Which Influence do School-Related Mathematical Problems have on Students' Perception of the Double Discontinuity? A Study on the use of Profession-Specific Problems in Academic Mathematical Courses for Upper Secondary Teacher Education

Many prospective secondary mathematics teachers struggle to see connections between the mathematics they learn at university and the mathematics they will teach in school. Klein (1908) described this phenomenon as double discontinuity. To address this problem, several German universities implemented so-called school-related mathematical problems that highlight connections between school mathematics and academic mathematics. However, only a few studies investigate the effect of school-related mathematical problems on the perceived double discontinuity. In this contribution, we report a questionnaire study with 98 students in a treatment group of prospective secondary teachers and a comparison group of mathematics majors aiming to supplement first results regarding the influence of school-related mathematical problems on students' perception of the double discontinuity. Our results indicate that school-related mathematical problems do not increase the perceived relevance of academic mathematics for the teaching profession but may prevent the perceived relevance from decreasing. Furthermore, this study indicates that the use of school-related mathematical problems can positively affect perceptions of connections between contents in school mathematics and academic mathematics. The former is in line with prior research, whereas the latter had not been found systematically in prior studies. We discuss implications for future research on the teaching innovation of school-related mathematical problems.