A Cognitive Model of College Mathematics Placement
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
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This study developed and validated the Cognitive Model of College Mathematics Placement and compared its effectiveness to that of Willinghams 1974 vertical placement model as well as the two empirical models. The Cognitive model was based on Skemps 1979 theory of intelligent learning and Wilsons 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.