in a single paper it is not possible just to touch upon all major aspects and
areas of the didactics of mathematics. so, it has been out of the question
to do justice to the field, let alone to the thousands of researchers who
have contributed to founding, shaping and developing it. instead of the few
findings put forward here, the selection of which was partly motivated by
expectations concerning their potential interest to research mathematicians
and other mathematics professionals, hosts of other findings could have
been selected for discussion with no lesser right and relevance. here is
one: