Marilyn Carlson, Bernard Madison, and Rich West
A shorter version of this article appeared in the February/March 2011 edition of MAA FOCUS.
A research-based modification of the Calculus Readiness (CR) test that MAA introduced in 1980 has been added to the MAA/Maplesoft Placement Testing Suite (PTS).
At the time, CR was a reform alternative to traditional algebra and trigonometry tests for determining appropriate preparation for calculus. CR has been very successful and is still an important part of PTS, but research since CR has provided new information about student preparation for calculus (Carlson, Madison, and West 2010). Taking advantage of that research, the Calculus Concepts Readiness (CCR) examination was developed and validated over a two-year period by a task force of Ray Cannon, Marilyn Carlson, William Martin, and Rich West (chair). Bernard Madison coordinated pilot testing and analyzed the resulting data.
Development of the CCR began with setting out an initial description of precalculus concepts (e.g., function composition, average rate of change, exponential growth, periodic behavior) that research had identified as important for learning calculus.
This initial description was refined into 22 reasoning abilities, understandings, and skills. Question wording and answer options for the multiple-choice questions were shaped by student interview data that illustrated common student thinking. As a result, 18 of the 25 CCR items assess or rely on understanding the concept of function; 5 items assess student understanding or use of trigonometric functions; 4 items involve exponential functions; and 10 items are applications in contexts.
Preliminary versions of the CCR were tested at four institutions to select the final 25 items and to provide item-level data. This testing also provided some validation of CCR scores as predictors of success in calculus. After the final CCR was drafted, pilot testing was conducted at three large universities: one private and two public. All the pilot testing results indicate that the CCR will be effective and reliable in deciding which students are ready for calculus.
Another benefitt of introducing the CCR exam is that it could strengthen precalculus curriculum and instruction. Currently, the research done in the last 20 years on how to prepare students for calculus—research that underlies the CCR exam—has had little influence on what is being taught. This oversight was revealed in weak performances on the CCR during pilot testing and cursory examinations of precalculus courses and textbooks.
Marilyn Carlson, Bernard Madison, and Rich West served on a CCR taskforce
MAA/Maplesoft Placement Testing Package Expands (MAA FOCUS, February/March 2011)