Klein’s Conception of ‘Elementary Mathematics from a Higher Standpoint’

Abstract

This chapter studies Klein's conception of elementarisation; it is first put into the context of other approaches for mathematics teacher education in Germany. Then, approaches in mathematics education and in history of education to conceive of the relation between academic knowledge and school disciplines are discussed. The wrong translation of Klein's German term ``hoher{''} in the long time prevailing American translation is commented on, in preparation for the analysis of the concept of ``element{''} in the history of science. Klein's practice and his introduction of the term ``hysteresis{''} to emphasise the independence of school mathematics are discussed. The last section reflects the consequences of the hysteresis notion for integrating recent scientific advances into school curricula.