A Comparison of the Relative Validity of a Measure of Piagetian Cognitive Development and a Set of Conventional Prognostic Measures in the Prediction of the Future Success of Ninth- and Tenth-Grade Students in Algebra

Abstract

For a total sample of 290 ninth- and tenth-grade students enrolled in the first-year algebra course at a suburban Los Angeles high school situated in a relatively affluent community, the major focus of this study was to compare the predictive validity of chronological age, a standardized algebra prognosis test, standardized scales of verbal and quantitative abilities derived from an achievement test battery, and an objective measure of formal or concrete stages of Piagetian cognitive development. Criterion variables included both final examination scores and course grades. It was concluded that chronological age, an algebra prognosis test, and mathematics subtests from a standardized achievement test battery appear to be the most promising predictors of success in algebra (with the relationship between age and the criterion measures being substantially negative). In addition, the conclusion was reached that when used in combination with readily available scores on several standardized tests of mathematics achievement and quantitative abilities, the developmental Piagetian measure can be expected to contribute very little to the strength of prediction of algebra success or to the accuracy of differentiation between successful and nonsuccessful students. On the other hand, if the developmental scale is employed as a single predictor or in combination with another predictor such as a standardized mathematics achievement test, then the Piagetian measure can be anticipated to afford a significant contribution to a valid forecast of performance in beginning algebra.