University students' achievement goals and approaches to learning in mathematics

Background. Achievement goals (AG) and students' approaches to learning (SAL) are two research perspectives on student motivation and learning in higher education that have until now been pursued quite independently. Aims. This study sets out: (a) to explore the relationship between the most representative variables of SAL and AG; (b) to identify subgroups (clusters) of students with multiple AG; and (c) to examine the differences between these clusters with respect to various SAL and AG characteristics. Sample. The participants were 680 male and female 1st year university students studying different subjects (e. g. mathematics, physics, economics) but all enrolled on mathematics courses (e. g. algebra, calculus). Methods. Participants completed a series of questionnaires that measured their conceptions of mathematics, approaches to learning, course experience, personal 2 x 2 AG, and perceived AG. Results. SAL and AG variables were moderately associated and related to both the way students perceived their academic environment and the way they conceived of the nature of mathematics (i.e. the perceptual-cognitive framework). Four clusters of students with distinctive multiple AG were identified and when the differences between clusters were analysed, we were able to attribute them to various constructs including perceptual-cognitive framework, learning approaches, and academic performance. Conclusion. This study reveals a consistent pattern of relationships between SAL and AG perspectives across different methods of analysis, supports the relevance of the 2 x 2 AG framework in a mathematics learning context and suggests that AG and SAL may be intertwined aspects of students' experience of learning mathematics at university.