This paper presents a study organising the teaching of
exponential functions in an attempt to re-establish a connection be-
tween research and education (or school mathematics) based on the
anthropological theory of the didactics (ATD). The teaching aims
at students developing new knowledge like scholarly knowledge,
which is developed from open-ended questions and is justified by
mathematical argumentation. The design is based on research and
study activities and requirements for upper secondary mathematics
in Denmark. In this study the emphasis is put on the media-milieu
dialectics and how this can be orchestrated in a fruitful manner.
The study shows improvements in student’s relation to proofs and
the student’s ability to read and write mathematics.