A Double Discontinuity and a Triple Approach: Felix Klein’s Perspective on Mathematics Teacher Education

Abstract

Felix Klein was the first to identify a central problem in the preparation of mathematics teachers: a double discontinuity encountered in going from school to university and then back to school to teach. In his series of books for prospective teachers, Klein attempted to show how problems in the main branches of mathematics are connected and how they are related to the problems of school mathematics. He took three approaches: The first volume built on the unity of arithmetic, algebra, and analysis; the second volume attempted a comprehensive overview of geometry; and the third volume showed how mathematics arises from observation. Klein's courses for teachers were part of his efforts to improve secondary mathematics by improving teacher preparation. Despite the many setbacks he encountered, no mathematician has had a more profound influence on mathematics education as a field of scholarship and practice.