The Calculus Concept Inventory–Measurement of the Effect of Teaching Methodology in Mathematics

The CCI has undergone extensive development and validation, funded by the National Science Foundation (Epstein and Yang [4]).It was developed by a panel of respected calculus educators and a consultant, nationally known for development and validation of standardized tests.The test shows good performance characteristics (see below) and exposes exactly what the FCI in physics showed.From the fall semester of 2006 through the fall semester of 2008, the test was given to approximately 5,000 students at test sites with many traditional programs as well as programs using alternative teaching methodologies.Test sites were in colleges and universities in the United States and about fifteen other countries.Comparison of gain from two widely divergent methodologies then becomes possible and is discussed in this paper.This paper also discusses the development and validation process in some detail.Those interested in using the test should contact this author (Epstein, email addresses in the footnote on the first page of this article).While this paper was being prepared, additional requests for the test have come in, typically one or two per week, but results received after 2006 are not included in this paper.All the more recent results seem to follow the pattern described below.The CCI is the second in an anticipated series of Basic Conceptual Understanding instruments for various levels in mathematics (including high school and earlier) that can hopefully serve to provide a scientific basis for discussions about teaching methodology and curricula.The first is the Basic Skills Diagnostic Test (BSDT), which has already been used quite widely nationally.We are currently seeking funding for an Elementary Algebra Concept Inventory.