Mediación de geometría dinámica en la demostración

Abstract

We are interested in finding teaching strategies that take advantage of the potential of dynamic geometry software to promote in students the spontaneous use of deductive reasoning to justify affirmations (introduction to the proof). We consider that students can use deductive reasoning implicitly in solving problems and we are interested in studying the conditions that lead to conclusions from initial data using logical implications, although they do not make explicit reference to such implications. This implicit use depends on the degree of conviction acquired on the implications that we call Geometric Events (HG), and we propose that this degree of conviction can be built thanks to the experimentation with the Software. We explore the variables that affect the design of a sequence of activities from the point of view of the Theory of Didactic Situations that seeks that students, through experimentation, identify HG and become convinced of its apodictic character, and then use those HG in reasoning implicit deductives to solve construction, verification, anticipation and proof problems. We propose the hypothesis that the fundamental situation that corresponds to the demonstration in the context of the geometric construction with SGD, is a situation in which, from a written construction protocol, it is requested to predict if certain properties are met and maintained when dragging.