The following text is a report on an individual learning process concerning the author's own teaching practice. The experiences give rise to the hope that – within certain limits – mathematics teaching may be improved by increased awareness among teachers. So the underlying basic questions are

• How can I – in teaching mathematics – become aware of the initial richness of the subject, the viewpoint and the aims of my considerations, as well as the applied strategies and tools? and

• How can I reveal them to the learners, taking into account their viewpoints as well as possible?

Classical teacher education – burden or help?

My practical training as a mathematics teacher at a German gymnasium made claims that I even then felt to be hardly implemented. This training would lead the pupils “as smoothly and elegantly as possible … along systematically prepared paths to systematically predetermined outcomes” (Andelfinger 1987: 3). My instructor, whom I very much appreciated, signaled this norm by tending to assess the lessons according to their planning – which may or may not have been “right.”

This manifested a view that the planning of lessons could be optimized with respect to a systematic implementation. That optimization was

• a neat mixture of anticipation of learning difficulties and control over the learning process by means of a methodically smooth and conclusive presentation of the subject matter as well as a questioning–developing teaching style

• location of the whole responsibility for the progress of the lesson in the hand of the teacher herself.