Abstract
Prior research acknowledges the need to further develop undergraduate mathematics instruction. The aim of this study is to investigate the relationship between instructional design and quality of learning. This quantitative study approaches the learning environment by comparing students’ approaches to learning, self-efficacy, and experiences of the teaching-learning environment in two undergraduate mathematics courses using different pedagogical approaches. The first course functioned within a traditional lecture-based framework with the inclusion of student-centred elements, and the second course was implemented with Extreme Apprenticeship, a novel student-centred teaching method. The analysis is based on the same cohort of students in these two contexts (N = 91). Students were clustered based on their deep and surface approaches to learning and three clusters were identified: students applying a deep approach, students applying a surface approach, and students applying a context-sensitive surface approach. The results show that the more student-centred course design succeeded in supporting more favourable approaches to learning, higher self-efficacy levels, and more positive experiences of the teaching-learning environment. In addition, all three clusters benefited from the more student-centred course design, with students applying a context-sensitive surface approach benefiting the most. Overall, the results suggest that it is possible to promote the quality of university mathematics learning with instructional designs that, besides content, take a holistic approach to the learning environment.
Highlights
In Finland, as in many other European countries, the main emphasis of university mathematics instruction has been on content delivery, and instruction relies heavily on lectures built around axioms, definitions, theorems and their proofs
The results suggest that students applied more favourable learning approaches, experienced the teaching-learning environment more positively and displayed higher selfefficacy levels in the more student-centred course design
As prior research acknowledges the positive impact of a deep approach to learning, it is encouraging to see that students were more likely to apply a deep approach to learning in the more student-centred course design
Summary
In Finland, as in many other European countries, the main emphasis of university mathematics instruction has been on content delivery, and instruction relies heavily on lectures built around axioms, definitions, theorems and their proofs. Opposite to passively receiving information from the lecturer, new studentcentred instructional practices have emerged with the emphasis on students’ own activity, responsibility and independence for learning (Baeten et al 2010). Konstantinou-Katzi et al (2013) call for an overall approach to university mathematics instruction that is adaptive to individual student’s needs, as such an approach has a positive impact on learning and on attitudes towards mathematics. Implementing this kind of adaptive instruction is challenging on a mass course scale, as recognised by Konstantinou-Katzi et al (2013)
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