Compared with other subjects mathematical education lacks environmental input. Children learn to read because they are surrounded by texts. They learn to write because they want to write messages to friends. Most of them use computers and want to drive a car. The green-house effect stimulates interest in environmental studies. History and palaeontology sell well on TV.

The need of mathematical skills for all has been challenged. One reason is the progressive division of labour which leaves mathematical issues to specialists. Another reason is the pervasive use of electronic devices.

Mathematical education is undergoing a substantial transformation which can be expressed in the short terms “Less doing mathematics – more learning to understand the role of mathematics in society."

A guideline could be to look closer at the so-called “fundamental ideas” of mathematics. The concept goes back to J. Bruner. Fundamental ideas
• recur in the historical development of mathematics (time dimension)
• recur in different areas of mathematics (horizontal dimension)
• recur at different levels (vertical dimension)
• are anchored in everyday activities (human dimension).

In addition fundamental ideas should help to
• design curricula
• elucidate mathematical practice and the essence of mathematics
• build up semantic networks between different areas
• improve memory.

A short overview on some proposals in this direction will be given and some examples are outlined.