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Title: SOLVING PROBLEMS INVOLVING THE AREA OF PLANE FIGURES AS A GEOMETRIC QUANTITY, FROM THE PERSPECTIVE OF DIDACTIC TRANSPOSITION

Title: RESOLUÇÃO DE PROBLEMAS ENVOLVENDO ÁREA DAS FIGURAS PLANAS COMO GRANDEZA GEOMÉTRICA, SOB A ÓTICA DA TRANSPOSIÇÃO DIDÁTICA 

Author(s):  Manoel dos Santos, Severino

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Advisor: Filgueiras de Araújo, Hugo, PhD

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Date of document: December, 23-2021

Abstract:

The present study aimed to analyze the area approaches as autonomous geometrical magnitude, and the articulation between the numerical and geometrical aspects of these concepts in a collection of math textbooks from 6th to 9th grade of elementary school and the procedures used by the students. 9th grade in problem solving of the object of study, area of the flat figures. This analysis finds the theoretical foundation of Douady and Perrin-Glorian, Bellemain, Baltar and Santos who proposes the area model as greatness and in the theory of didactic transposition proposed by Yves Chellard that deals with the changes occurred in knowledge. The methodological procedures were based on Teixeira and had the analysis of a collection of mathematics textbooks and then there was an application of a test with students who use the books. Eighty students from four different grades all from the 9th grade of a public school in the city of Gravatá participated in this research. The activities of the test were built so that they could give students the freedom to choose the procedure to solve the proposed problems, seeking three aspects, one to bring to the test the variables proposed by the textbooks, the other was to disassociate the test of the test. textbook and finally, if the procedures used by the students would have a likely influence of the teacher. The results of this research indicate that the focus on quantities and geometric conceptions is insufficient and that numerical procedures are superior in all textual discussions. In both the textbooks and the procedures used by the students, the focus on numerical conception is evident, essentially on the prototypical figures presented by the textbooks. The analyzed collection privileges the numerical procedures in the area calculation and only in two moments works composition and area decomposition. This approach would count what is indicated in the literature review, early associating a number to surface which leads to a confusion between the length and area quantities. The proposed activities showed the prevalence of numerical aspects in the resolution of the area problems of the flat figures.

Keywords:  Textbook,  Area of Flat Figures, Numerical and Geometric Aspects,  Didactic Transposition.

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