Conceito de área: da composição e decomposição de figuras até as fórmulas




The objective of this research is to investigate across the use of composition and decomposition of plan forms, until the demonstration of the formula, how the area concept can be showed in the significative and motivating way to the students. To do it, we direct our studies from some hypothesis: 􀀹 How the reconfiguration processes of polygon forms contribute to the assumption of the polygon area concept? 􀀹 How this process benefits the passage of the empirical to deductive? We basis our research in the theory Duval purpose and in your different ways to learn a form, detaching mainly the operative apprehension, in the Vergnaud theory, about the fields concepts , in the development geometric idea of the Parzysz and the Freudenthal ideas about on local organization in a deductive process and in a dynamic geometry using the software Cabri-Géomètre. Through of the engineering didactic methodology, we developed a teaching didactic sequence formed by three blocks. In the first block, the activities was developed using concrete material, which all deductions and validations was realized in an empirical form. In the second block, it was realized in an informatics laboratory, using a resource called Cabri-Géomètre (software), the same observation made before was verified and validated across the geometrics constructions, indicating the mathematic properties existing in the forms across of the dynamic geometry. In the third block, across the deductive activities, which objective to introduce the formulas to the area calculus, we find to systematize which was verified in the blocks earlier. The experiment analysis of the sequences showed that the process of the plan polygon forms reconfiguration contributed to the appropriation of the area concept and this process was very significant and helpful to the passage between empirical and deductive


matematica -- estudo e ensino decomposition matematica reconfiguração geometria Área decomposição reconfiguration geometry composição geometria educacao matematica area composition

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