ENSINO DESENVOLVIMENTAL E INVESTIGAÇÃO MATEMÁTICA COM O GEOGEBRA: UMA INTERVENÇÃO PEDAGÓGICA SOBRE O TEOREMA DE TALES

Abstract

The research sought to identify the contributions of the theory of developmental education combined with mathematical research for the teaching and learning of Thales' Theorem. This question stems from the problems in which it operates the teaching of mathematics in the context of Brazilian school today, especially in high school, where there is little student learning in relation to fundamental concepts of this discipline. This study was based on principles of developmental teaching theory of Davydov and mathematics research from the bridge of ideas. The Geogebrasoftware was used on the student activity for the study of Thales' Theorem. Thus, the overall objective was to clarify what are the contributions of developmental teaching theory to teaching and learning of Tales theorem when combined with mathematical research, with the support of the Geogebrasoftware. The specific objectives, we sought to identify the changes presented in student learning over the completion of the formative educational experiment on the Thales' Theorem; what mathematical research with Geogebra can add the classes and expand conceptual basis of the students, develop the geometric vision in the plan as well as expand the ability to make conjectures, interpret and solve problems related to Thales' Theorem. The research was qualitative in nature, through training teaching experiment, with the empirical field a school of state schools of the State of Goiás. In this school was searched a second grade high school class, with the participating students, their parents and the math teacher who also worked as a collaborator of the research. Data were collected through non-participant direct observation, questionnaires, semi-structured interviews, organizedand analyzed according to the procedures of qualitative analysis. The results show that the combination of principles of developmental teaching theory to mathematics research and the use of the Geogebrasoftware potentiated the investigative aspect of the theorem study activity of Tales by the student. The introduction of the Geogebrasoftware enabled realize dynamically integration between algebra and geometry, allowing the student to the active work with the theorem of Thales object, facilitating the identification of its conceptual core and relationships that involve. Students expressed that the study of Tales theorem, as proposed, contributed to the understanding of the most significant geometry, facilitating learning. It is concluded that the Tales theorem teaching structured based on the Davydov theory and mathematics research through the Geogebrasoftware , can result in better learning of this concept by the students. Therefore, it is essential that the teacher be aware of developmental teaching theory and mathematical research, as well as the features of the Geogebrasoftware .