Conceptions for relating the evolution of mathematical concepts to mathematics learning—epistemology, history, and semiotics interacting: To the memory of Carl Menger (1902-1985)

There is an over-arching consensus that the use of the history of mathematics should decidedly improve the quality of mathematics teaching. Mathematicians and mathematics educators show here a rare unanimity. One deplores, however, and in a likewise general manner, the scarcity of positive examples of such a use. This paper analyses whether there are shortcomings in the—implicit or explicit—conceptual bases, which might cause the expectations not to be fulfilled. A largely common denominator of various approaches is some connection with the term "genetic." The author discusses such conceptions from the point of view of a historian of mathematics who is keen to contribute to progress in mathematics education. For this aim, he explores methodological aspects of research into the history of mathematics, based on—as one of the reviewers appreciated—his "life long research."