Sokratisch Mathematisieren

Motivated by Plato's writings, the Socratic Method was conceived and applied by various pedagogues. The German philosopher Leonard Nelson has also conceptualized this method at the beginning of the twentieth century as a scientific as well as a didactic method in the context of Neo-Kantian critical philosophy. He was engaged firstly in the fundamental question whether learning is possible, which is mentioned as a paradox in Plato's Meno. In this respect, Nelson dealt with the topic of the genesis and validity of knowledge, following the philosophical conceptions of I. Kant and J.F. Fries. Furthermore, as the philosopher of the Hilbertprogramm, Nelson explored also the foundations of mathematics and logic. Based on these investigations, he introduced the critical method, which he adapted from I. Kant and J.F. Fries, as a scientific method. He identified this method on the one hand in the Platonic dialogs of Socrates as the method of research and teaching and on the other hand in David Hilbert's contributions as the axiomatic method. Hence, he named the method after Socrates and claimed this to be the appropriate method for teaching philosophy and mathematics.
In this dissertation, I will introduce Nelson's Socratic Method, specifically in the context of mathematics, and examine it philosophically. Based on the described theories on the method and own experiences of teaching in Isfahan Mathematics House, the practice of the Socratic Method in mathematics classroom will be then discussed