Um estudo sobre a resolução algébrica e gráfica de sistemas lineares 3x3 no 2º ano do ensino médio

Abstract

The present study describes a qualitative research whose aim is to design, implement and analyze a didactic sequence that approaches the algebraic and graphical solutions of linear-quadratic systems with the aid of educational software Winplot. The didactic sequence was applied to students in the 2nd year of Colégio Madre Alix High School, a private institution located in Sao Paulo. Our objective was to answer the following research question: Can the high school students understand the resolution of 3 by 3 linear systems when using an approach that favors the conversion and processing of representation register coupled with a computing environment? In order to support our research process, we rely on Raymond Duval s Theory of Semiotic Representation Registers (2003) as we believe in the relevance of the records conversion while approaching to this subject in order to build the students knowledge. The chosen methodology was Artigue s Didactics Engineering assumptions (1996), as it is used in Mathematical Didactics Researches including an experimental part. The results of our research show the relevance of using the educational software Winplot as contributing to the visualization and understanding of solving linear systems in 3D. We hope that our research points towards further studies on the conversion of graphic record as a starting record. This study generated a product that contains a didactic sequence for teaching through activities that address the study of 2 by 2 and 3 by 3 linear systems where we contemplate the records and representations of natural language, algebraic, table and graphs which may better equip teachers