INVENTION OR MATHEMATICAL CREATION AND DIDACTIC PHENOMENA

• Autor(a) principal: Menezes, Marcus Bessa de
• Data de Publicação: 2020
• Outros Autores: Moser, Alvino
• Tipo de documento: Artigo
• Idioma: por
• Título da fonte: Revista Reamec
• Texto Completo: https://periodicoscientificos.ufmt.br/ojs/index.php/reamec/article/view/10901
• topic: Invenção Matemática; Sala de aula de Matemática; Transposição Didática; Aprendizagem autônoma; Mathematical Invention; Mathematics classroom; Didactic Transposition; Autonomous learning

This theoretical essay aims to address the mathematical invention discussed by Jacques Hadamard and to relate it to teaching practice, based on existing didactic phenomena. This research justifies the fact that if mathematics is an invention or creation, and this assumption needs to be evidenced in the teaching objectives, since, in general, the teachers want the students to learn classical contents and ready to be appropriated by them. In part 2, of the text, Hadamard's concept of mathematical invention is presented, describing its four phases: preparation, incubation, lighting and verification; and to analyze, in the author's perspective, the role of the unconscious in mathematical illumination, supported, above all, by Poincaré's testimony. In part 3, it deals with the didactic phenomena that occur in the mathematics classroom (transposition and contract) and their roles for the student's autonomous learning. The research methodology is bibliographic and documentary. We have as main contribution the influence exerted by the phenomena, showing that it is not enough to adapt the knowledge to be taught, but also to verify what is effectively learned. The conclusion highlights that learning, as a phenomenon that takes place in the first person, requires the student's autonomy and, consequently, it is necessary to stimulate their potential for creativity which, instead of being content to appropriate the contents produced by specialists, seeks to build their own mathematical knowledge, encouraging him to be, in turn, an inventor or creator of his own solutions.