FORMULATION AND SOLVING PROBLEMS ABOUT VOLUME AND CAPACITY IN THE LIGHT OF THE THEORY OF CONCEPTUAL FIELDS
Problem Formulation and Resolution; Theory of Conceptual Fields; Volume and Capacity.
This research aims to analyze the formulation and resolution of problems (FRP) about volume and capacity by high school graduates, in 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: the goals and anticipations, the rules of action and the operational invariants related to these concepts. In this direction, we seek to answer the following questions: What are the similarities and differences presented by the students in the FRP of volume and/or capacity? What types of volume and/or capacity FRP activities do students have more or less difficulty with? Which rules of action and operative invariants are most recurrent in volume and/or capacity FRP?. We anchor the research in qualitative and quantitative approaches. We had the participation of one hundred and eleven students from a sailor training school, located in the metropolitan region of Recife. For the construction of data, six activities were proposed for the students to formulate and solve the problems formulated by them, namely: from a figure; from a given problem, create a similar one; from a given beginning continue the problem; of 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, continuing the problem and less difficulty in FRP from a given problem, creating a similar one. The FRP from a question was the one that presented more rules of action and similar operative invariants, while the one that presented the greatest dispersion was the FRP from a given beginning, continue a problem. In general, measurement situations using formulas and the transformation of measurement units were the most used in problems formulated by students, to the detriment of production and comparison situations.