Teaching real numbers and continuum in secondary school: an ontosemiotic approach to the investigation of teachers' choices

In this paper, we present a case study concerning teaching and learning of real numbers and continuum in the Italian high school. In the research, secondary school in-service teachers, after answering a questionnaire designed to investigate their resources, orientations and goals, have been asked to declare and motivate their didactical choices concerning the teaching and learning of real numbers and continuum. Data have been analysed within a framework including OSA. In particular, two goals were: to investigate how far teachers' resources, goals and orientations affect the process of decision-making and to look for criteria of didactical suitability used by the teacher to argument in favour of their declared choices. After discussing the epistemological complexity of these mathematical objects, we present a case study, in order to make emerge, among other results, the role of OSA in such a research.