A Comparison of Advanced Placement and College Students on a Calculus Achievement Test

Abstract

The articulation of secondary school and college mathematics is a critical problem facing educators today (National Council of Teachers of Mathematics, 1980; Staff, 1984). The placement in college mathematics courses of students who have taken calculus in secondary school is an especially critical and difficult task. Calculus can be taught at various levels, and its subject matter components can receive varying degrees of emphasis. The Advanced Placement (AP) program attempts to provide a uniform and high-quality calculus course for secondary school students by publishing a detailed course syllabus, encouraging special training for AP instructors, and administering an examination that validates a student's AP Calculus experience (College Entrance Examination Board, 1984). Nonetheless, some evidence suggests that AP Calculus students have difficulty earning advanced placement and credit for the calculus they learned in secondary school (Lefkowitz, 1971; Neatrour & Mullenex, 1973; Pocock, 1974; Rash, 1977; Sklar, 1980; Sorge & Wheatley, 1977). One reason for this difficulty may be that AP Calculus students are not achieving at the same level as college students. Many research studies have attempted to compare the performance of AP Calculus students on their entry into college to that of their non-AP college classmates (Austin, 1975; Bergeson, 1967; Burnham & Hewitt, 1971; Chamberlain, Pugh, & Schellhammer, 1968; Fry, 1973; McKillip, 1966; Paul, 1971; Robinson, 1970; Ruch, 1968). AP students in these studies performed better than their counterparts, but this difference could possibly be attributed to the AP students repeating some or all of calculus. These studies provide no information about the students' level of achievement based strictly on their AP course.