Da história da matemática à sala de aula: explorando problemas históricos para o ensino de probabilidade

Abstract

The History of Mathematics, when implemented in teaching, can contribute to the construction of mathematical knowledge as well as to a shift towards a more positive and affective perception of Mathematics. This study aims to identify and analyze the pedagogical potential and limitations of a didactic approach based on historical problems for teaching probability in basic education. To achieve this, we designed and implemented a proposal based on three historical problems to teach probability concepts. The first is the Dice Problem, proposed by Galileo Galilei (1564 – 1642), which addresses concepts such as random experiments, sample space, events, and types of events. The second is the Problem of Points, which marks the beginning of probability theory and was solved by Blaise Pascal (1623 – 1662) and Pierre de Fermat (1601 – 1665). In this problem, we explored the definition of probability calculation. Lastly, the Monty Hall Dilemma, although having references to various versions in ancient texts, gained popularity through the TV show Let’s Make a Deal, hosted by Monty Hall, and the controversial solution submitted by Marilyn vos Savant (1946 – present). Here, we addressed the concepts of conditional probability. This proposal was implemented with a third-year high school class at a public school in a city in the southern region of Minas Gerais, involving 30 regularly enrolled students. Adopting a qualitative research approach, multiple data collection procedures were employed (field diary, completed activities, audio recordings), with the data analyzed by authors who suggest that a historical approach has the potential to change the perception of Mathematics and assist in the construction of mathematical knowledge. In this way, we identified and analyzed these potentials in the implemented proposal, highlighting that historical problems greatly contribute to the presentation of probability concepts while revealing Mathematics as a human construct. There is evidence of contributions for students, such as showing that no specific groups, such as men or geniuses, are predestined to practice Mathematics; demonstrating that the work of mathematicians is not necessarily solitary; showing the possibility of multiple solutions to the same problem, with their acceptance depending on historical context; and illustrating the relevance of mathematical or real-world problems in the construction of mathematical thought. Additionally, there are indications of contributions toward the presentation of mathematical concepts and theories, which allows us to understand certain reasons related to Mathematics. However, limitations were noted, such as the proposal not engaging all students due to reasons like lack of identification or difficulty in executing the activities.