Deduction and construction of a discrete probability function (Binomial and Geometric) with analytical development of expected value and variance

Abstract

The present work deals with the construction and deduction of a discrete probability function, where the objective is the understanding of the mathematical foundations of probability for its correct application, interpretation and verification in solving probability problems. For this purpose we rely on the theory of didactic situations of Brousseau (1997) and Sadovsky (2005). Teaching strategies are proposed with didactic model materials that improve student learning by promoting the analysis and understanding of various foundations of probability (Panizza, 2003). The importance of close communication between teachers and students in the teaching-learning process for the resolution, interpretation and verification of probability problems is highlighted. The software used in this research was Wolfram Mathematica, which facilitates mathematical writing, calculations, and the construction of graphs using a simple interface. This software makes work easier by fostering student autonomy in the development of skills for analysis and problem solving. We believe that these materials will contribute to the improvement of teaching-learning processes on the fundamentals and concepts of probability.