Avenues for teaching the scandal of irrational numbers
In contrast with rational numbers, whose difficulties have been addressed by numerous studies from a pedagogical standpoint, little research offers guidance on the teaching of irrational numbers. To better grasp the issues involved, we examined the evolution of this concept and then established a framework drawing upon its historical and cultural dimensions. Based on a cognitivist approach and using didactic experimentation as our method of research, we sketched a portrait of secondary three (14-15 year old) students’ understanding of different sets of numbers, and more specifically irrational numbers, to be able to identify the characteristics of a strategic approach to teaching this concept. The results contribute to the knowledge on how to conceive the teaching of irrational numbers at the secondary level, and offer various avenues by which to pursue the study of this concept from a didactic standpoint.