Teorema de Bayes: uma proposta para o ensino médio
Arquivos
Data
2022-11-18
Autores
Reis, Saulo Cavalcante dos 
Orientadores
Teles, Renato de Sá
Tipo
Dissertação de mestrado
Título da Revista
ISSN da Revista
Título de Volume
Resumo
Esta dissertação de mestrado objetiva apresentar uma proposta de ensino do Teorema de Bayes para alunos do ensino médio, tendo em vista o cumprimento de algumas competências a serem desenvolvidas nesses alunos segundo a BNCC. Antes de expor o teorema, uma história contemplando a origem e o desenvolvimento do teorema é apresentada de modo não-exaustivo, focando em personagens sem os quais o teorema não seria concebido como método sistemático de busca de conhecimento, ou sem os quais também não se poderia enxerga-lo como parte da matemática aplicada. Segue-se daí uma formalização teórica da probabilidade, fornecendo bases para os últimos dois capítulos. Primeiro, para que o experimento mental originário de Thomas Bayes seja corretamente compreendido e, segundo, mostrar duas propostas de ensino do teorema: facilitar a descoberta de informações faltantes ou desconhecidas na resolução de problemas da probabilidade, e também enquanto método de evitar vieses de julgamento probabilístico em situações da vida real.
This masters' dissertation seeks to propose a way of teaching Bayes' Theorem for High School students, aiming to accomplish certain goals in the development in students previously suggested in BNCC. Before presenting the theorem, a history concerning the origin and development of the subject is presented in a non-exaustive fashion, focusing on characters without whom the theorem would not be thought of as a systematic way of searching for knowledge, or without whom it would not be possible to see it as part of applied mathematics. Then, it is presented a formal theory of probability, thus providing the ground on which the last two chapters are founded. First, to make the mental experiment originating Bayes' theorem to be correctly grasped and, second, to show two proposals of teaching the theorem: to ease the discovery of missing or unknown information in problem solving, and also as a method to avoid biased probability judgements in real life situations.
This masters' dissertation seeks to propose a way of teaching Bayes' Theorem for High School students, aiming to accomplish certain goals in the development in students previously suggested in BNCC. Before presenting the theorem, a history concerning the origin and development of the subject is presented in a non-exaustive fashion, focusing on characters without whom the theorem would not be thought of as a systematic way of searching for knowledge, or without whom it would not be possible to see it as part of applied mathematics. Then, it is presented a formal theory of probability, thus providing the ground on which the last two chapters are founded. First, to make the mental experiment originating Bayes' theorem to be correctly grasped and, second, to show two proposals of teaching the theorem: to ease the discovery of missing or unknown information in problem solving, and also as a method to avoid biased probability judgements in real life situations.