The development of a didactic sequence for teaching fundamental trigonometric equations in basic education

The research is related to the teaching and learning of Fundamental Trigonometric Equations. The guiding question of the research was: How will a Didactic Sequence, developed according to the structuring model (UARC), with the aid of concrete material and software, contribute to improvements in the teaching and learning process of Trigonometric Equations? To answer this question, the general objective was defined to propose the development of a Didactic Sequence to enhance the teaching and learning of Fundamental Trigonometric Equations. The didactic sequence is structured according to the construct of Articulated Units of Conceptual Reconstruction (UARC), according to Cabral (2017). Dissertations and textbooks on the subject were analyzed, in addition to a questionnaire via Google Forms being applied to high school mathematics teachers and alumni with questions relevant to the research; the data collected corroborated the methodological objectives outlined. The teaching sequence was applied to an experimental class, while the control class was taught in a traditional way. At the end of the classes, both groups took a test to verify their learning. The analysis of the results is based on the theories of Microgenetic Analysis by Góes (2000) and Discourse Analysis by Mortimer and Scoot (2002). The transcribed learning evidence, together with the average grades on the learning verification test of the experimental class, indicated that the use of the teaching sequence for teaching fundamental trigonometric equations with the help of manipulative materials proved to be an efficient methodological alternative for teaching.