Education, division & derivative: Putting a Sky above a Field or a Meadow

The sky is a tentative suggestion for extension group theory, that has supervariables with flexible domains, that would allow the formulation of dynamic rational functions, such that division by zero is prevented by manipulation of the domain. This would allow an algebraic approach to the derivative. Meadows are no alternative to such an approach. The world needs Academic Schools in which teaching is merged with empirical research on didactics.