Graduates of the mathematics degree programme component in the Master of Education, profile ‘teaching degree Gymnasium’ [teaching degree secondary school]  know the mathematical concepts and constructions that are the foundation of mathematics at school, can analyse them and justify them from a broad perspective, can structure and interlink mathematical areas and highlight connections to mathematics at school, can adequately present mathematical facts and situations both orally and in writing, and can independently acquire mathematical content, have the ability to argue conclusively and precisely and can constructively respond to objections, can review lines of argumentation in terms of validity, clearly present mistakes or gaps and assist in correcting or specifying mistakes, are aware of mathematical fields of practice and can model extra-mathematical problems, find and apply appropriate mathematical methods to deal with the models and clearly communicate solutions, can name, understand and explain essential mathematical references in everyday life, public texts and general language on the basis of their general mathematical education.