Series of problems in Clairaut’s Elements of Geometry: interaction between historical analysis and mathematics education research

Abstract

In this paper, I propose an analysis of the structure of Clairaut’s Éléments de Géométrie (1741), a book presenting geometrical knowledge organized around problems, with rich metadiscourse connecting problems and other elements of mathematical content. This analysis is inspired both by the “Series of problems at the crossroad of cultures” interdisciplinary history of sciences project, in which texts from various cultures structured around problems were analysed, and by ongoing mathematics educational research on the Hungarian Guided Discovery approach, where “series of problems” play a central role in the planning and implementation of teaching trajectories. I show how a dialog between the analysis of Clairaut’s historical text and mathematics educational research contributes to the reflection on the construction and analysis of inquiry based teaching trajectories in mathematics education.