In university mathematics education, students do not simply learn mathematics but are shaped and shape themselves into someone new - mathematicians. In this study, we focus on the becoming of "dis"abled mathematical subjects. We explore the importance of abilities in the processes of being and becoming in university mathematics. Our…

This study aims at better understanding of the use of self-assessment to support high-achieving students in first-year university mathematics. The students, who had not previously self-assessed their skills and knowledge in mathematics, were given two self-assessment exercises during a calculus course: they assessed their prior knowledge and…

In this article, we report from a group (N=98) of students from two campuses of one Finnish university, on their study habits, and to what extent they use different kinds of learning materials in university mathematics courses. Our results show that the older students are more communicative with their teachers, whereas the younger students ask for…

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…

MathCheck is a relatively new online tool that gives students feedback on their solutions to elementary university mathematics and theoretical computer science exercises. MathCheck was designed with constructivism learning theory in mind and it differs from other online tools as it checks the solutions step by step and shows a counter-example if…

In this paper we report a study in which we have developed a teaching cycle based closely on Bloom's Learning for Mastery (LFM). The teaching cycle ameliorates some of the practical problems with LFM by making use of the STACK online assessment system to provide automated assessment and feedback to students. We report a clinical trial of this…

One major issue in mathematics teacher education regards the role of university-level mathematics in teacher knowledge. In the context of a design-based research project, an advanced mathematics teacher education course aimed at strengthening the connections between university-level mathematics and school mathematics was developed. In this paper,…

This paper utilizes concept mapping as a tool for conscious and deliberate knowledge building in mathematics and its extension to algorithms. Currently, alleged defects in mathematics education are obvious: instead of conceptual elaboration, everyday praxis relies on routine computations that are likely to lead into alienated concepts with weak…

It is no surprise that all mathematics teacher education programs attempt to increase future teachers' knowledge, since teachers' knowledge has an effect not only on their teaching but also on their students' achievements. However, measuring the relationship between teachers' knowledge and their education is overly demanding. In this study we…

This article outlines the effect of the collaborative educational tool ViLLE when learning business mathematics in higher education. ViLLE validates students' answers during the assessment process and provides immediate feedback, enabling students to receive feedback and guidance about the correctness of their answers. The learning results in the…

The papers in the monograph address different topics related to mathematics teaching and learning processes which are of great interest to both students and prospective teachers. Some papers open new research questions, some show examples of good practice and others provide more information about earlier findings. The monograph consists of six…