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

First-year mathematics instructors at universities across North America and the globe have been noticing a decline in the mathematics skills and preparation of their incoming students, who have been failing out of first-year mathematics courses at alarming rates. Though some universities have implemented placement or diagnostic tests to measure students' preparedness, many still use high school grades as the only indicator of readiness for university mathematics. However, researchers have questioned how effective these high school grades are at predicting success in university mathematics classes due to factors such as mis-aligned teaching methods, curriculum, and grade inflation. This study analyzes 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 in an attempt to quantify previous research in a large-scale, longitudinal manner. Results show that there is a significant disconnect between these grades, that the disconnect has been growing over time, and that it is is quite significant for students who are not performing well at the Calculus level. Recommendations moving forward include the implementation of placement examination in a wide-scale manner, and increased communication and collaboration between K-12 and university mathematics educators and administrators.