The selection and orchestration of resources by first year students to study mathematics
First year students at Eindhoven University of Technology study obligatory courses in mathematics, such as Calculus (approximately 1800 students) and Linear Algebra (approximately 120 students). A survey was carried out by Birgit Pepin (4TU.CEE leader at TU/e) and researcher Zeger-Jan Kok to find out how first-year mathematics/engineering students have selected and used digital, traditional, social and general resources for their learning of these subjects. The survey provides insight in study behavior of students and helps in designing blended learning environments in an informed way.
Mixed methods study
Calculus and Linear Algebra courses increasingly use a blended approach in which digital and traditional resources are made available to the students (so-called curriculum resources; Pepin & Gueudet, 2018). In addition, it was suggested that students might use, for example, their peers as a resource (so-called human or social resources) and resources on the internet (general resources). The question remains which resources students select from the ones on offer, and for which purpose? Which resources do they consider the most important to study mathematics? Are there groups of students who show similarities in this respect? Questions like these are relevant to understand the study behavior of students and to design blended learning environments in an informed way.
Birgit Pepin and Zeger-Jan Kock interviewed focus groups of students and administered a survey to investigate how first-year mathematics/engineering students at TU/e have selected and used resources for their learning of Calculus (at three different levels, A, B and C) and Linear Algebra. They also investigated retrospectively the resources students used at school. As resources they considered everything that helped students develop their mathematics practice (Adler, 2000). That could be a textbook or a digital homework system, but also a conversation with a peer or a tutor.
Focus group interviews
Results from the interviews showed that in high school, students often relied on traditional resources. The most important of this was the mathematics textbook, but past exam papers and, in some cases, the teacher were also important. At university, these resources remained important for many, but at the same time student practices changed, in particular for the large Calculus course. This was possibly due to the plethora of resources available, which led to many students developing (and having to develop) their own sequencing and orchestration of resources. The interviews showed several individual actual student study paths, in which different kinds of resources were included (e.g. peers; curriculum; own identified). However, this varied between the Calculus and the Linear Algebra courses, in the sense that in the Linear Algebra course (approximately 120 students) the students could relatively easily follow the designed learning trajectory (planned by the course leader), with the relevant resources lined up accordingly. At the same time, for the large Calculus courses (in total approximately 1800 students) students could not easily identify clear learning trajectories, with the large number of resources associated with this course. Neither could they completely fall back onto their ‘default’ position from high school; to do all exercises on offer was not an option. They had to find their own ways of managing the large number of learning supports on offer for passing their examinations. Hence, the type of course and its organization had an influence on students’ selection and use of resources.
Student survey
In the survey there were items on the frequency of use, and on the relative importance of particular resources. Among others, we used statistical methods to look for groups of students (clusters) across the university courses, who had similar ideas regarding the relative importance of resources.
With respect to high school, the survey results were in line with the interviews. With respect to university, we found differences among the Calculus and Linear Algebra courses. For example, students of Linear Algebra found the collaboration with other students in class an important resource. This can be understood in terms of the organization of the course, where the Linear Algebra tutorial sessions depended on this type of collaboration. Regarding the importance of resources, we found three groups of students across the courses: Group one, the smallest, considered the explanations by the lecturer the most important resource. Also, at high school they attached more importance to teacher explanations than students in the other groups. The second group consisted of students who found the textbook the most important resource. The third and largest group consisted of students who considered other materials, such as the lecture notes, past examinations, worked examples, and the digital homework environment the most important resources. An example for Calculus B is shown in figure 1.
Figure 1. Importance of resources versus frequency of use; Calculus B, first group (left) and third group (right).
To some extent these results are in line with the idea of different actual student study paths. Comparison of one lecturer’s Calculus class in two consecutive years showed that there were shifts in both the perceived relative importance and reported frequency of the use of particular resources.
Potential implications
In terms of implications for practice, we suggest that lecturers need to consider actual student study paths for their course design, in particular when a large number of resources are offered as a matter of course (but not aligned with particular learning paths). Students might need to be taught how to develop their own successful learning paths aligned with the relevant resources, in order to grow with and finally enjoy their mathematics experiences at university.
More information
If you are interested to know more about this study, please contact:
Zeger-Jan Kock: z.d.q.p.kock@tue.nl
Birgit Pepin: b.e.u.pepin@tue.nl