Relevant CAT: Conceptual Diagnostic Test

Discipline: Mathematics

Description:
Patterned after the Force Concept Inventory in physics, which has generated a significant revolution in physics teaching, the CCI measures/ conceptual understanding/ (not computation skill) in the most basic principles of differential calculus. Information on gain on the test and its correlation with teaching methodology will be available very shortly. Faculty and researchers in mathematics and mathematics education are encouraged to make use of the test and to contribute the results found to the growing database. There is no charge to obtain the test. Of particular interest will be results from calculus courses using non- lecture based methodologies. Interested college and university personnel, and appropriate high school math teachers should contact the author.

Example questions similar in format to the CCI

If you know that a function f(x) is positive everywhere, what can you conclude from that about the derivative f’(x)?: a) the derivative is positive everywhere b) the derivative is increasing everywhere c) the derivative is concave upward, d) you can’t conclude anything about the derivative

Tool:

The tool can be sent to colleges and universities by contacting the author, Jerome Epstein. Authorized representatives of schools and school systems also should contact the author. Security of the test is essential.

Authors:
Jerome Epstein (Department of Mathematics, Polytechnic University, 6 Metrotech Center, Brooklyn, NY 11201, (718) 260-3572, jepstein@duke.poly.edu).

Selected References:
The classic study of the Force Concept Inventory is at:

Hake, R.R. 1998a. "Interactive-engagement vs traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses," Am. J. Phys. 66: 64-74; online as ref. 24 at <http://www.physics.indiana.edu/~hake>.

An abstract of the talk on the Calculus Concept Inventory at the Joint Mathematics Meeting in New Orleans is in the book of abstracts for the conference, or can be obtained from the test author. A journal article or two on the test should appear in 2007. Please contact the author for further information.