International Cooperation Addresses Gaps in Mathematical Understanding

A lack of understanding in arithmetic from an early stage can have serious consequences for a child’s educational path. Not only does it make continued learning in mathematics significantly more difficult, but it can also lead to psychological issues, fear of failure, and poor academic performance — all symptoms of missed opportunities to acquire basic mathematical competencies.

This phenomenon is not confined to the German education system; it is observed internationally. To counteract it, learning gaps must be identified early on and children’s understanding of numbers must be developed accordingly. In response to this, Prof. Dr. Volker Ulm at the University of Bayreuth launched the EU-funded project BASIC-MATH under the European cooperation programme “INTERREG Bavaria – Czech Republic 2021–2027”. The aim is to train both student teachers and qualified teachers in Bavaria and the Czech Republic in this area. Over the course of the project, the two universities will also develop a concept for providing effective support to pupils with significant difficulties in mathematical understanding.

In April 2025, the first project meeting of the two working groups was held at the University of South Bohemia in České Budějovice. The researchers at the University of South Bohemia and the University of Bayreuth have enjoyed a close working relationship for over 20 years through various joint research projects. The target group of the project comprises student teachers training for secondary education (Realschule and Gymnasium in Germany) and for the second stage of elementary education in the Czech system. A total of 46 student teachers from both universities took part in the meeting and presented a variety of projects they had developed in seminars over the course of a semester. These seminars raise students’ awareness of the fact that some pupils leave primary school without a solid understanding of numbers or basic arithmetic and therefore require targeted support. The projects presented ranged from practical support activities in the classroom — such as mathematical games — to case studies on one-to-one support.

One group of students presented a diagnostic maths test containing questions aligned with primary school curricula. The test is administered at the beginning of the school year to Year 5 classes in lower and upper secondary schools. Based on the results, teachers can identify pupils with gaps in their mathematical understanding and provide appropriate support. During the project meeting, the group presented the test and discussed individual pupils’ responses, demonstrating how specific errors can reveal deeper misconceptions. The test is freely available online.

Another student group presented differentiated teaching strategies for mathematics lessons. This approach allows pupils to work at different paces, on varying levels of difficulty, and on a range of topics. It enables individual support for pupils still struggling with content from earlier school years, while also creating opportunities for more advanced pupils to develop their talents further.

Further cross-border meetings for student teachers from both universities are planned: one in Bayreuth in 2026 and another in České Budějovice in 2027. All student teachers at the University of Bayreuth specialising in mathematics are invited to participate by attending an associated seminar in the winter semester.