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Artículos

Vol. 11 N.º 1 (2008): Marzo

A SEARCH FOR A CONSTRUCTIVIST APPROACH FOR UNDERSTANDING THE UNCOUNTABLE SET P(N)

Enviado
maio 22, 2024
Publicado
2008-01-24

Resumo

No presente estudo nos preguntamos se os indivíduos constroem estruturas mentais para o conjunto P(N) que dá significado a expressão "todos os subconjuntos de N". Os aportes de nossa investigação em relação a esta pregunta tem duas vertentes. Primeiramente, indentificamos as perspectivas construtivistas que seriam ou poderiam ter sido utilizadas para descobrir os mecanismos de pensamento acerca dos conjuntos infinitos, em particular o conjunto dos números naturais. Segundo, para determinar se esses mecanismos de pensamento dos indivíduos em relação ao conjunto P(N) podem ser interpretados em termos de uma ou mais das perspectivas consideradas, analisamos a forma de pensar de oito matemáticos. Além das concepções negativas, isto é, de que P(N) não é, os resultados de nossas análises trouzeram a dúvida sobre se os indivíduos compreendem o conjunto P(N) além da definição formal. Falamos das possíveis implicações de nossas descobertas e indicamos futuros temas de investigação que poderão surgir deste estudo.

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