Besides homework assignments, optional quizzes are a commonly used means for formative assessment in tertiary mathematics education. Instructors, for example, implement these to help students detect gaps in their understanding, or to foster a continuous and active engagement with the content. The extent to which these goals are reached, however,…

Preservice mathematics teachers are sometimes trained in programs so that they have both their own courses and joint courses with mathematics majors from the beginning of their studies. While this is thought to provide them with both deep mathematical knowledge and teaching-specific content right from the start, many of them report disaffection…

Preservice teachers study an academic discipline (e.g. mathematics) and -- just like students majoring in that discipline -- have a certain level of connectedness to it. While studying, students may compare themselves to peers studying the same discipline within alternative degree programs, characterized by different study contexts. Notably,…

The transition from school to university is a challenging process for many students which is reflected in high dropout and low examination success rates during the first year at university. Qualitative studies have found hints that students' beliefs play an important role during the transition. Due to their dialectic nature with cognitive as well…

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…

Mathematics plays a significant role in many study programs. However, several studies show deficiencies and a decline in beginning undergraduates' skills in mathematics in many content domains. However, it remains unclear whether they have improved in so-called process competencies like modeling, mathematical reasoning, or using different…

The transition from school to university mathematics is a challenging process for many students, which is reflected in high dropout rates during the first year at university. Using mediation analysis, we want to shed light on the role of students' attitudes towards mathematics--especially their interest in mathematics and their mathematical…

In this paper we provide a description of the project DrIVE-MATH, highlighting the main goals, intellectual outputs, outcomes, the involved partners, and activities and reports from the three-years' project. At the end we discuss the impact of the new proposed Education models at various levels, from students, to HEIs, to stakeholders.

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…

In many countries STEM degree programs face high dropout rates, which are often attributed to insufficient mathematical preparation of incoming undergraduates. However, it is largely unclear which mathematical prerequisites universities expect from their new STEM undergraduates. There are hardly official documents and it is even an open question…

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…

Students' expectancy-value beliefs play an important role in shaping their educational choices and behaviors. Drawing on Eccles and Wigfield 's (2020) situated expectancy-value theory, we investigated short-term changes in students' expectancy-value beliefs in gateway math courses for beginning university students. In Study 1a, we collected data…