  We provide a theoretical framework for analysing and comparing different
forms of organizing introductions to mathematical analysis at the secondary
level, then illustrate it by two characteristic examples from certain periods
of change in the 20th century, as they occurred in Denmark. We conclude by
extracting from this a fundamental dilemma for the teaching of analysis at
secondary level in view of the requirements and affordances provided by
computer algebra systems on the one hand, and contemporary utilitarian school
pedagogies on the other hand.
