Abstract
The goal of the research, in which some high school teachers with PhD in Mathematics was asked to answer a questionnaire concerning the teaching and learning of real numbers and continuum and was then interviewed, was to investigate the interplay between resources, goals and orientations in the phase of transformation of knowledge in knowledge to be taught in the particular case of real numbers and continuum. As a main result we show how some beliefs concerning the epistemology of real numbers, the goals of mathematics education in the high school and the students’ conceptions lead him to choose a very intuitive approach to the transformation of knowledge and to leave aside all his expertise as a mathematician when he faces the problem of didactical transposition. Also we show that some historical issues that the teachers are not aware of completely or partially could help them in planning more suitable didactical activities in the high school.
