Tecnologias digitais no ensino de Função Afim: Estudo de caso a partir da Teoria Antropológica do Didático

Abstract

Digital Technology is increasingly present in the life of the human being and has been generating impacts in its various sectors of activity, as is the case of education. These impacts have been challenging teachers and the school community as a whole to reinvent their ways of acting, thus, our study intended to reflect this influence in the Mathematics teaching. For this purpose, we have set as an objective to analyse the set of conditions and restrictions which act on Mathematics knowledge diffusion, at the school institution, with the use of digital tools for the teaching of First Degree Polynomial Functions. This research assumes a qualitative nature, with an exploratory and descriptive characteristic, and in a case study format. It brings, as theoric contribution, the Anthropological Theory of the Didactic (ATD), from the French Yves Chevallard, and some reflections about the digital technology in teaching, with Borba and others. We have identified, as limitations and restrictions on the use of digital resources in the construction and in the communication of mathematical knowledge, aspects like: the physical infrastructure; the didactic book; the initial and continued formation of the teacher, as well as its conception about the use of technological resources; the school calendar; and even the fact that the school is full-time. Regarding the possibilities, we can mention aspects like: the dynamic explorations of linear function representation, the interactivity, the time optimization and the connections of graphic constructions and concepts - in a dialectic of the ostensive and non-ostensive objects. We conclude that the mathematical activities, from the praxeologies developed without the presence of the technology or when it was simply juxtaposed to the practice, were connected to techniques without a lot of complexity, through formulas and calculations algorithms. Whereas the praxeologies of the activities with the use of technologies gain, in addition to the optimization of time in the graphic constructions, a dynamism by means of the technique 'drag and observe'. This has an empirical aspect and assumes a different meaning proposed by the ATD, appears as an alternative concept. The 'drag and observe' can mediate the relation theoric-perceptual (in the ostensible dialectic of objects) and bring a new perspective in the praxeologies of mathematical activities, in the connections between mathematical representations, in the constructions of conjectures and inferences, which allow to understand properties and formalize concepts of linear function in a teaching through research.