Didactic transposition of concavity of functions: From scholarly knowledge to mathematical knowledge to be taught in school

Abstract

In an institution �, a praxeology � is generally a modification of a praxeology �* coming from a collective of institutions �*, where the modification is conceptualised by the phenomenon of institutional transposition. This paper presents a praxeological analysis of the concept of concavity of functions as expressed in a mathematics textbook for Norwegian upper secondary school. The analysis shows how the institutional (here, didactic) transposition has “moved” the mathematics presented in upper secondary school away from the mathematics taught at the university and how this transposition has resulted in a poor logos block of the mathematics to be taught