Higher education in the Federal Republic of Germany - devolpments and recent issues

Center of European Studies, Graduate School and University Center of the City University of New York

Preformal proving: examples and reflections

The starting point of our reflections is a classroom situation in grade 12 in which it was to be proved intuitively that non-trivial solutions of the differential equation f' = f have no zeros. We give a working definition of the concept of preformal proving, as well as three examples of preformal proofs. Then we furnish several such proofs of the aforesaid fact, and we analyse these proofs in detail. Finally, we draw some conclusions for mathematics in school and in teacher training.