There has been plenty of research in mathematics education in schools but until recently there has been a dearth of research at the undergraduate level. Research at the undergraduate level has increased over the last ten years but has concentrated mainly on first level mathematics courses that attract large numbers of students from a range of disciplines, particularly engineering. The majority of students within these courses are not mathematics major students.
To address this gap in the literature, this thesis describes the conduct and findings of a longitudinal study of students majoring in mathematics and statistics. Students were followed through the three years of their undergraduate program to address three research questions.The first research question deals with the mathematics that students are presented with during their degree and how these ideas are taught and assessed. The second and third questions investigate students’ learning behaviours and attitudes, how these change during their degree and how these are related to achievement.
The first research question was “What are lecturer and student perceptions of the nature and difficulty of key concepts in undergraduate mathematics courses?” To address this question, 39 interviews were conducted with 27 lecturers to determine the key concepts in 28 mathematics and statistics courses. Students were surveyed to determine their perception of the relevance and difficulty of these concepts. The lecturers identified many mathematical concepts in their courses but they also included ideas such as critical thinking and problem solving as key concepts. The student responses indicated that students recognise the importance of the key concepts identified by the lecturers but found them to be of varying degrees of difficulty.
The second and third research questions were “What learning behaviours do students use to study mathematics at university?” and “What are students’ attitudes towards mathematics and to what extent do these attitudes change as they progress in mathematics?” These questions were addressed by soliciting comments from students several times during their undergraduate degree programs; through an initial attitude survey (1074 responses), course-specific surveys (645 responses) for up to two courses each semester per student, and interviews with 20 students near the end of their degrees. Learning behaviours were analysed by considering the different approaches to learning used by students (deep, strategic and surface). Attitudes that have been shown to be related to students’ learning were looked at, including enjoyment and relevance. The initial attitude survey found students to be positive towards mathematics at the start of their degree.
The students who responded to the course-specific surveys were divided into two groups of likely “major” students and “non-major” students. Comparison of the survey responses of these two groups of students indicated that they exhibited differences in their attitudes and learning behaviours. The “major” students were higher achievers and had more positive attitudes towards their courses, finding them more enjoyable and perceiving them as more relevant and beneficial than the “non-major” students. The surveys also showed that they engage in more independent learning and less social learning than the “non-major” students. In terms of changes of attitudes, the “major” students found their third level courses more enjoyable than their first level courses; however there was a drop in their perceived relevance rating between the two year levels. In terms of learning behaviours, in their third level courses the “major” students obtained help from lecturers and tutors more than they had in first level courses. The main attitude found to be associated with achievement was enjoyment; this replicates what has been shown in the literature and the relationship between these are discussed in the thesis. There were two learning behaviours found to be associated with achievement and these were both indicative of an independent learning approach.
A key contribution of this thesis has been the collection and analysis of twenty case studies of maths major students that allowed deeper understanding of the survey responses and exploration of other learning issues not covered in the surveys. To illuminate the general responses obtained from the surveys, four students with pseudonyms of Tom, Paul, Kate and Ben, were selected so as to highlight the differences in students’ learning experiences. These four case studies are investigated in detail and then analysed with the results from the other interviews enabling naturalistic generalisations to be made to other major mathematics students.