José Anastácio da Cunha (1744-1787) e aspectos de seu ensino: “Sobre a natureza das quantidades negativas”

• Autor(a) principal: Santos, Ângela Maria dos
• Data de Publicação: 2018
• Tipo de documento: Tese
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da PUC_SP
• Texto Completo: https://tede2.pucsp.br/handle/handle/21278
• topic: Cunha, José Anastácio da [1744-1787]; Números negativos; Matemática - Estudo e ensino; Numbers, Negative; Mathematics - Study and teaching; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

This study focuses on José Anastácio da Cunha (1744-1787) and the manner in which he conceived and performed the teaching of mathematics. Selected letters from 1785, addressing a debate about negative quantities, constituted the primary sources for examining da Cunha’s teaching practice. The study articulates ponderations on mathematical education—drawing on the views of Glaeser and Schubring on epistemological obstacles—and the history of mathematics—based on Veyne, Le Goff, and Grattan-Guinness with regard to core definitions of history and the treatment of source documents. In order to examine da Cunha’s teaching in this context, the articulation took the form of a narrative primarily based on original documents, considering the context in which events took place, subsequently evidencing the range of conceptions about negative quantities that coexisted in his time, and the possible epistemological obstacles encountered. As far as possible, the narrative conveyed in the letters was reconstructed, supporting the identification of the personages and teaching institutions involved and highlighting the mathematical concepts and definitions addressed. This effort shed light on da Cunha’s unique approach amid the clash of ideas that occurred at the time with regard to the nature of negative quantities, revealing him as an exemplary teacher, in the best sense of the word. The documents analyzed revealed da Cunha to be a mathematician concerned with rigor and the value of demonstrations—a stance evident from his earliest readings of mathematical books and later echoed in his oeuvre and teaching-related activities. In his professorial practice, he was not only receptive to debating on an extensive range of contents, but proved respectful of his interlocutors as human beings, regardless of class or social status. Da Cunha was also open to questioning about matters for which he had no definitive answers, and encouraged his students to outdo him and, if necessary, correct his conclusions. The present analysis of his teaching-related activities in the realm of negative integers revealed da Cunha to have been a teacher concerned with the future careers of his students and alumni and a mathematician who strove to promote the furthering of knowledge