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.

中文翻译：

---

大学数学的辅助学习质量：两种教学设计的比较

先前的研究承认有必要进一步发展本科数学教学。这项研究的目的是调查教学设计和学习质量之间的关系。这项定量研究通过在两种使用不同教学法的本科数学课程中比较学生的学习方式，自我效能感和教学环境的体验，从而接近学习环境。第一门课程在传统的以演讲为基础的框架内运作，其中包括以学生为中心的要素，第二门课程采用一种以学生为中心的新颖教学方法-“极限学徒”（Extreme Apprenticeship）来实施。分析是基于这两种情况下的同一批学生（N = 91）。根据学生的深度学习和表面学习方法对学生进行聚类，并确定了三个聚类：采用深层学习方法的学生，采用表面学习方法的学生和采用上下文相关表面学习方法的学生。结果表明，以学生为中心的课程设计成功地支持了更有利的学习方法，更高的自我效能水平以及更积极的教学环境体验。此外，这三个类别都受益于以学生为中心的课程设计，而采用上下文相关表面方法的学生受益最大。总体而言，结果表明，通过教学设计可以提高大学数学学习的质量，该教学设计除内容外，还应采用整体方法来学习环境。