“Literally I Grew Up” Secondary–Tertiary Transition in Mathematics for Engineering Students beyond the Purely Cognitive Aspects

1.1 Critical Requirements for a Successful Transition

Overall, numerous models have been used to describe transition and clarify transition issues. Cheng et al. (2015) describes how all models address three different shocks (academic, social, emotional) that mathematics students undergo when entering higher education. In their qualitative study on critical requirements for a successful transition from student perspective, Trautwein and Bosse (2017) describe four different dimensions, Personal, Organizational, Content-related, and Social, that cover a range of needs students have to handle to make the secondary–tertiary transition. The four dimensions find their counterparts in the shocks (academic, social, emotional) addressed by the models depicted by Cheng et al. (2015). Underlying the academic shock are the critical requirements from the organizational dimension (e.g., coping with the quality of teaching and supervision; dealing with assessment conditions) and the content-related dimension (e.g., meeting curricular demands and pace of the courses). The critical requirements from the personal dimension are responsible for the emotional shock (e.g., balancing areas of life; managing the workload; coping with pressure to perform). The social shock finds its counterpart in the social dimension (e.g., building peer relationships; collaborating in teams or interacting with academic staff).

In line with international studies, Heubeil (2014) shows that dropout rates in mathematics and mathematics-related subjects are significantly higher than in other subjects. This has led to focus empirical research on transition problems in mathematics-related subjects mainly on the cognitive challenges and shocks arising from the nature of the discipline (e.g., Gómez-Chacón, Griese, Rösken-Winter, & Gónzalez-Guillén, 2015). The way of presenting mathematics at university is in a dense, formal, and systematic structure known as “definition-theorem-proof” (Nardi, 2008). Mathematical rigor increased abstract formalism instead of descriptiveness, and mathematical proof instead of performing calculations often poses problems to students (Gueudet, 2008). These problems are all related to the content-related dimension and contribute to the transition problem. Even though various methods of teaching mathematics using new approaches were developed in the last years, there seem to be indications that not much happened after all in practice (e.g., Melhuish, Fukawa-Connelly, Dawkins, Woods, & Weber, 2022). Moreover, even if the “student centered learning” is recognized as the “new paradigm,” it seems to be a lot left to be done when applying the methods in practice (e.g., Woods & Weber, 2020).

Students’ first encounters at the university level can be considered in respect of the differences between the university and the school as educational institutions (Winsløw & Grønbæk, 2014), that is, the organizational dimension. The design of the learning process and the quality of teaching and teaching styles differ from those in schools (Clark & Lovric, 2009). This implies a need for students to become autonomous learners: “acquisition of a certain level of autonomy in learning is often seen by university teachers as the main stumbling block in the secondary tertiary passage” (De Guzmàn et al., 1998, p. 751). The strategies successfully applied to school mathematics often do not help for university studies where the teaching is more impersonal (e.g. Pampaka, Williams, & Hutcheson, 2012) and the supervision ratio is less favorable. As a result, students may not receive sufficient support from instructors when experiencing difficulties that are expected with the increased workload and academic standard (Trautwein & Bosse, 2017).

The transition to university is often accompanied by a move to a new city or to one’s own apartment. As a result, the social environment in which students are situated also changes. The cohort size and the class climate at university (e.g. constantly changing classmates) differ from that at school, making it more difficult to establish strong social ties. The social shock needs to be resolved in the entry phase of the study period so that students can find their place in the new social environment. In a study with mathematics students in Sweden, Stadler, Bengmark, Thunberg, and Winberg (2013) found that as students progressed in their studies, they became less dependent on the teacher and increasingly built their knowledge with the help of other materials and especially their peers. In addition, social inclusion contributes to students’ identity formation, stress management, and improved academic performance (Stadtfeld, Vörös, Elmer, Boda, & Raabe, 2019). The above issues clearly show how important the social integration of students is for their academic success.

All of the above challenges have an impact on students’ feelings and emotions. For this reason, some researchers “attempted to integrate both models [socio-institutional and psychological-individual] by using psychological factors, for example, to explain the integration of students into the academic and social environment of higher education” (Hüther & Krücken, 2018, p. 187). The change in the organization of learning and teaching style may cause students to become overwhelmed with the demands and the new required working attitude (Trautwein & Bosse, 2017). The student–lecturer interactions are less personal comparing with upper secondary school and students can feel left alone and unsupported in the learning process. The lack of connectedness with peers further reinforces this tendency and can affect student’s psychological and socio-emotional wellbeing (Hughes, 2016). Already burdened by difficulties and failures, the unclear role of mathematics for the career path often hinders motivation and creates negative emotions on students’ side (Bergsten & Jablonka, 2015), which ultimately promotes poor academic performance and high drop-out rates.

The four dimensions (personal, organizational, content-related, and social) proposed by Trautwein and Bosse (2017) are thus also well founded from a theoretical perspective and are well suited as a starting point for empirical investigations. In the present study, we concentrate on the issues beyond the purely cognitive aspects. Based on a questionnaire, to identify common challenges and difficulties, as well as differences, an international comparison of the transition problem at three European mid-sized universities is carried out. We ask: What dimension(s) beyond the purely cognitive aspects influences the secondary–tertiary transition in mathematics for first year engineering students?

2.1 Participants

In total, 499 first year students from three European universities took part in the courses where the questionnaire was handed out. However, 191 students (39%) were excluded from the sample since they were not engineering students (e.g., prospective teachers) or due to incomplete data. This left a final sample of 308 participants for the subsequent analyses. Participants were distributed across the different countries as follows: 36 (12%) from Germany (DE), 170 (55%) from Sweden (SE), and 102 (33%) from Turkiye (TR). Sixty-six percent of participants were male (M), 33% were female (F), and 1% did not indicate their gender. Most students took the course during their first semester, but 40 of the Turkish students took the course during their second semester and 3 students from Germany took it during their second or third semester.

The German university is an institution located in the south of Bavaria. The engineering program offered is mainly computer science. The second university is a Swedish university offering a large spectrum of engineering programs on Bachelor/Master level. The third university that is part of the study is an institution located in the Anatolian region of Turkiye. It has a strong engineering program that consists of civil, industrial, computer, electric–electronic, and mechanical. In-depth mathematics courses are mandatory for the engineering students in the first semesters in all three universities. The institutions are consider mid-size universities in their specific countries.

2.2 Instrument

A questionnaire with 16 items was designed to collect information about possible transition difficulties from upper secondary school to university. Participants received the survey electronically through their emails by invitation and were asked to fill in the survey anonymously and voluntarily. The survey consists of four parts with three Likert-type questions for each part and four open-ended questions. We asked open-ended questions to be able to delve deep into the topic and give students an option of free-form answers. The data coding and analysis were carried out using the Dedoose software and IBM SPSS Statistics 27. The analysis of the external non-responses showed no systematic patterns with respect to central background variables. The analysis of internal non-responses showed no pattern indicating threats to validity in the items used.

In their qualitative study on critical requirements for a successful transition from student perspective, Trautwein and Bosse (2017) discovered 32 critical requirements that can be classified into four different dimensions (see Table 1). The requirements written boldface are carefully addressed in our questionnaire and the ones written in regular style are only partially addressed. The requirements written in italics are left out due to GDPR (the General Data Protection Regulation) rules or not applicable to our study.

2.3 Focus in this Study

In the present study, we focus on the part of the questionnaire that can be categorized according to the Trautwein and Bosse’s (2017) personal, organizational, and social dimensions (see Table 1) and that are linked to the beyond cognitive aspects of the transition. The students were asked to assess the degree of social integration, motivation, interest, inspiration, eagerness, confidence, success, and stress when making the transition from school to university. All these characteristics can be related to the personal dimension and its requirements. The students were also asked about having problems dealing with their time in a responsible and meaningful way and if the time they spend on their studies has increased at university. Other items that can be related to the personal dimension and the specific requirements include: the pace of study at university compared with upper secondary school, and the requirements of managing the studies.

The questions that can be related to the organizational dimension, and the specific requirements presented above, are focused on the level of support from teachers concerning learning strategies, the feedback the students get from their teachers, the level of the teachers’ expectations, the quality of the lectures at university, and the requirements of managing the studies.

The questions related to the social dimension are focused on the degree of easiness in socializing with other students, the degree of difficulty in collaborating with other students, the degree of wellbeing of students, having different classmates on different courses, and the degree of being well integrated in the student clubs.

2.4 Analysis Procedure

The study is a mixed-method design, using a “sequential exploratory design” (Robson & McCartan, 2017), containing different phases of data analyses. The open-ended questions were analyzed using qualitative content analysis (e.g., Bryman, 2004). A priori categories from Trautwein and Bosse (2017) guided the qualitative content analysis. IBM SPSS Statistics 27 was used to analyze the data statistically.

Since it is not possible to measure different aspects of the secondary–tertiary transition using one single item, two composite measures were constructed. First, we used factor analysis to extract relevant items related to personal dimension and organizational dimension respectively. We theoretically analyzed the components, and based on our analysis, we decided to collapse components 2 and 3 (see Table 2). In the next step of the analysis, we used the two composite measures to explore students’ expressed emotions regarding critical difficulties and requirements of transition assigned to content-related and social dimensions.

In the first composite measure “Coping, balancing and managing workload,” the following five items were used: the pace of study, the level of difficulty, the teacher’s expectations, increasing time on studies, and requirements of managing studies. In the second composite measure “Support, feedback and quality of teaching,” three items were used: the quality of lectures, support from teachers concerning learning strategies, and feedback from teachers. When exploring the dimensionality using Principal Component Analysis, we can see that the first composite measure explains 49% of the variance and the second 57% of the variance. Then, we controlled the two dimensions using multiple correspondence model (see Figure 1). Based on the model summary, we decided to use the composite measures, even though the reliability statistics are below lower bound (see, e.g., Peterson, 1994).

Figure 1

Model summary of multiple correspondence model.

1. Ethical considerations: The study underwent ethical reviews at the involved universities. The following long and proven tradition of intervention research in the education sector was followed. All the relevant national regulations, institutional policies, in accordance the tenets of the Helsinki Declaration, have been followed. The study has been approved by the authors institutional review board or equivalent committee at each university. The participating researchers did not process any sensitive personal data and the study in itself was not a major intervention in the participants’ lives. The study was based on voluntary participation (the participants were free to opt in or out of the study at any point in time), informed consent (participants knew the purpose, benefits, and risks before they agree or decline to join), and anonymity (the identities of the participants was not known and personally identifiable data was not collected).

3.1 Results from Analysis of Open-Ended Questions

Looking into the responses to open-ended questions may be the bridge to understand the personal, social, and organizational dimensions in more depth. The analysis shows that students’ struggle balancing the different areas of life, coping with the formal regulations and the quality of teaching. Several students point to the aspects of adulthood: “literally I grew up” writes one of the Turkish male (TRM) students, and a Swedish female (SEF) student express: “I feel that a little extra self-discipline is required, otherwise it only works if you put in the time required”. The aspects of loneliness are underscored by some students, here an excerpt from a German male (DEM) student:

In the first semester, it is basically already a very big change from school to university for me. You have to invest a lot more time because you only know a few people who can help you or with whom you can review certain content. Overall, it is very difficult for me to get started, especially in such demanding lectures like Lin Alg 1, because I am very much on my own.

Students also highlight the importance of building peer relationships, as a male student from Sweden said, “haven’t really got any study group which is sad. Sits mostly alone in studies but it would be good to have someone to brainstorm ideas with.” Students mentioned the importance of collaborating in teams and having more space to interact with academic staff, as one Turkish student said, “It was more difficult to ask questions to teachers in upper secondary school. On the other hand, teachers at university are insisting us to ask questions” (TRF). On the contrary, a student from Sweden said “almost no contact with the teacher at all. Gets more boring and less motivating when you have no personal contact in my opinion” (SEM).

When it comes to coping with social climate of university, a Swedish student said, “At the university, there is a much larger community and even though Corona has been affected so we cannot hang out with so many, you still get to know each other in a different way than in upper secondary school.” One female and one male Turkish students also highlight the opportunities that universities provide, respectively, “university has many more socializing options and different groups of people. It’s easier to find groups of friends” (TRF) and “we have more opportunities to socialize at the university. People are more social and mature” (TRM). Another Turkish student added their views from a different perspective, “there was a friendlier atmosphere in upper secondary school, but we cannot find this at university. At university it is more like a workplace. When you make a mistake, there is absolutely no return.”

We also see students’ struggling with how to handle the course offer. As one of the Turkish female students describe: “Our lessons are harder and we need more social life. It is very difficult to have both a social life and academic life and I do not know how to manage it.” Also, students from Germany and Sweden outline similar experiences:

The way you study is completely different from upper secondary school because I have much more personal responsibility and there is no support to seek from the teachers now, as in the same way as upper secondary school (SEF).

The biggest difference between upper secondary school (or, Adult Education in my case), is that at university there is less time with lectures/reviews than at upper secondary school, and consequently less time with the teacher. Learning at the university is more dependent on being able to study for knowledge in course literature and online, in upper secondary school you get, as I said above, much more oral teaching (SEF).

It sucks not understanding things right away and then sometimes you have doubts about your own competence and intelligence (DEM).

One of the organizational aspects that differ between the universities is if the tutoring is held in the main language or not. In the Turkish university, the lectures are held in English:

While English is already a difficult language, trying to learn all these math terms can take time. Like in upper secondary school, at university our aim is not only to pass the class, but able to use what we have learned in professional life and for that, we must work harder. Unfortunately, it can be difficult to know this and work accordingly (TRF).

There are also many students that are pleased with the situation. They put forward both the quality of teaching: “We had a higher degree of quality in the lectures than in upper secondary school. Very good and well-planned lectures” (SEF), and some of them highlight the importance of good study environment: “Much nicer work environment from both teachers and other students. Nice study places at the university as well” (SEM).

5.1 Limitations

The data collection was during the COVID-19 lock down. We know that the COVID-19 has had an impact on all of students and teachers (Nilsberth, Liljekvist, Olin-Scheller, Samuelsson, & Hallquist, 2021; Teke-Lloyd, Türk, & Bengü, 2022). We cannot overrule its importance regarding crucial parts in the transition problems, i.e., the shocks (academic, social, emotional) addressed by the models depicted by Cheng et al. (2015). There were differences in how the universities handled remote teaching. How the situation (COVID-19) affected the transition is not examined in this study.