Comparative judgement as a learning tool in university mathematics

Students’ views of benefits and drawbacks

Abstract

Comparative judgement (CJ) draws on the idea that it is easier to judge which of two objects weighs more, than to judge the weight of one object. In education, CJ can be used to rank students’ responses to a task, as an alternative to assessing each response due to marking rubrics. Research has shown rankings made by students to be valid and reliable, and hence possible to use as a base for summative assessment. Moreover, research has indicated that assessment by CJ can serve as a learning activity for students, i.e., enhance students’ learning.

This paper reports from an exercise in a calculus course, where the students judged each other’s responses by CJ. One of the purposes of the exercise was to explore whether the CJ-process would provide a learning opportunity for the students. The exercise was compulsory, but the results did not count towards their final grade. First, the students were required to respond to the conceptual task “How would you describe the derivative?” Their one-page responses were uploaded to the web engine No More Marking(NMM). NMM randomly selects pairings of responses, where students by a mouse click should judge which response shows the best understanding of the derivative. Each student should fulfil at least 11 such pairwise judgements.

The research data contain students’ responses to the task (N = 64), output from NMM based on students’ judgements (N = 61), and student interviews (N = 5). However, the results of this paper are based mainly on data generated by the five interviewees. Excerpts from the interviews support that CJ can improve students’ learning. Despite this, output from NMM shows the interviewees spent rather short time on their judgements. This ambiguity reveals the question of whether active participation in CJ can improve students’ learning still needs further exploration.