A Cognitive Model of College Mathematics Placement
Abstract
This study developed and validated the Cognitive Model of College Mathematics Placement and compared its effectiveness to that of Willingham's (1974) vertical placement model as well as the two empirical models. The Cognitive model was based on Skemp's (1979) theory of intelligent learning and Wilson's (1971) Model of Mathematics Achievement. The Cognitive model was validated using historical mathematics placement data from the graduating classes of 1989, 1990, and 1991 at the United States Air Force Academy. The study focused on the precalculus -- calculus placement decision. The Cognitive model uses novel, or analysis level, placement test items in an attempt to assess the degree of connectedness of students' schemas and non-analysis items to assess the degree of accuracy and completeness of their schemas relative to the requirements of a precalculus course. Placement test scores may be partitioned to give analysis and non-analysis subtest scores which can then be used to predict students' achievement in calculus. Students are placed into precalculus if their predicted final calculus grades are below the cutoff score identified with the methods of Appenzellar and Kelley (1983).
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1989
- Accession Number
- ADA218275
Entities
People
- Frank J. Swehosky
Organizations
- Air Force Institute of Technology