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In this study, we investigated undergraduate mathematics students' (N = 267) attitudes towards proving. The students were taking an introduction-to-proof type course that was situated at the beginning of the mathematics curriculum and lasted for one term. Four attitude variables were measured at the beginning and at the end of the course with a new self-report instrument: self-efficacy, anxiety, appreciation and motivation. The instrument was based on two existing instruments on mathematics attitudes and proof-related self-efficacy. We studied how these four attitude variables were related to the students' prior skills and their gender at the beginning of the course, how the attitude variables changed during the course, and how they affected the students' performance in the final course project. Our results indicate that students' prior performance is linked to their proof-related self-efficacy, anxiety and motivation at the beginning of the course. Female students exhibited lower efficacy and motivation levels than male students. During the focus course, students' self-efficacy increased and anxiety decreased. The gender gaps in self-efficacy and motivation persisted throughout the course. In addition, high motivation in the beginning of the course predicted good performance in the final project. Based on our results, we conclude that an introductory course on proving can enhance students' attitudes, and we suggest that these attitudes are taken into account in teaching as they can affect students' performance. Finally, we urge researchers and professionals to earnestly consider ways to mitigate gender differences in mathematics.

Over the past 9 years, we have implemented, developed, and refined a novel student-centered teaching method called Extreme Apprenticeship in university mathematics context. In this paper, we report the theoretical orientation behind the method, as well as its practical implementation. We also reflect on our experiences gained from using it in our teaching.

In this article we describe a long-term departmental change effort in one mathematics department. The change began with one instructor adopting the Extreme Apprenticeship instructional model. This modest shift served as the catalyst for a series of subsequent, systemic improvements. We believe that this innovation and the resultant change demonstrate how instructional change can serve as a catalyst for broader change, rather than a change that focuses solely on instruction. We use four frames from the literature on organizational development to characterize the changes that have occurred in this department. This in-depth case study describes the department's current culture and how it developed, and we suggest that this explanation could serve as a guide for other departments seeking change.

This study explores the relationship between approaches to learning and self-regulation of learning. Approaches to learning characterise students’ intentions and strategies regarding learning and studying, divided into deep and surface approaches together with organised studying. Self-regulation of learning is a process of monitoring and directing one’s affect and behaviour in learning. It is known that self-regulation correlates with approaches to learning, but the direction of influence has not been demonstrated empirically. Measurements were taken in a first-year mathematics course on 103 Finnish undergraduates. Cross-lagged panel analysis was used to study the direction of time-lagged influence. The results revealed that significant influence existed from self-regulation to deep approach and organised studying, and from lack of regulation and external regulation to surface approach. Based on the results, we conclude that it is important for researchers and practitioners to take self-regulation into consideration when measuring approaches to learning or designing interventions. [ABSTRACT FROM AUTHOR]