DISCRIMINANT ANALYSIS APPLIED TO PREDICT SUCCESS IN ADVANCED PLACEMENT MATHEMATICS: CALCULUS AB OR CALCULUS BC (STATISTICAL, SECONDARY SCHOOL, REGRESSION ANALYSIS, COVARIANCE ANALYSIS, COLLEGE BOARD)

This predictive, research study addressed the problem of selecting, or not recommending, students for participation in one of the two Advanced Placement mathematics courses. A statistical analysis of sixteen predictor, and six categorical, variables normally found in the records of secondary school juniors was conducted using non-parametric, multinomial tests, analysis of variance and covariance, multiple regression analysis, and discriminant analysis to determine their relative reliability in predicting qualifying performance on the Calculus AB or Calculus BC examinations.;The study population consisted of a sixteen-year data set of 982 AP calculus graduates of Punahou School in Honolulu, Hawaii. Found not to be significant at (alpha) = .05 were the categorical variables year, sex, and racial extraction. Statistically significant at (alpha) = .05 were course and API, a four-level indicator which classified every calculus student by other AP courses taken: only calculus; English, language, history, and the arts; physical sciences not requiring calculus; or physics which required calculus.;Multiple regression analysis at each API level produced two sets of prediction equations (maximum and optimum) for the end-of-course Cooperative Calculus test. The pre-calculus, Advanced Mathematics grade and the ATP's Mathematics Achievement Test, Level II were found to be the most reliable predictors of both success and achievement.;Both two- and three-group discriminant analyses were performed to resolve the questions, "Should this junior take Calculus AB or Calculus BC?" and "Is this junior's likelihood of success on either AP calculus examination high enough to recommend Calculus AB or Calculus BC; and if so, which course?" Discriminant analysis produced equations which correctly classified 85 percent of the 982 candidates in the two-group case, and 80 percent in the three-group analysis. The derived classification equations were applied to a six-year data set from another independent school in Hawaii as an external validity check. Correctly classified were 82 percent of the 276 students in the two-group case, and 77 percent in the three-group analysis.;A thirty-one year historical overview of the growth of the Advanced Placement Program in mathematics is presented together with fifty-three tables of descriptive data on AP mathematics students. The two- and three-group classification equations used in the internal and external validity checks are included.