Various studies have shown that epistemological beliefs affect personal learning and teaching performances. Therefore, epistemological beliefs have become an attractive object of research with different methods of survey. A distinction can be made between denotative and connotative aspects of beliefs, the former being reflected upon, explicit…

Mathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is known about how such consultations proceed in detail. On the basis of models from the literature and recorded…

How is the content of university programs selected and structured? How does it evolve? In the anthropological theory of the didactic, external didactic transposition designates the processes through which knowledge to be taught is delimited and developed for delivery within a school institution, including universities. This paper presents a first…

In this paper, we provide an overall perspective on the teaching and learning of discrete mathematics. Our aim is to highlight what research has been conducted in this area and to connect it to existing research ideas for future work. We begin by characterizing discrete mathematics and its role in the school curriculum, highlighting themes,…

In this paper, the authors discuss their experiences with ungrading at a small public university in the U.S. and a large public university in Germany. The courses described are Calculus 1 and a content course for pre-service secondary teachers of mathematics. The professors teach differently: one with lecture, the other with inquiry-based…

At the University of Paderborn, the course "Introduction into the culture of mathematics" is required for all first-year students who enter the study program for future mathematics teachers at lower secondary level (grade 5-10). In this inquiry-based transition-to-proof course, we use four different kinds of proofs (the generic proof…

The Russian and international legislation ensure equal educational rights to all people regardless of whether have a disability or not. However, traditional approaches to organization of educational activities often do not provide a high enough level of education (including higher education) for people with disabilities as they do not take into…

E-learning has made course evaluation easier in many ways, as a multitude of learner data can be collected and related to student performance. At the same time, open learning environments can be a difficult field for evaluation, with a large variance in participants' knowledge level, learner behaviour, and commitment. In this study the…

The Matrix Algebra portion of the intermediate mathematics course at the Schmalkalden University Faculty of Business and Economics has been moved from a traditional classroom setting to a technology-based setting in the PC lab. A Computer Algebra System license was acquired that also allows its use on the students' own PCs. A survey was carried…

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…

In modern expectancy-value theory (EVT) in educational psychology, expectancy and value beliefs additively predict performance, persistence, and task choice. In contrast to earlier formulations of EVT, the multiplicative term Expectancy x Value in regression-type models typically plays no major role in educational psychology. The present study…

This paper reports on the results of an observational parallel study conducted simultaneously at 2 universities--one each in New Zealand and Germany. It deals with university engineering students' difficulties in the formulation step of solving a typical application problem from a first-year calculus course. Two groups of students (54 in New…

The paper's aim is to note a remarkable (and apparently unknown) relation for right triangles, its generalisation to arbitrary triangles and the possibility to derive these and some related relations by elimination using Groebner basis computations with a modern computer algebra system. (Contains 9 figures.)