By Spencer Bagley, University of Northern Colorado; Jim Gleason, University of Alabama; Lisa Rice, Arkansas State University; Matt Thomas, Ithaca College, Diana White, Contributing Editor, University of Colorado Denver
(Note: Authors are listed alphabetically; all authors contributed equally to the preparation of this blog entry.)
Concept inventories have emerged over the past two decades as one way to measure conceptual understanding in STEM disciplines, with the Calculus Concept Inventory (CCI), developed by Epstein and colleagues (Epstein, 2007, 2013), being one of the primary instruments developed in the area of differential calculus. The CCI is a criterion-referenced instrument, measuring classroom normalized gains, which specifically is the change in the class average divided by the possible change in the class average. Its goal was to evaluate the impact of teaching techniques on conceptual learning of differential calculus.
While the CCI represents a good start toward measuring calculus understanding, recent studies point out some significant issues with the instrument. This is concerning, given that there seems to be an increased use of the instrument in formal and informal studies and assessment. For example, in a recent special issue of PRIMUS (Maxson & Szaniszlo, 2015a, 2015b) related to flipped classrooms in mathematics, three of the five papers dealing with calculus cited and used the CCI. In this blog we provide an overview of concept inventories, discuss the CCI, outline some problems we found, and suggest future needs for high-quality conceptual measures of calculus understanding.