Entre palavras, quadros e números: uma análise ontossemiótica da construção do conceito de razões trigonométricas com a utilização de histórias em quadrinhos

This research had as main objective to investigate the implications of the development of a didactic sequence for teaching and learning from the perspective of an onto-semiotic approach to trigonometric ratios concept, having a comic book (HQ) as a guiding didactic resource. Therefore, we did an intervention in a class of 1st year of High School of a public school in Gravata-PE, having as a heoreticalmethodological approach the Onto-semiotic Approach of the Knowledge and Mathematical Instruction – EOS. At first, we applied a diagnostic questionnaire for the initial understanding of the students' knowledge about the concept. Secondly, the sequence was implemented to analyze the emerging semiotic conflicts and the didactic adequacy’s validation, using the theoretical tools underlying the EOS. Among the results, we identified that students’ initial knowledge about trigonometric ratios and associated notions evidences conceptual gaps regarding the intended institutional meanings, such as proportionality, angles in similar figures, likeness ratio and right triangle identification in several representations. The didactic adequacy analysis showed that the sequence in the approach to comics and history of mathematics provided the work with problem situations, enabling the progressive development of learning with students, and it was possible to understand the trigonometric ratios in the right triangle. We consider didactic adequacy as high and point to work with problem situations and comics as a viable alternative in teaching and learning mathematics.