The Validity of Pre-Calculus Multiple Choice and Performance-Based Testing as a Predictor of Undergraduate Mathematics and Chemistry Achievement.

There has been concern over the validity of the Algebra Diagnostic Test (ADT) used to determine the actual level of student preparation for the first quarter of calculus as taught at the University of California, Santa Barbara. It has been hypothesized that performance-based questions, along with the more traditional multiple choice questions, could provide a better assessment of students' understanding of pre-calculus materials for the Hughts-Hallet curriculum. In this study, a two-part test was written to test for ability and initiative in solving multiple level tasks and to provide for pre-calculus assessment. The performance-based test developed was a four-category examination testing algebra, function, proportion, and geometry. Qualitative and quantitative analyses were conducted to find relationships between test scores and subsequent grades in algebra, calculus for the hard sciences, calculus for the social sciences, and chemistry. The performance-based test had significant correlations with grades in all four classes. Multiple choice testing had a higher correlation than performance-based testing, but a combination of both provided the best test to predict mathematics or chemistry achievement. Mathematics and chemistry achievement are correlated with the following examination portions: symbolic manipulation of algebraic expressions, graphing of functions, symbolic properties of functions, trigonometric functions, logarithmic functions, word problems, geometry, and numerical data or number sense. Symbolic manipulation skills are statistically significant in predicting grades in all four classes. Students who display fluency with function concepts are statistically shown to be successful in calculus and chemistry classes. Six appendixes contain the developed instrument, a multiple-choice test, data scatter plots, tables of data, course descriptions, and a precalculus diagnostic test. (Contains 18 tables, 20 scatter plots, and 4 references.) (SLD)