This project designs, develops, pilots, and validates a test, the Calculus Concept Inventory (CCI), that measures conceptual understanding of the few most basic principles of differential calculus. Both the framework for the CCI and its development and validation are rooted in the experience of the Force Concept Inventory (FCI) in physics. Both tests are based on the most common student conceptual misunderstandings that block any meaningful ability to understand and apply the subject. It is essential that schools and faculty have a validated test to measure whether students leaving calculus have conquered these misconceptions.
The great intellectual merit is in the use of modern scientific methods to both develop and validate such an instrument, and the investigators are well versed in these methods. The FCI has had a dramatic effect in improving physics education, and is abundantly shown to be able, in a reproducible way, to document results dramatically better from Interactive-Engagement methodologies than from standard Lecture-Demonstration approaches. It is very important to know whether this critically important finding remains valid in calculus (and other math courses). The CCI is able to do this. Such an instrument is needed in mathematics. The ability to document convincingly whether a given teaching methodology really does what it claims to do (in mathematics as well as physics) has a broad national impact. Without such documentation, decisions on how to teach are based largely on the personal faith of faculty, and subjective decisions. A well-validated CCI, which this project provides, gives an independent and reproducible measure of whether teaching methodology is the dominant factor for conceptual understanding in calculus that the FCI has shown it to be in physics. The CCI lends itself to greatly improved teaching of calculus to thousands of college and high school students and spawn similar conceptual tests, also needed, in other parts of the math curriculum.
