Open Access

This study investigated the acquisition of skills by future maths teachers in Rhineland-Palatinate during their final internship phase before entering the so-called `Vorbereitungsdienst´, a kind of in-depth in- ternship/ practical training. In order to record the students' learning progress, a pre/post-test approach was chosen in which the participants each analysed five short teaching sequences in an online questionnaire and then answered questions on mathematical argumentation. So the test reflected a central content of the internship, the observation and reflection of maths lessons. All video sequences were focussed on aspects of mathematical argumentation in the classroom. Ma- thematical reasoning not only describes one of the general competences laid down in the educational standards and curricula for the subject of mathematics, but also goes beyond the other general com- petences in terms of its fundamental importance for mathematics lessons. In the test group, a total of 54 trainees was surveyed at the beginning and at the end of their in-depth internship in four internship periods in 2022 and 2023. The control group consisted of 28 student tea- chers of mathematics, who were also surveyed twice at 3-week intervals without completing a school placement in the meantime. The collected data sets, which essentially consist of free text responses, were analysed using the qua- litative content analysis method. In addition, the interpretative uncertainty that arises here was mini- mised through backward testing. In this way, the quantity and quality of the video analysis as well as the knowledge and understanding of mathematical argumentation could be determined and com- pared for each respondent in both tests. As a result, the study confirms previous findings regarding the perception of teaching by experts and novices and also the fundamental increase in knowledge through practical phases. In addition the study shows that both quantitative and qualitative response behaviour improved after the practical training and the test participants were able to identify aspects of argumentation in the lesson excerpts and justify their importance for good mathematics teaching. This was more successful in teaching si- tuations that are not very dynamic than in teaching situations that are very dynamic, such as those arising from conversational situations. In addition, a deeper understanding of the competence `ma- thematical argumentation´ could be demonstrated after the internship and it could be seen that the didactic knowledge and the ability to analyse videos correlate more strongly with each other in the post-test than in the pre-test. The effects described were only evident in the test group, but not in the control group without the work placement.