An analysis of the relationship between high-school pre-calculus and university calculus grades

Abstract

Recently, first-year mathematics instructors at universities across North America and around the globe have been noticing a decline in the mathematics skills and preparation of the incoming student body, and these students have been failing out of first-year mathematics courses at alarming rates . Though some universities have implemented placement or diagnostic tests to measure the preparedness of their incoming students, many still use high school grades as the only indicator of students' readiness for university mathematics. However, researchers have found mixed results in terms of the effectiveness of high school grades at predicting success in university mathematics courses Salim & Al-Zarooni, 2009) due to factors such as the miss-alignment of teaching methods, students' entering knowledge, and skills, the curricula in high school and university, and high school grade inflation. This dissertation includes two studies. The first study analyzed the relationship between grade 12 Pre-Calculus grades and first-year university Calculus grades at a large Canadian university over the period from 2001-2015. The results show that the disconnect between high school grades in mathematics and university grades in mathematics has been growing over time, and is significant for students who are not performing well in university Calculus. Recommendations include the implementation of placement examination, and increased communication and collaboration between K-12