced with this problem, the United Nations General Assembly has declared the 2011-2020 period as the Decade of Action for Road Safety, aimed at reducing the number of road deaths by 50% and saving about five million lives. 3 After five years, 88 countries have reduced the number of road fatalities. Nevertheless, there is still deep and persistent concern about countries that have increased the number of fatalities over the same period.
The worldwide number of road deaths remains high (1.25 million deaths per year), with the greatest incidence in low-income countries, such as Brazil, which, according to the National Mortality Information System (SIM), had a total of 38,265 deaths resulting from traffic accidents in 2016. 4,5 In 2014, 4,665 accidental deaths of children and adolescents aged zero to 14 years were reported in Brazil -traffic accidents were the main cause, accounting for 38% of fatalities. 6 Thus, preventing traffic accidents is an ongoing challenge and should, therefore, be taken seriously. 7 Childhood must be understood as an autonomous social category, as it has its own dynamics within society. Time and space are fundamental for discoveries and a healthy life. However, when associating the physical, perceptual, cognitive, social, and attitudinal conditions of children in the current urban space, we realize how vulnerable they are to the risks of traffic accidents. 8 The statistical data on traffic safety for children are worrying, and it is necessary to adopt educational strategies for accident prevention. Traffic education is a pedagogical process that aims to shape and transform the attitudes of human beings toward a collective and healthy life, seeking to improve the quality of life through responsible behaviors in order to reduce these events. 8 Drawings and graphic symbols are some of the first forms of spontaneous communication used by children. Thus, this study adopted the Edutherapeutic Method, a technical-educational, psychopedagogical, and therapeutic tool developed by Rodrigues, in Portugal 9 , which is suitable for children with specific educational and health needs. This line of research has been conducted in Portugal and has allowed the assessment of perceived health and its interventions. 9,10 By using drawings as a research tool, the present study aimed to describe children's perception of risk and preventive factors related to traffic accidents using the Edutherapeutic Method. Children are expected to have reasonable knowledge about risk and preventive factors for traffic accidents, especially regarding the use of safety devices, traffic lights, and crosswalks.

METHOD
This is a qualitative descriptive study that analyzed the expressive language of children's drawings. This analysis is known as the Edutherapeutic Method, which investigates the informative and recreational power through drawing/writing/ image, joining children's cognitive and emotional blocks, as well as facilitating interaction between children, educators, and health professionals. 10 The data collection instrument was an adapted drawing/ writing sheet 9 distributed to a total of 173 children attending the 3 rd , 4 th , and 5 th grades of elementary school from two public schools in the city of Lagarto, Sergipe, Brazil, in 2014. Lagarto is the most populous municipality in the inland of Sergipe and the third largest in the state, with an estimated population of 103,576 inhabitants 11 and a total of 12,430 cars, that is, one car for every eight inhabitants. 12 With the increasing number of vehicles traveling on urban roads, the city and its population face mobility challenges and problems found in other Brazilian cities, including limited public transport (which was implemented in the city of Lagarto in 2016), excess vehicles, and the resulting congestion of roads and disrespect for pedestrians.
The schools were selected by simple randomization in the site random.org. At the end of the process, six classrooms were chosen, with a total of 173 students. This total was defined by convenience, as the sample is non-probabilistic. The study population consists of 89 boys and 84 girls, aged 7 to 14 years (with two 7-year-old children attending the 3 rd grade). Despite the age group evaluated, we did not differentiate between the information collected from children and adolescents because the criterion chosen by this study was the random selection of classrooms and not age.
We emphasize that children participate in school activities related to traffic education every year, during the week dedicated to this theme, since article 76 of the New Brazilian Traffic Code states that traffic education should be promoted in preschool, elementary school, and high school. The month selected for the national road safety week is September, when most Brazilian schools address the issue in the classroom. The questionnaire was administered one month after this event.
The inclusion criteria to participate in the research were: knowing how to read and write; completely and legibly complete the drawing/writing sheet. There were no exclusion criteria.
The drawing/writing sheet was distributed, and the questionnaire composed of closed questions was administered by previously trained undergraduate Nursing students from Universidade Federal de Sergipe (UFS), located in Lagarto, Sergipe. The activity took place in the same classrooms the students attended, and they had 30 minutes to finish.
The drawing/writing sheet was divided into four areas: two at the top, in which the children made drawings of actions that prevent and cause traffic accidents; and two at the bottom, where they wrote the message related to their drawings. We underline that the analysis only considered the written content, and the researcher did not perform a psychodynamic analysis of the drawing. The themes expressed were classified and ranked according to priority areas for reducing the risk of traffic accidents, according to the Brazilian Traffic Code (Código de Trânsito Brasileiro -CTB), 13 based on the analysis of the drawings and the evaluation of four experts in the field, selected for their experience in health education for children and traffic education.
After transcribing the data into a Word document, we used the Content Analysis proposed by Bardin. 14 This analysis involves classifying topics relevant to the research question and the student's oral/written production, allowing us to define a priori and a posteriori analytical categories. Categorization is a fundamental aspect of content analysis and consists of a back and forth assessment between the theory and the material under analysis, which usually leads to various developments and reworkings of the material until the analytical categories are defined. 14 In this process, the record units were coded to allow only gender identification; for example, in the code "F38m," "F" means drawing/writing sheet; the number 38 is the subject's interview order; and "m" corresponds to male. Although some drawings allow an immediate interpretation, we adopted the strategy indicated by the literature -double-code reading (drawing and writing) -, valuing the meaning the child attributes to their drawing, expressed in writing. 15 The research was authorized by the Secretariat of Education of Sergipe, the administration of the schools, and the Research Ethics Committee (REC) of UFS, since it involves human beings, under opinion No. 298,534, respecting all ethical-legal requirements, as per Resolution No. 466/12, especially those regarding the consent of the children's parents and the involvement of teachers.
After analyzing the expressive language of the children's drawings, the following thematic categories and subcategories emerged: • Positive factors for the prevention of traffic accidents according to children's perception: preventive driver behavior, preventive pedestrian behavior, preventive behavior of all road users, road signs, engineering, and proper traffic enforcement. • Risk factors for accidents according to children's perception: risky driving behavior, motorcyclist risk behavior, pedestrian and cyclist risk behavior, lack of road signs, and inadequate traffic enforcement. Table 2 presents the preventive factors for traffic accidents perceived by the children based on the analysis of their drawings. In this category, children show the importance of preventive behavior in road traffic, be it by wearing a seat belt or by not consuming alcohol while driving, and mention that these behaviors must be adopted not only by the driver but also by the pedestrian who should cross the street on the crosswalk after looking both ways. Traffic behaviors that belong to all road users include respecting road signs and traffic lights, paying full attention to the surroundings. Table 3 shows the children's perception of negative factors for the prevention of traffic accidents based on the analysis of their drawings. The children were very clear when demonstrating risk behaviors, such as high speed, disregard for road   signs, drinking while driving, and even risky maneuvers performed by drivers. With respect to risk behavior, pedestrians and cyclists were shown displaying the behavior of many children in traffic, who run between cars and ride bikes holding onto a moving vehicle. However, the children's perception goes beyond road users, as they also point out the lack of road signs and adequate traffic enforcement.

DISCUSSION
The results provide support for educational activities and interventions about prevention aimed at schoolchildren, which is one of the goals proposed by Brazil to the United Nations (UN) in the Life in Traffic Project regarding the National Plan of Action for Road Traffic Safety for the decade 2011-2020. This plan was a worldwide agreement to reduce the number of traffic accident deaths. 3 In it, the Brazilian initiative addresses surveillance, prevention of road traffic injuries and deaths, and health promotion. 16 When analyzing the children's drawing/writing sheets on accident prevention factors, the emphasis was placed on preventive driver behavior, also known as defensive or safe driving, which is considered the best way to drive and behave in traffic. This driving style allows the individual to recognize dangerous situations in advance and predict what may happen to their passengers, their vehicle, and/or other road users. 17 Among the preventive behaviors, children highlighted speed control to avoid accidents, as well as the importance of using protective equipment, such as seat belts. Studies show that driving at high speed is one of the behaviors that jeopardize traffic safety and that measures, such as seat belt use, have been taken to prevent accidents or reduce possible injuries when they occur. 18,19 A new characteristic related to preventive driver behavior is the prohibition of alcohol consumption while driving. This is one of the main protective factors for the prevention of traffic accidents. 20 Alcohol consumption while driving has been reported as the cause of 30% of all traffic accidents and approximately 70% of those resulting in severe or fatal injuries. 21 Regarding pedestrians, the participating children mentioned the importance of crossing the street at the crosswalk and looking both ways before and while crossing, ( Table 2). Half of all traffic deaths worldwide occur among the most vulnerable road users: motorcyclists (23%), pedestrians (22%), and cyclists (4%). In 2015, the number of pedestrian deaths in Brazil reached 4.6/100 thousand inhabitants, 2 and the attention given to the needs of these people, who represent 49% of all road traffic deaths worldwide, has been insufficient.
At present, the answer given to traffic problems is focused on changing the behavior of all road users, so it is necessary to understand the main determinants and risk factors for aggressive traffic: drivers whose behavior is inappropriate and undesirable; inattentive pedestrians or those who disobey road signs; neglectful, poor, careless, and pointless surveillance; inadequate, bumpy, poorly designed, poorly marked, and poorly lit roads and streets; and vehicles deemed unsafe for traffic. 22 Once the various factors that lead to aggressive traffic are understood, it will be possible to devise strategies for its prevention. 23 Participants demonstrated the relevance of road signs for accident prevention, as well as the need for traffic enforcement and investment in traffic engineering to make traffic faster, safer, and more efficient. 24 On the other hand, one of the main problems is the drivers' lack of attention to road signs, which causes a great number of accidents. 24 The change in behavior of road users is directly related to enforcement, which must be regular and proficient, but remains inefficient and in need of improvement. 25 Risk factors are related to human factors (people's behaviors and actions); road-environmental features (related to the surrounding road or environment); vehicles (their design or mechanical failure); institutional characteristics (laws, method of enforcement, and investment in transportation and safety); and socioeconomic aspects. 26 The main factors involving the driver are: haste, alcohol consumption, speeding, neglect, recklessness, disregard for road signs, impatience, and inability to manage risk. 27 Some drawings and phrases produced by the participants addressed the fact that driving under the influence of alcohol was prohibited. This behavior is considered one of the main causes of traffic accidents for reducing the ability to react appropriately to stimuli (reflexes), decreasing peripheral vision, changing body control, increasing aggression, and causing sleepiness and drunkenness. Alcohol affects all tissues and has a significant impact on the nervous system. 28 The CBT Brazilian Traffic Code amendments, through Law No. 12,760/2012, propose penalties to the individuals driving with any alcohol concentration per liter of blood or alveolar air 29 . However, 60.3% of drivers have not yet changed their behavior after the introduction of this new law. 28 Concerning motorcyclists, the students described the very dangerous maneuver of balancing the motorcycle on one wheel in their drawings. In Article 175, the CTB considers the use of a vehicle to demonstrate or perform dangerous maneuvering, such as sudden jerking, skidding, or braking with tire sliding or dragging, a serious violation. 30 14. Bardin L. Análise de conteúdo. Lisboa: Edições 70; 2011.
As to cyclists, one risk attitude highlighted by the children was holding onto a moving vehicle. Bicycle accidents are not very prominent as a cause of death, but it is important to emphasize that cyclists should be considered more vulnerable than other drivers. 8 Accidents involving cyclists are related to the use of the bicycle for leisure activities or to cycle to school, lack of bike lanes, poor road conditions, lack of recreational areas, ignorance of laws, lack of balance, underestimation of risks, and lack of protective equipment. 8 Finally, this study identified that children have an adequate perception of preventive and risk factors for traffic accidents. Thus, this study reached its objective: analyze the expressive language of drawings, using a drawing/writing sheet, and identify the preventive and risk factors for traffic accidents perceived by the child.
The data collection instrument revealed its technical-educational and research potential, facilitating the interaction between educators, health professionals, children, and technical-educational tools, which are useful for planning and implementing actions, even with the limitation regarding the follow-up period of the study, given that the students were not monitored in the subsequent months to ascertain the long-term influence of the educational activity. Therefore, it is important to expand the use of the method in Brazil and incorporate it in public health policies in schools, training professionals involved in health care and child education, to promote appropriate traffic behavior.
The set of thematic axes found in this research contributes to preventive educational practices related to traffic accidents, aimed at children in school environments, representing one of the principal goals proposed by Brazil, according to the National Plan of Action for Road Traffic Safety for the decade 2011-2020. There was no difficulty in implementing the method in the Brazilian context. Adopting this method is essential to promote preventive traffic education for children. We believe that the method can be used in new educational contexts, allowing immersion in the local culture, while creating a space for dialog and learning.

Funding
This study did not receive funding.


extfieldsofstudy: Physics Psychology

text:
MOOC Student Learning Analytics For Automotive Technology Programme In Vocational College

This study aims to study the analysis of how students learning and see what they do in their Massive Open Online Course in the learning of Automotive Technology Course at Technical and Vocational Education Training institutions. This study used analytics tools, data and reports as part of an educational endeavor. At the beginning of each learning session, all students will be able to participate in this course. The participation of students enrolled in this large-scale course makes it challenging to help students individually achieve their learning objectives. Through the analytical features offered by the MOOC platform, it has made it easier for course coordinators and educators to view student learning activities in the online supplementary restraint system (SRS) course conducted through the MOOC. The findings of student learning analytics found that there are several types of learners and the tendency to follow learning by competency unit in online learning using open learning. Therefore, in this study, the analytical assessment of TVET student learning is used in achieving TVET course learning objectives. The use of learning analysis among TVET students can be used to observe interest and achievement in each unit of competency and identify students at risk during their learning process by analyzing student engagement on the page. By analyzing these interactions, learning analytics has the potential to provide predictive insights about future challenges. These predictions are used to evaluate the adaptability of the content presentation and improve the performance of the learning TVET MOOC process in the future.

Introduction
These days, big data and data analytics are both hot topics in the world of technical and vocational education [1]. Big Data is an explosion of information in tandem with the growth of the mobile device use the ecosystem with fast processing capabilities, high-speed Internet access, and mature data storage technology. The development of the Big Data phenomenon is also closely related to the production of a different variety, in large volumes and at high velocities of data. It can drive the growth of innovations to educator [2] and provide opportunities for educational institutions [3], industry and government agencies to improve the quality of services, otherwise introducing new services that have never appeared before. Big data analytics consists of the process of examining, cleaning, changing, and modeling data to find useful information for making decisions. Here, big data analytics can be seen as a support application in supporting a decision through the information generated [4]. This is because the information acts as evidence of something involved in the decision to make. Big data analytics is also a combination of skills in the use of information technology techniques, such as appropriate programming languages, to analyze data and art in understanding the resulting information. Also, it can be formulated and translated into visual forms that can help the user make a decision.
The previous student learning analytics research has generally analyzed the effects of learning by providing results from collecting and analyzing the data that affect learning. However, there are several studies on the types of analysis of student learning that are commonly performed in the elearning environment [5] and the types of learning behavior data that are useful for students and teachers [6]. However, these data are only for public education institutions, and there is very little data on student learning analytics students for technical and vocational education institutions (TVET) especially for automotive technology programs. This study aims to explore vocational student learning styles and learning activities that can be used in data analysis learning to measure student literacy [7] in Supplementary Restain System (SRS) and system diagnostics tools. Specific research questions are as follows: 1) What are the types of students in a technical and vocational education training (TVET) student online learning the course? 2) What competencies and content appear most often in student learning, which determines their online learning?, and 3) What are the learning activities that better explained and predicted the students' learning outcomes?. The results of this study are expected to provide significant guidelines in the research on learning analytics such as vocational student learning instructional design [8], analytics modeling, and Improve MOOC dashboard adequately evaluated by target users [9].

Overview
Learner interactions in the online education environment such as logging for virtual learning management systems [10] leave many of our media use or digital traces containing information including individual interests, social groups, behaviors, and location. This huge amount of aggregate data that is sourced from as many students as possible is known as Education Data Mining (EDM). The International Education Data Mining Association states that EDM [11] is an emerging discipline, concerned with developing methods for exploring the unique and increasingly large-scale data that come from educational settings and using those methods to better understand learners and the settings which they learn in [12]. Some agreed that EDM is a new discipline based on the Data Mining (DM) grounds. It means that the baseline is composed of models, tasks, methods, and algorithms. A researcher may want to explore data to find out descriptive patterns and predictions that characterize learners' behaviors and achievements. Moreover, domain knowledge content, assessments, educational functionalities, and applications [13]. The collection, measurement, analysis and reporting of data about learners and their contexts, for purposes of discovering patterns, understanding and optimizing learning and the environments in which it occurs is known as Learning Analytics [14][15].

Educational Data Mining in Technical And Vocational Education Training (TVET)
In Malaysia, to empower and improve TVET, a big record data will be developed by all ministries on the TVET empowerment cabinet committee. This data is expected to assist in the collection of data on demand from the industry to plan labor market [16], employment projections or to focus on critical areas. The participation of these various government agencies is expected to expand and empower TVET campaigns at the national level while providing TVET standing with other professional fields. Analytical data on student learning for general courses, niche courses, and long-life learning courses are readily available as most universities and educational institutions offer these courses online. Online service course providers should provide services accessible to all students by ensuring access to these services using all types of devices, easy-to-find, and accessible databases, and recommend content relevant to individual needs based on learning pattern analysis [17].

Student Learning Analytics
Student learning analytics in Technical and Vocational Education Training (TVET) related to educational data mining is the process of measuring, collecting, analyzing, and reporting on data about students and learners [18]. Once analyzed, the data can help course coordinator and subject matter expert better understand learning and optimize the teaching environment accordingly [19]. The intelligent data provided from learning analytics can help predict and advise on the behaviour of TVET students [20], either in an entire class or individually. The ultimate goal is to use the real-time data provided by learning analytics to encourage better teaching and learning and lead to more positive outcomes [21].

Method
To evaluate the analytical learning of vocational students, a MOOC for SRS courses was developed using the Design and Development Research (DDR) process [22]. This MOOC has been through the analysis phase up to the evaluation phase according to the ADDIE approach [23]. The design of this study was to invite all students using letters to educational institutions, email, and social media. Students are informed that the course will be held from May to the end of November. The Supplementary Restraint System (SRS) online course through this MOOC is a free course offered to all students. Once the course begins, students of all ages, from different locations, educational institutions, academic backgrounds, economic backgrounds and socio-cultural backgrounds, can all learn together in this course [24] through connectivism [25]. Student learning through MOOCs in the classroom or in workshops can be done using a desktop computer, phone or tablet but easier by using m-learning [26]. The course coordinator and the instructor will find out how many students have enrolled in the course, enrollment date, completion date, comment, and kudos.
Throughout the course, over 24 weeks, course coordinators and teachers can access data on student learning activities by looking at the student administrator icon. The MOOC platform will display all information about students individually [27]. An analysis is a process of adding acumen to data using algorithms. It is based on a set of mathematical and statistical algorithms known as machine learning techniques.

Figure 1. MOOC Learning Outcomes review process
This course is to look at the achievement of students' knowledge through the cognitive domain, students' practical skills through the psychomotor domain, and students' attitude and value skills [7] while operating the SRS on vehicles. Learning outcomes of students aspired by the course coordinator and subject matter expert will be included in the analysis until the course evaluation stage.  Figure 2. MOOC course quality criteria The next MOOC content review process is to review whether it meets the criteria or does not meet the features set by the Openlearning.com design team. Among the criteria required in reliable MOOC are high-quality learning outcomes, module, learning activities, content, and resources. Any content and module that has exceeded the specified criteria will be marked as achieved, and if it does not exceed the specified criteria will be marked as not achieved. The instruments and modules used in this study comply with National Occupational Skills Standard (NOSS) face-to-face learning modules issued by the Department of Skills Malaysia (DSD) and Vocational College Standard Curriculum (KSKV). This document has been prepared according to competency units so that students can more easily follow the learning process [28].

Results
This study indicates that there are several types of students in technical and vocational education training (TVET) who attend online SRS courses, as in MOOC [29]. These groups of students have accomplished all learning activities and undergone a few domains in the content standard, which are knowledge, applied skills, and attitude. Their accomplishment has explained the learning outcomes sets earlier.
They are which content standard is the student most interested in learning, which of the following knowledge, applied skills, and attitude is the standard of learning that most students complete and which are learning activities that can explain the course learning outcomes of the students that are obtained correctly [30].

Type of TVET student in Online Learning
There are five types of students identified in this online course based on the Phil classification [31].

Figure 3. MOOC Lurkers student
Lurkers student is a person who lurks inside MOOC but does not participate [32]. However, they do not carry any kind assessments of knowledge assessments or practical work assessments that have been included in the MOOC by the course coordinator or subject matter expert, as shown in figure 3.  Figure 4 shows active students are students who plan to take courses through the MOOC; they attended lectures from the beginning of the study to the last session, completed homework, interacted with other students, and completed all assessment forms. The highest number of students in this group received certificates because they had completed the course [33]. Passive participants are students who use every course material, watch lecture videos, complete all the quizzes, and participate in homework and course projects provided by teachers or subject matter experts. However, they do not interact with students or peers or with the other partner. There is no interaction was occurred that shown in figure 5.

Figure 6. MOOC non-completers student
Non-completers student is a group of students who cannot complete online learning [34]. The majority of students tend to fall into this category. Figure 6 shows that they have access to MOOCs course material to help them learn and succeed in the course. Mostly, the student tries to use the resources of the course but is unable to complete the entire course. In the Observer students category, they enrolled for the course. They signed in and explored the course competency unit. However, observer students, as shown in figure 7, do not carry out any kind of assessment other than viewing the video of the activities contained in the content of the study [35].

Figure 8. Student Progress Overview
This MOOC platform provides an overview of student progress shows in figure 8. The coordinator or subject matter expert can observe several things, such as the date of this class starts, and the current cohort of students. Another is the type of student enrollment for the free or paid class, the number of students who have participated in this course, the number of comments in this class, and the frequency of activity done in this course.

Figure 9. Students in the class
The coordinator or subject matter expert observe student's involvement in the class whether the student is a lurker student, active student, non-active student, non-completer student and observer student by looking at the course completed as shown in figure 9. The MOOC platform also provides the convenience of emailing selected students. The reminder will include the student's progress bar and a link back to the course so that they can continue with the activities.  Figure 10 shows the next features that facilitate the coordinator or subject matter expert in the MOOC platform that provides an analysis of student learning daily. Throughout the month, admin can observe student engagement data and the usage patterns of the developed SRS MOOC.

Figure 11. Student Comments Over Time
The course coordinator and subject matter expert can view analytical analysis for comments and questions found during the class, as shown in figure 11. The MOOC platform also provides a likes view of each comment posted.  figure 12, tells pages that are always accessible to MOOC students/users. Learning habits of vocational students while using MOOC can be seen. From the course description to the last learning activity, the SRS installation guide indicates which course coordinator and subject matter expert competency most students have access to, as well as the percentage of students viewing pages that have been developed. They also can observe the percentage of students who have completed the page developed and the number of comments uploaded on each page that has been developed.

Standard competencies and content appear often
There are six competencies in the course offered to students throughout the course from the beginning to the end of the semester The findings in table 1 show that most students are more likely to be interested in learning in competency three, where 34.32% of the total MOOC students have seen this competency. Competency 1 shows that 35.70% of students have completed, which remarks 1344 comments.

Student learning activities
There are two discussion rooms, knowledge assessment, practical assessment and problem solving provided by the course coordinator and subject matter expert for students to complete during the course. Each activity represents student learning outcomes within the National Occupational Skills Standard (NOSS). 105 The findings show that most students are more likely to solve the problems in this MOOC of 32.59%. The practical assessment shows that 34.07% of students have completed practical assessment through MOOCs and comments made by students during knowledge assessment on learning activity of 228 comments were shown in table 2. Student learning tools used in this study still do not have additional mechanisms or questionnaires to provide students' general background characteristics, socioeconomic status, ethnicity, computer or mobile devices literacy, and so forth [36].

Discussion
This study aimed to explore student learning analytic analysis of vocational students participating in online learning activities through MOOC. Therefore, the purpose is to answer the following questions: 1. What competencies and content appear most often in student learning, which determines their online learning? 2. What are the learning activities that better explained and predicted the students' learning outcomes?
The findings confirm that the most common learning competency related to the student learning concept of the supplemental restraint system is the setup scan tool, of which 35.70% of the students completed the competency. Next is the second most frequently used learning competency for students is the SRS airbag scan tool, with a percentage of students who have completed the competency of 34.32%. The third most frequently used learning competency of the students is 33.16%, which replaces the impact sensor. The fourth learning competency that most students complete is the third learning competency replace airbag module & clock spring. The second most competent student completed was the seat belt & pre-tensioner competency of 33.02%, and the lowest student competency was the sixth competency, which provided 31.27% SRS diagnostic installation & report.
Another interesting topic for discussion in the analytical exploration of student learning is the relationship between MOOC design and students' most accessible pages. Based on expert consensus results, the complete course description should be provided to the user so that it is easy to get all the information about the course followed by the highest percentage seen by 91.60%, viewed by 1545 users, and received 658 user comments. In this study, the pages that most students did not see were the Course Coordinator, where only 13.33% saw who the supervisor was and the instructor who taught in the course. In a nutshell, the pages that were interested most among users in this MOOC are service tool page (SRS) with 40.74% of users completed, 39.75% of students completed, 599 views, and 458 comments. Meanwhile, the page least viewed by students is preparing scan tools with only 29.38% viewers, 38.52% of students completed, 137 views and 205 comments. Students may be less likely to view this page because they are familiar with the automotive scan tool in other courses.
Among the two discussion rooms provided to students, the alpha discussion room recorded a student percentage of 28.89%. One of the factors that contributed to the high number of students viewed is that the alpha discussion room. It is designed to produce graphs and text that are more userfriendly during the learning process using MOOC compared to the beta discussion room that uses text only. Between knowledge assessment and practical assessment, the number most viewed by students is the knowledge assessment that has shown an increase of 1.23% from the practical assessment, and the number of students completed showing knowledge assessment has shown a decrease of 2.71% from the assessment of skills.

Conclusion
This study has highlighted that student analytics learning analysis examining data obtained from the supplementary restraint system (SRS) courses implemented through the Massive Open Course (MOOC). It has provided feedback to course coordinators or instructors and may change their teaching style in the classroom or during the workshop. This student's learning data is derived from courses conducted through an analytical process to systematically evaluated assessments from beginning to end. Analytical learning provides some opportunities for students to study in vocational education that can improve content and course quality. It also reduces dropout rates and increases students' performance, to identify and promote success factors, as well as to understand students' pathways leading to skills competency and alocate costs efficiently, which in future work we will take into consideration more indicators.