High School Calculus and First-Quarter College Calculus Grades

Abstract

Teaching calculus in school has been one of the more controversial aspects of the school mathematics curriculum. (See Butler, Wren, & Banks [1970, pp. 532-533] for a discussion of the history of calculus as a school topic.) In spite of the controversy there is little empirical evidence on the effects of teaching calculus in school. Neeley (1961) analyzed selected achievement data and concluded that high school calculus is largely a waste of time (p. 1005). However, Hildebrant (1962) pointed out that this conclusion did not follow from the data. McKillip (1966) found that for students who did not receive advance placement, one semester or less of school calculus did not significantly affect first-quarter college calculus grades, but two or more semesters of school calculus did significantly improve first-quarter college calculus grades. Shimizu (1969) found no evidence to support the belief that school calculus improved college performance. However, the statistical test used involved correlations and did not compare average college calculus grades. Thus the conclusion does not seem to follow from the analysis reported. Hubley and Maclay (1970) reported that students in an advanced placement calculus course did well on the advanced placement exam. However, no statistical tests were made. Sorge and Wheatley (1977), in a study of college calculus grades and amount of school calculus, concluded that if students study calculus in school they should do so for one year or not at all (p. 645). One weakness of these studies is that the ability of the students in the different groups was generally not considered. For example, calculus is likely to be the 12th-grade mathematics course for high-ability students in