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.
History
School
Science
Department
Mathematics Education Centre
Citation
ALCOCK, L. and SIMPSON, A., 2011. Classification and concept consistency. Canadian Journal of Science, Mathematics and Technology Education, 11 (2), pp. 91-106