From a University of Wuerzburg page on Mathematics teaching in Germany:
2.2 Goals of mathematics teachingSyllabi point out leading ideas and goals for mathematics teaching concerning:
- mathematics as a theory and as a tool for solving problems in natural and social sciences, including modelling;
- experiences with fundamental ideas in mathematics like the idea of generalization, the need for proving, structural aspects, algorithms, the idea of infinity, and deterministic versus stochastic thinking;
- methods of getting insight like inductive and deductive reasoning, methods for proving, axiomatics, formalization, generalization/specification, heuristic work;
- variation of argumentation levels and representation levels in all fields and aspects of mathematics teaching; and
- historical aspects of mathematics.