Um estudo sobre a articulação entre validações empíricas e teóricas no ensino de Geometria com professores da rede pública - Trevisan, Eberson Paulo (2016)
SUMMARY: This research aims to analyze how essential mathematic elements learning is related, regarding the geometry, to the construction of educational proposals to work with empirical and theoretical validations developed by a group of teachers who teach mathematics in public schools of Mato Grosso. The elements taken as essential in the research come from the theories presented by Raymond Duval, specifically the Theory of Semiotics Representation Records and the differences between deductive speech and other forms of speech, and the several ways to view a picture and its relations with the different seizures in geometry presented by Durval. Methodologically, the work is part of a qualitative research approach where we seek to use some of the assumptions of the methodology of Didactic Engineering described by Artigue (1996) to obtain and sustain the elements presented in the research. The data generated and analyzed have aroused from the didactic work proposals made by teachers along with a set of pre-selected activities and separated into three classes according to certain characteristics that could favor the analysis of the use of the elements that emerged from previous analyzes. We emphasize that, as a result, we noticed the lack of value of the work with the preparation of validations that aimed to build theoretical tests, gaining empirical evidence where the vast majority are limited to pragmatic evidence, empiricism naive type, in classification Balacheff (1988). The produced theoretical tests often presented mathematical mistakes in their elaborations, but refer to the recognition of an own form of speech, the deductive one. Both theoretical tests and those produced empirically were presented with greater appreciation of the use of a perceptual apprehension of forms, and less search using the operative seizure and/or discursive which requires the application of an inventor look at the geometric figures favored by the dimensional deconstruction of form and needed to get new elements not initially provided for the use of new properties in the construction process of a mathematical proof in geometry. It is noteworthy, therefore, that we did not detect the presence of certain elements of the theory of Duval influencing buildings of validations, but the prominent absence of these figures and possibly directly influences the flow in the classroom.