An analysis of grades and placement in the transition from pre-calculus to calculus at the University of Manitoba

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Barr, Darja
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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 (Crowther, Thompson & Cullingford, 2007; Hourigan & O’Donaghue, 2007; Kajander & Lovric, 2005; Rylands & Coady, 2009). 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 (Finnie et. al, 2010; Geiser, 2007; 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 and university mathematics educators and administrators. iii The second study looked at the effectiveness of the ALEKS placement test at predicting students’ readiness for first-year Calculus. Results show that including this mathematics placement test along with high school grades and some demographic variables can help predict the students’ success in Calculus more validly. Recommendations include the implementation of the ALEKS placement test for entry into university Calculus courses, as well as some additional measures that could aid in placing underrepresented minority students more appropriately. Furthermore, the sharing of information between university and high school mathematics teachers is recommended.
Mathematics, Education, Transition, Calculus, PreCalculus