When we talk about the legacy of Felix Klein, we are interested in the significance of Felix Klein’s work for mathematics education, for our current theory and practice, and above all, for tomorrow’s ideas concerning the teaching and learning of mathematics. We are interested in Felix Klein as a mathematician and as a mathematics teacher, but most of all we are interested in his ideas on teaching and learning mathematics, the problems he saw at university and at high school, and the solutions to these problems that he suggested. We are interested in these solutions because we recognise that we are nowadays confronted with similar or even the same problems as 100 years ago. Speaking about Felix Klein’s legacy means hoping to get answers to some of the problems we are struggling with today. Speaking about Felix Klein’s legacy today means giving answers to—at least—three basic questions:
- 1. Which situations and which problems at the end of the 19th and the beginning of the 20th century can be seen in analogy to present situations?
- 2. How did Felix Klein react to these problems and which solutions did he suggest?
- 3. What do we know nowadays about the effect of the answers and solutions provided by Felix Klein 100 years ago?
Analogies between the situation 100 years ago and today can immediately be seen if we think about the current discussions concerning the goals and contents of teacher education at university, especially the problems of students, with the transition from high school to college or university and the transition back to high school. The problems with these transitions are expressed in Felix Klein’s most famous statement, the “double discontinuity” from the introduction to Elementary mathematics from a higher standpoint, Volume I: