In this book, Mario Gerwig demonstrates both theoretically and through practical classroom experience how it is possible to enable students to achieve a genuine and profound understanding of proof in mathematics education. He utilizes the genetic method of Martin Wagenschein and the educational theory of Wolfgang Klafki, along with the didactics of teaching art built upon them. Three didactically designed teaching units - the discovery of axiomatic systems, the Pythagorean theorem, and the continuation of the prime number sequence - illustrate that one of the most distinctive characteristics of mathematics - proof - does not have to play a secondary role in the classroom.