A study of creative reasoning opportunities in assessments in undergraduate calculus courses

In this article we present the findings of a research study which investigated the opportunities for creative reasoning (CR) made available to first year undergraduate students in assessments. We compared three first year calculus courses across two Irish universities using Lithner’s framework. This framework sets apart imitative reasoning (IR) (analogous to rote learning and mimicry of algorithms) and CR (which includes plausible mathematically-founded arguments). We report on the differences between reasoning opportunities in specialist and non-specialist courses and compare our findings with those of other similar projects. In addition, we will provide a critical reflection on Lithner’s framework as a method for classifying tasks in calculus courses and suggest a modification.