Knowledge transformation between secondary school and university mathematics

Mathematics at school level and mathematics at university level represent one discipline; however, the foundations differ significantly (Freudenthal 1973). Mathematics taught at the university level seeks to describe knowledge within a coherent frame of axioms, definitions, and theorems and their proofs. School mathematics lacks this rigor and makes use of more intuitively accessible knowledge. This difference is crucial and an important cause for difficulties which students encounter when coming to the university. Learning mathematics at this level means in particular mastering the transformation between a phenomenon-oriented view on the subject and a description in terms of formal language. Accordingly, knowledge transformation is more than a translation process but includes the modulation of corresponding components. In the following, we will exemplarily describe how students encounter this transformation in their first year at the university.