Trigonometria no triângulo retângulo: um experimento didático-formativo fundamentado na teoria do ensino desenvolvimental

Abstract

The research was carried out at the Federal Institute of Education, Science and Technology Goiano - campus Rio Verde, in the Technical courses in Administration and Buildings, integrated to the modality of Education of Youths and Adults, of the National Program of Integration of the Professional Education with the Basic Education in the Youth and Adult Education Modality - PROEJA, in Mathematics IV. Methodologically, a qualitative research was carried out based on the Theory of Developmental Teaching. Authors like Libâneo and Freitas; Ponte, Brocardo and Oliveira; Rego, Sancho and Hernández; Vaz, among others, contributed to the investigation. The question that guided the research was: "How to organize a didactic-formative teaching-learning experiment of trigonometry in the triangle rectangle, based on the theory of developmental teaching?". Seeking to answer this question, we planned activities of trigonometry study in the triangle rectangle with the use of Geogebra software tools. The experiment was carried out during the months of February, March, April, May and June of 2018. The students answered a questionnaire, which was proposed with the purpose of obtaining data to analyze the profile of the subjects of the research, answered a diagnostic evaluation that was applied with the objective of identifying students' preliminary knowledge regarding trigonometry contents in the triangle rectangle, presented seminars related to the history of Trigonometry, among other tasks, carried out activities of construction and investigation of geometric figures using Geogebra software tools. Resolved problems problems of application of the studied contents. The actions carried out during the didactic-formative experiment were proposed with the intention of awakening zones of proximal development that could allow the analysis of the development of the subjects of the research. Despite the difficulties presented, the proposed tasks allowed the research subjects to move from the empirical concepts to the scientists, the interaction of the students, and the mediations contributed to the appropriation of the software tools and the concepts studied. It is believed that the organization of the didactic-formative study of trigonometry in the triangle rectangle produced something fundamentally new in the development of the research subjects.