Felix Kleins "Elementarmathematik vom höheren Standpunkte aus" : eine Analyse aus historischer und mathematikdidaktischer Sicht

In the early 20th century, there arouse a demand for a course of university studies considering the special needs of future teachers. One of the well known representatives of this movement is Felix Klein. Inter alia, he held lectures in "Elementary mathematics from an advanced standpoint". In the work at hand, the lecture’s manuscripts are analysed concerning the underlying intention and inner structure, in order to adjudicate on the relevance of Klein’s lectures for the present teacher’s education.
The results show, that Klein adheres closely to several principles, such as the principle of mathematical interconnectedness, the principle of intuition ("Primat der Anschauung"), the principle of application-orientation and the genetic principle. Those principles contribute to the development of Klein’s advanced standpoint to a large amount. In addition, Klein conveys a multitude of perspectives, that broaden this advanced point of view: a mathematical perspective, a historical perspective as well as a didactical perspective on the discussed mathematical contents. As a result, in the lectures two different orientations can be declared: Klein regards "elementary mathematics from an advanced standpoint" as well as "higher mathematics from an elementary standpoint".
By contrasting Klein’s lectures with alternative contemporary concepts,
they are reassessed concerning their sustainability. In the course of this, Klein’s principles and perspectives prove of use for a systematical comparison of lectures on elementary mathematics.