Student readiness, engagement and success in entry level undergraduate mathematics courses

dc.contributor.authorDame, Lorraine Frances
dc.contributor.supervisorMacGillivray, Gary of Mathematics and Statisticsen_US of Philosophy Ph.D.en_US
dc.description.abstractThe results of this thesis can be used to help identify students at risk of an unsuccessful entry level undergraduate mathematics (ELUM) outcome early in their course by using a student's score on a diagnostic test, using a student's high school performance or tracking graded homework submissions. The quantitative results suggest that optional additional remediation is not addressing students' need for remediation and that struggling students do not frequently engage with departmental supports offered. They also suggest how a suite of pedagogical changes to an ELUM course can be associated with increased student success rates if managed carefully. It is commonly known that prior mathematical knowledge and success in current math courses are strongly linked. Through observational studies at UVic it is found that a significant proportion of students beginning one of several ELUM courses do not demonstrate the high levels of preparation required to succeed and that optional additional remediation is not addressing this issue. In Calculus I, we can infer that more than half of the population of graduating high school students in British Columbia meet or exceed the minimum prerequisite of a B in Principles of Math 12 at UVic. However, entering Calculus I students scored a mean of only 51% on a diagnostic test of important topics from Grade 7 to Grade 12 level mathematics. Almost 90% of the Calculus I students that were identified as at risk by results of the diagnostic test had an unsuccessful outcome. In addition, although nearly half of Calculus I students who entered with a B in Principles of Math 12 failed the Calculus I final exam, passing the remedial course Precalculus is only required for students with a C+ or less in Principles of Math 12. Thus an insignificant proportion of students are adequately prepared for Calculus I by passing the remedial course while many struggling students do not get the remediation required for them to succeed. The quantitative results indicate that the strength of the link between levels of prior mathematical knowledge and ELUM success varies by course. According to Astin (1984) increasing student engagement positively correlates with higher satisfaction levels. Thesis results show that a student who misses more than one graded homework (used as a measure of engagement) will very likely fail the final exam. They show that a student who does not express satisfaction with his/her individual performance is also very unlikely to engage frequently with departmental supports offered such as instructor office hours or the UVic Math Assistance Centre. The results of these observational studies influenced pedagogical changes to the course Logic and Foundations that were designed to increase student engagement. These changes included a more accessible textbook, giving in-class quizzes on assigned readings, fostering a positive course experience, intervening with students at-risk and assigning less weight to the final exam. Analysis of course outcomes shows that the failure rate significantly decreased during this term. Student outcomes were not initially improved after similar modifications to Calculus II, but many of these changes to Calculus II have been maintained through subsequent terms in which improved student outcomes have been observed.en_US
dc.rights.tempAvailable to the World Wide Weben_US
dc.subjectMathematics Educationen_US
dc.subjectstudy and teachingen_US
dc.subjecthigher educationen_US
dc.titleStudent readiness, engagement and success in entry level undergraduate mathematics coursesen_US


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