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Vol. 11 Núm. 1 (2008): Marzo

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

Enviado
mayo 22, 2024
Publicado
2008-01-24

Resumen

En el presente estudio nos preguntamos si los individuos construyen estructuras mentales para el conjunto P(N) que da significado a la expresión "todos los subconjuntos de N". Los aportes de nuestra investigación en relación con esta pregunta tienen dos vertientes. Primeramente, identificamos las perspectivas constructivistas que han sido o podrían haber sido utilizadas para describir los mecanismos de pensamiento acerca de los conjuntos infinitos, en particular el conjunto de los números naturales. Segundo, para determinar si estos mecanismos de pensamiento de los individuos acerca del conjunto P(N) pueden ser interpretados en términos de una o más de las perspectivas consideradas, analizamos la forma de pensar de ocho matemáticos. Mas allá de las concepciones negativas, o sea, de lo que P(N) no es, los resultados de nuestro análisis nos hicieron dudar sobre si la comprensión de los individuos del conjunto P(N) se extiende más allá de la definición formal. Hablamos de las posibles implicaciones de nuestros descubrimientos e indicamos futuros temas de investigación que podrían surgir de este estudio.

Citas

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