A geometria fractal no processo de ensino-aprendizagem-avaliação de probabilidade geométrica

Abstract

After a review of the literature on journal portals such as CAPES, and on several postgraduate program websites about the Geometric Probability theme, in thirty-eight years only thirty-three works had published, including dissertations, monographs, scientific articles, short courses and workshops. It is noteworthy that twenty-four of these works had located by Ritter and Bulegon (2016), presented in their article: “A literature Review on studies concerning the likelihood Geometric”. In it, the authors mapped the works published from 1982 to 2016. Another nine works were located through a search carried out for the preparation of this research, looking for publications from 2017 to 2020. Of all these works found, only two present the themes Geometric and Fractal Probability. In Addition, related to the fact of the Geometric Probability concept is not presenting in the most of the textbooks, also considering the necessity of promote the practice of the Mathematics’ teacher and the adequacy to BNCC (Base Nacional Comum Curricular), this work presents a sequence of teaching-learning-assessment of Geometric Probability for high school through results generated from Fractal Geometry. The theory of the Three Pedagogical Moments by Delizoicov and Angotti (1990) it is used as a methodological reference for the construction of the sequence. The suggested activities also take into account the concept of Manipulable Materials for the construction of Fractals. The teaching-learning-assessment sequence presented in this work addresses both two-dimensional and three-dimensional situations, since the results used to work the concept of Geometric Probability are generated from the construction and calculation of the area of the Sierpinski Triangle, which is a two-dimensional fractal, and the construction and calculation of the volume of the Menger Sponge, which is a three-dimensional fractal. This research is theoretical, of bibliographical exploratory nature, on the specific theme of Geometric Probability involving elements of Fractal Geometry. The foundations for conducting the research were given through the study of publications on the subjects considered. The teaching-learning-assessment sequence was not applied and, therefore, its efficiency in the teaching-learning process was not verified, leaving its application as a suggestion for future work.