This article investigates the extent to which undergraduates consistently use a single mechanism as a basis for classifying mathematical objects. We argue that the concept image/concept definition distinction focuses on whether students use an accepted definition but does not necessarily capture the more basic notion that there should be a fixed basis for classification. We examine students’ classifications of real sequences before and after exposure to definitions of increasing and decreasing; we develop an abductive plausible explanations method to estimate the consistency within the participants’ responses and suggest that this provides evidence that many students may lack what we call concept consistency
