Comparing high-school and college instructors’ beliefs about college calculus preparation

Abstract

The expectations gap – the difference between the level at which high schools prepare students and the preparation colleges expect – is believed to be accountable for hindering access to, and success in, higher education. It has been largely attributed to misalignment of priorities and lack of communication among policy makers and educators and should inform instruction at both levels. This study compared expectations of college calculus instructors and of instructors who teach calculus-preparatory courses, in college or high school, on what makes for important preparation for the first college calculus course. A total of N = 293 instructors teaching precalculus and calculus at the high school and college levels, in the United States, completed a survey that assessed participants’ beliefs on three major areas related to calculus preparation and success: the critical content prerequisites for calculus, the importance of different calculus teaching and learning elements discussed in the literature, and the ways in which college calculus instructors are willing to accommodate under-prepared students. This study confirms the existence of an expectations gap on a rather narrower issue ‘adequate preparation for college-level calculus', in terms of content and pedagogy. The significance of the finding and its implications for bridging the expectations gap are discussed.