Otto Toeplitz's 1927 Paper on the Genetic Method in the Teaching of Mathematics

Abstract

Argument“The problem of university courses on infinitesimal calculus and their demarcation from infinitesimal calculus in high schools” (1927) is the published version of an address Otto Toeplitz delivered at a meeting of the German Mathematical Society held in Düsseldorf in 1926. It contains the most detailed exposition of Toeplitz's ideas about mathematics education, particularly his thinking about the role of the history of mathematics in mathematics education, which he called the “genetic method” to teaching mathematics. The tensions and assumptions about mathematics, history of mathematics, and historiography revealed in this piece dedicated to educational ideas are what make Toeplitz's text interesting in the study of historiography of mathematics. In general, the ways historiography of mathematics and teaching of mathematics, even without an immediate concern for history, are deeply entangled and, in our view, worth attention both in historical and educational research.