High school teachers' choices concerning the teaching of real numbers: A case study

The goal of this paper is to present a case study in which a high school teacher with PhD in Mathematics was asked to answer a questionnaire concerning the teaching and learning of real numbers and then he was interviewed in order to investigate the interplay between his resources, goals and orientations in the decision-making process. As a main result, I show how some orientations concerning the epistemology of real numbers, the goals of mathematics education in the high school and the students’ conceptions and difficulties lead him to choose a very intuitive approach to the teaching of real numbers and to leave aside all his expertise as a mathematician.