Um estudo sobre polígonos a partir dos princípios de van Hiele - Domingos, Jailson (2010)
This master work with focus on mathematics education is linked to the Graduate Program of Education of Center of Education at Federal University of Espírito Santo. Our research of qualitative nature investigates visualization and initial characterization of polygons using the van Hiele principles combined with the use of didactical materials. We tried to answer the question: What students and teachers learn about polygons and the development of geometrical thinking when using tangram, geoboards and kites construction in 6th grades classes of fundamental middle school? In this work geometry teaching is based on van Hiele, Pavanello and Lorenzato. In order to analyze the relation between problem solving, didactical materials and geometry teaching we used Polya and SantosWagner. We used in the field research an initial and a final diagnostic test and a didactical sequence formed by three unities of activities: one using the tangram, another one with geoboards and another one with kites’ construction. Our study has been developed from March until September 2009 with grade six students from a public municipal school from Vila Velha, ES. We have collected the data through interviews to the students and classroom activities with the cited unities. Our analysis from the students’ answers to the diagnostic tests and the collected data in the study indicate to us that tangram, geoboards and kites are didactical materials which help in the visual recognition of polygons and its characteristics. The didactical research activities helped the polygon concept formation and the discussion of the concepts of convex and non convex polygons. We verified that the students were interested in the activities, learned with them and led us to search how to label polygons with more than 20 sides. We believe that we could have explored more the potential of such didactical materials if instead of using for so long each material we would have prepared smaller didactical sequences incorporating the use of the three materials