As research about the professional knowledge of mathematics teachers related to overarching concepts in mathematics is scarce, this study focuses on the research question of whether pre-service teachers are able to analyse mathematical contents and to link such contents according to mathematics-related overarching concepts. Based on a new test instrument with open questions and on a top-down coding methodology, descriptive data about frequencies of codes is reported and gives an overview on the quality of the pre-service teachers’ answers. The sub-samples of more than 100 German and more than 40 Austrian pre-service teachers also afford exploring whether effects of school culture can be observed for these samples. The results indicate that the pre-service teachers often were unable to discern big ideas behind mathematical contents and to link elements of content matter according to these big ideas. The findings call for an emphasis in teacher education not only on a solid content matter knowledge base, but also on overarching concepts and meta-mathematical ideas.