A PLACEMENT PROCEDURE USING REGRESSION ANALYSIS AT THE UNITED STATES COAST GUARD ACADEMY

Abstract

ABSTRACT Mathematics departments throughout the United States are concerned with the large number of failures and dropouts in freshman calculus courses. Some studies put the figure as high as fifty percent. Currently considerable effort is being expended by educators and professional mathematics organizations to reverse this trend. It is clear that standardized test scores (aptitude) and high school grades are not a measure of calculus readiness. The Mathematics Department at the United States Coast Guard Academy has been using a multiple linear regression model to predict grades in the first semester calculus course. The model uses the available data on incoming cadets as one part of a total placement procedure. Information gleaned from such procedures reduces errors stemming from underestimating or overestimating a student's capabilities in calculus courses. The literature is replete with studies that predict term or cumulative grade point averages. Very little has been done to predict performance in individual courses. The regression model includes standardized test scores, high school rank, types of mathematics courses taken in high school, three achievement related exams and several other independent variables. The three achievement related exams: Algebra Diagnostic, Trigonometry Diagnostic and the Precalculus take approximately two hours to administer and are the best predictors for success in the first calculus course. These exams are readily available through the Educational Testing Service and the Mathematics Association of America. Information gleaned from placement programs will benefit the student and an item analysis of the placement exams could aid in establishing course content for the precalculus program.