Stu,dents' and Lecturers' Perceptions of Factors Influencing Students' Success in First-Year Undergraduate Mathematics Courses.

Qualitative data from lecturers and students were used to identify factors which were perceived as making the most important contributions to students' academic success or failure in fIrst-year mathematics courses. A questionnaire based on this information highlighted similarities and differences in the perceptions of lecturers and students about influences on students' success and failure. The results confIrm the importance of motivation and suggest further research is needed in the areas of active learning and student effort and workload. Introduction Most universities offer a range of first-year mathematics courses which cater for students of varying background knowledge and career aspirations. While in the past the assumption was that students entering a standard fIrst-year mathematics course had recently completed a complementary mathematics course at secondary school, it is increasingly evident that students in calculus and algebra courses come from a wider spectrum. On enrolment students are advised of the recommended prerequisite mathematical background - but what emphasis should we place on this, and what should our response be to the mature student who successfully studied mathematics many years ago, or the otherwise successful student who, despite a weak background in mathematics, needs mathematics as a prerequisite for another major? Models of learning (Anthony, 1996b; Biggs, 1993) all suggest that presage, process and context factors interact to influence outcomes of learning. While student presage factors such as prior content and metacognitive knowledge, and previous learning experiences are acknowledged as signifIcant factors many of the other factors influencing students' success occur after enrolment. Teaching strategies, student motivation, approach to studying, cultural expectations, and. numerous other factors are likely to influence students' success in undergraduate mathematics courses. Research Study The purpose of this study was to identify specifIc factors which are seen as having important influences on students' level of success. In support of the view that perceptions are not stable entities within cognitive structures but are dynamic and context dependent (Prosser, Trigwell, & Taylor, 1994) the study is specifIc to fIrst-year mathematics courses. Moreover, because teaching and learning processes jointly influence learning outcomes the study is based on the perceptions of both lecturers and students. Crawford, Gordon, Nicholas and Prosser's (1994) study involving beginning mathematics students stressed "the need for a shift in attention away from teaching and learning as independent activities towards a more systemic examination of the relationships between the two activities and the context in which they occur" (p. 344). An exploration of potential differences in lecturers' and students' perceptions will provide an opportunity for both teachers and students to assess their respective roles in the learning process. The study was conducted in three phases involving exploratory open-ended questionaries, Likert-type questionnaires and student interviews. The fIrst two phases, which are reported in this paper, use a similar methodology from an earlier study (Killen, 1994) which involved students and lecturers across all university disciplines. Phase One In an attempt to identify factors which have important influences on success 65 students (from a range of fIrst-year mathematics courses) and 22 lecturers and tutors (all experienced in fIrst-year undergraduate teaching) were asked to complete a questionnaire on which they responded freely to two items: "List fIve factors that you think are most