Designing and evaluating an online course to support transition to university mathematics

Abstract

We describe the design and evaluation of an innovative course for beginning undergraduate mathematics students. The course is delivered almost entirely online, making extensive use of computer-aided assessment to provide students with practice problems. We outline various ideas from education research that informed the design of the course, and describe how these are put into practice. We present quantitative evaluation of the impact on students' subsequent performance (N = 1401), as well as qualitative analysis of interviews with a sample of 14 students who took the course. We find evidence that the course has helped to reduce an attainment gap among incoming students, and suggest that the design ideas could be applied more widely to other courses.

Comparing example generation with classification in the learning of new mathematics concepts

“…The single most common incorrect answer for each part was an integer (typically "1"). This is consistent with student reports of 'gaming the system' that emerged in interviews with students about the course (Kinnear, Wood, et al, 2021, section 4.2.2), suggesting that students were not sure how to answer and were submitting a trivial response in order to see the solution. Only one student gave a correct answer to G1c on their first attempt: 16…”

“…The concepts of increasing/decreasing sequences and boundedness of sequences were the targets of the intervention, so that the classification task used by Alcock and Simpson (2017) could be used as one of the initial learning tasks. The experiment took place in an authentic teaching context: an online course offered to incoming undergraduate students (Kinnear, Wood, et al, 2021), where students work through a series of online quizzes that combine exposition with exercises . The experimental tasks were embedded in the existing course materials, during week 9 of 10, when the topic of sequences is covered in the course.…”

“…Finally, there were two classification tasks on the target concepts in the final assessment of the week (FarC1 and FarC2). Students' scores in the final assessment contributed to their overall grade for the course (as detailed in Kinnear, Wood, et al, 2021).…”

A Collaboratively-Derived Research Agenda for E-assessment in Undergraduate Mathematics

“…Another course design decision concerns the frequency and timing of e-assessment. For instance, some courses make extensive use of e-assessment with weekly (or even more frequent) tasks for students to complete (e.g., Kinnear et al, 2021;Heck et al, in press). Question 30 invites a comparison of different approaches, such as between the use of shorter more frequent e-assessments throughout a course, and fewer e-assessments (e.g., at the end of substantial topics).…”

A collaboratively-derived research agenda for e-assessment in university mathematics

“…Another course design decision is about the frequency and timing of e-assessment. For instance, some courses make extensive use of e-assessment with weekly (or even more frequent) tasks for students to complete (e.g., Kinnear et al, 2021;Heck et al, 2022). Question 30 invites a comparison of different approaches, such as between the use of shorter more frequent e-assessments throughout a course, and fewer e-assessments (e.g.…”