Potentials and Articulations of Knowledge of the Mathematical Analysis for Teaching Action in High School: An Epistemic Analysis of Notions of Sets from the Perspective of the Onto-Semiotic Approach

Background: the area of mathematical analysis is generally seen as something of a complex nature that contributes little to the formation of teachers of basic education in mathematics teaching degree courses. Objectives: in this sense, this article presents an analysis of the potential that knowledge from the mathematical analysis, particularly in notions of sets, presents for the development of didactic-mathematic knowledge required for teaching practice in high school. Design: using the theoretical assumptions of the onto-semiotic approach to mathematical knowledge and instruction (OSA), with regard to the didactic and mathematical knowledge of mathematics teachers, this qualitative research presents an epistemic analysis carried out on the notions of sets in the context of the mathematical analysis, seeking to relate the objects highlighted there with relevant knowledge at the high school level. Setting and Participants: the investigative scenario is theoretical research, therefore without participants. Data collection and analysis: the data source was a teaching-degree mathematical analysis book and a high-school book with focus on sets, which were analysed against the theoretical assumptions of the OSA. Results: the analyses showed that the knowledge of sets can be articulated at different levels of education, especially on the use of mathematical proofs and different languages, highlighting the potential for their contextualisation in high school mathematics teachers’ practice. Conclusions: with this study it is possible to highlight the importance of analysis in the constitution of didactic and mathematical knowledge, as well as its importance for high school mathematics teachers’ practice