Didactic transposition of rational numbers: a case from a textbook analysis and prospective elementary teachers’ mathematical and didactic knowledge

Abstract

This study aims to present a detailed analysis of didactic transposition of rational numbers from knowledge to be taught into taught knowledge occurring in a teacher education institution. The knowledge to be taught of rational numbers is analysed from the mathematics textbook used by prospective elementary teachers in a mathematics education course. The analysis focuses on mathematical praxeology, especially the type of task and technique. Then, the taught knowledge is investigated from 32 prospective elementary teachers’ collaborative work on two hypothetical teacher tasks (HTT) related to operations with rational numbers.

Keywords

• didactic transposition
• hypothetical teacher tasks
• mathematical and didactic knowledge
• mathematical knowledge to be taught
• praxeology
• taught knowledge