Esquemas em ação para aprendizagem significativa da grandeza volume: implicações para a formação inicial de professores

Abstract

This research explored the schemes in action referring to the Volume Quantity, in the context of the initial formation of Mathematics teachers, by means of the elaboration and application of tests, whose proposed problem-situations articulated different ways of mathematical representations in order to be solved. According to Malheiros (2011), it is qualified as a research with a qualitative approach, which aims to explore the investigated phenomenon through descriptive and interpretative analysis. The target public were the students of the Mathematics Teachers Degree Program of the Universidade Federal de Santa Maria [Santa Maria State University] (UFSM), enrolled in the Spatial Geometry subject, during the second semester of 2017. The instruments for data collection were: official documents, observation, journal, survey and two tests, these with different aims, however the result of both are connected: the first is supported by the Meaningful Learning Theory, while the second is supported by the Theory of Conceptual Fields, which presents problem-situations of measurement, comparison and production, according to Baltar (1996), and that require the coordination between these kinds of representations (board): geometric, numeric and quantity, in accordance with Régine Douady and Marie-Jeanne Perrin-Glorian (1989). It has been checked that, in the face of the analyzed curricular reforms, the system of teaching/learning of the Spatial Geometry subject presents a gradual improvement. Nevertheless, it lacks of updating, before the constant demanding of official documents for education. It is highlighted, in the investigated context, that despite the notorious knowledge transmitted by the professor of the subject as well as the efficient use of the TIC’s as an educational resource, it is verified an issue which is out of the reach of whoever teaches the subject, since the struggles come from the absence and/or fragility of subsumer concepts, which are necessary for the learning of Volume as a quantity. Among these struggles, it is possible to highlight: the conversion of measurement units; application of theorems which sustain the resolution of problem-situations in the field of Spatial Geometry; comprehension of the area and volume independence of the form and its linear measurements. It has been also verified an emphasis in the geometric and numeric scenario as and obstacle for the learning of Volume as Quantity.