Formulação e resolução de problemas sobre volume e capacidade à luz da Teoria dos Campos Conceituais

Abstract

This research aims at analyzing the Formulation and Resolution of Problems (FRP) about volume and capacity by students who graduated from High School, of a military training course, in the light of the Theory of Conceptual Fields. Among the contributions of this theory, we highlight the situations that give meaning to the concept of volume and capacity: measurement, comparison, and production, as well as the components of the schemes: goals and anticipations, action rules, and operational invariants related to these concepts. The question that guides this research is: What aspects to consider in the formulation and resolution of problems of the magnitudes volume and capacity, from the Theory of Conceptual Fields? We anchor the research in qualitative and quantitative methodologies. We had the participation of one hundred and eleven students of a military training school, located in the metropolitan region of Recife - PE. For the construction of data, six activities were proposed for the students to formulate and solve the problems formulated by the students, namely: from a figure; from a given problem, to create a similar one, from a given beginning, to continue the problem; from a question; from an answer and from a sentence. Data analysis allowed us to identify, among the results, that students had greater difficulty in FRP from a given beginning, to continue the problem, and less difficulty, in FRP from a given problem, to create a similar one. The FRP from a question was the one that presented more rules of action and similar operative invariants. In contrast, the one that presented the greatest dispersion was the FRP from a given beginning, to continue a problem. In general, the measurement situations using formulas and the transformation of measurement units were the most used in the problems formulated by the students, while the comparison and production situations were the least incidents.