Supporting quality of learning in university mathematics

Abstract

During the last decades of higher education research, new student-centred learning environments have emerged with the emphasis on students’ own activity, responsibility, and independence for learning. Still, in the context of university mathematics, teacher-led instruction remains the most frequent instructional practice. Although the urgent need for developing more student-centred university mathematics learning environments is acknowledged in the literature, research focusing on this area is scarce. This doctoral dissertation addresses the research gap by creating new knowledge on how student-centred learning environments can support mathematics students’ quality of learning at university.

To offer a holistic perspective, quality learning is conceptualised with three theoretical concepts, namely students’ approaches to learning, academic self-efficacy, and self-regulation of learning. The students’ approaches to learning (SAL) tradition comprehends an approach to learning as a combination of students’ aims for learning and the processes used to achieve them. Typically, two distinctive approaches are considered, a deep approach aiming to understand, and a surface approach aiming to reproduce knowledge. The tradition values a deep approach to learning and its development during university studies. The notion of academic self-efficacy refers to a person's belief in their ability to perform a specific task in a specific context. Self-efficacy has been identified as the strongest indicator of study success in higher education. In addition, self-efficacy has a central role in the disciplinary context of mathematics, as it increases especially women’s retention in mathematics-related majors. The notion of self-regulation of learning (SRL) characterises how students regulate their cognition, behaviour, motivation, and emotions to enhance their personal learning processes. In this doctoral dissertation, self-regulation of learning is viewed as both an individual and a social practice, and in this vein, the notion of co-regulation refers to a transitional process of acquiring self-regulation skills.

Learning environment refers to “the social, psychological and pedagogical contexts in which learning occurs and which affect student achievement and attitudes” (Fraser, 1998). In this doctoral dissertation, the same students are investigated in two parallel student-centred mathematics learning environments, offering an opportunity to address the role of the context on students’ quality of learning. The two learning environments were chosen for their well-established but different student-centred instructional practices; Course A functioned within a typical lecture-tasks-small groups framework with the inclusion of student-centred elements, and Course XA was implemented with Extreme Apprenticeship, a form of inquiry-based mathematics education with a flipped learning approach.

The results of this doctoral dissertation are based on both quantitative and qualitative data. The quantitative data consists of students who answered an electronic questionnaire in both courses (N=91). The questionnaire included items measuring students’ approaches to learning, self-efficacy, self-regulation of learning, and experiences of the teaching-learning environment. In addition, data collected during the courses (number of completed tasks, participation, and course exam results) were merged with the questionnaire data. All participants of the prior quantitative data collection point were invited for an interview on a voluntary basis. The qualitative data consists of 16 semi-structured interviews where the students reflected on their experiences in both learning environments.

This doctoral dissertation summarises four studies, each articulating the quality of learning in the university mathematics context from different perspectives. Study I quantitatively contrasts students’ approaches to learning, self-efficacy, and perceptions of the learning environments in the two learning environments. In addition, the study identifies three student subgroups: 1) students applying a deep approach to learning, 2) students applying a surface approach to learning, and 3) students applying a context-sensitive surface approach to learning. Study II is a follow-up of Study I and takes a qualitative approach when contrasting the student subgroups and their aims for learning and the actualised learning processes in the two learning environments. Study III quantitatively examines gender-specific differences in self-efficacy, and Study IV takes a mixed-methods approach when contrasting students’ self- and co-regulation of learning in the two learning environments.

The results of this doctoral dissertation show that there can be substantial variation in students’ quality of learning between different student-centred learning environments. The central elements of the learning environment contributing to the quality of learning were tasks, lectures, scaffolding, and student collaboration. In particular, student collaboration was focal in supporting students to move away from undesired learning practices, such as applying a surface approach to learning or unregulated learning. Moreover, the results demonstrate that disrupting the typical course structure by a flipped learning approach elicited various benefits for the quality of students’ learning. In this vein, this doctoral dissertation argues for a holistic approach to design university mathematics learning environments and promotes pedagogical development as a significant factor in supporting students to learn mathematics within higher education. Overall, this doctoral dissertation demonstrates how discipline-based higher education research can advance both the fields of university mathematics education and higher education towards the development of research-based student-centred learning environments.