Situações para a aprendizagem da prova - em matemática: Estado da pesquisa e questões em aberto
DOI:
https://doi.org/10.23925/1983-3156.2024v26i2p281-343Palavras-chave:
Didática da matemática, Teoria das situações didáticas, Prova, Demonstração, ArgumentaçãoResumo
Pesquisas sobre a complexidade epistêmica, lógica e discursiva da aprendizagem de provas têm gerado uma literatura abundante nas últimas duas décadas. Seus resultados contribuem para uma compreensão mais precisa das dificuldades encontradas pelos alunos e do trabalho dos professores. Sustentam a concepção de situações, em particular situações de validação no sentido da Teoria das Situações Didáticas (TSD) (Brousseau,1998), em que a prova funciona como ferramenta de resolução de problemas. No entanto, permanece a dificuldade de apreender a prova como objeto, a fim de reconhecer suas especificidades matemáticas e institucionalizá-la como tal. Este é o problema de que trata este texto. Este texto complementa as apresentações feitas no Seminário Nacional de Didática da Matemática, em 2017, e no [1]CORFEM, em 2019. O objetivo comum a essas três palestras era aprender e ensinar a prova antes da sua introdução [2]como uma forma canônica de prova em matemática. Após uma introdução que recorda o contexto institucional e científico, a primeira parte (secções 2 a 4) é dedicada ao estado da investigação, retomando os relatórios de trabalhos significativos, relacionados com diferentes abordagens; e a segunda parte (secção 5) apresenta propostas para formar uma base para a investigação futura. A conclusão centra-se nas questões abertas pela necessidade de engenharia situacional específica para incentivar e acompanhar a gênese e o reconhecimento dos padrões de prova na sala de aula de matemática, antes do ensino explícito da prova.
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