Supporting transition to university mathematics: Evaluating an online course

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In this post, Dr Richard Gratwick and his colleagues share an evaluation of an online course in the School of Mathematics, which widens access to university mathematics and had positive outcomes for the students enrolled. This post is part of September-October’s Learning and Teaching Enhancement theme: Innovation in Science Teaching.

For eighteen months, we have all been rapidly developing online versions of our courses, pushing us beyond our comfort zones in an already stressful world. Few of us have been able to stop and evaluate our approaches to teaching online. Here, I  summarise a recently published article, co-authored with George Kinnear and Anna Wood, which evaluates a (pre-pandemic) online course. This research was funded by a PTAS project, “Supporting Transition to University Mathematics with Blended Learning”.

In 2018-2019, George Kinnear and I first delivered the course Fundamentals of Algebra and Calculus (“FAC”) for the School of Mathematics. The course was introduced to provide better support for incoming students with a range of mathematical backgrounds, in particular those students with entry qualifications below those of most of their peers (thus constituting a Widening Participation initiative). It was delivered (almost entirely) online.

The course material is all accessed through the STACK computer-aided assessment system. Within this, students work through short blocks of expository text, worked examples, interactive diagrams, and concise video clips, all embedded within a sequence of exercises and questions. The course design draws on a variety of ideas and evidence from cognitive science and education research.

We evaluated the course with both qualitative and quantitative methods, drawing on three cohorts of students (2018-2020 entry). We considered what impact the course had on students’ performance in mathematics, and students’ experiences of and responses to the course design.

Using our School’s Diagnostic Test as a pre- and post-test gave the most striking outcome: FAC seems to eliminate an apparent attainment gap. On entry, the FAC cohort performed on average 14 percentage points lower than their peers. After the course, this discrepancy was eradicated, with FAC and non-FAC students performing alike. So in this sense, the course appears to have had exactly the desired effect.

Interviews with students gave us valuable qualitative data. Most students found the course beneficial and would recommend it to others. Some, however, raised difficulties related to the design of the course which chime now with what we hear more generally about experiences of online teaching during the pandemic.

Students perceived the course to have a high workload. This led some to adopt a strategic approach to the course (“gaming the system”), working through material only to gain the marks. Some students became frustrated with the high marks required to progress through the material. On the other hand, this same grading system seemed to promote good study habits, with students taking greater care and pursuing deeper understanding. The online delivery left some students feeling isolated. But many appreciated the flexibility of studying online, allowing them to study at times and places of their choice. This particularly benefitted students with personal situations that would otherwise have limited their ability to engage with their studies.

None of these findings is overtly discipline-specific, or relevant only to undergraduate teaching. The educational principles behind the course design, and the student responses to their implementation, are relevant to any discipline in which a course might be delivered (almost) wholly online. This, we have of course now learned, is every discipline.

The full article ‘Designing and evaluating an online course to support transition to university mathematics’ can be found here:

Richard Gratwick

Richard is a Lecturer and Deputy Director of Teaching in the School of Mathematics, and a Fellow of the Higher Education Academy. In the 2018 EUSA Teaching Awards, he won the van Heyningen Award for Best Teaching in the College of Science and Engineering.

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