Разрешение студентами некоторых парадоксов бесконечности в объективе методологии гроссуана
https://doi.org/10.32517/0234-0453-2023-38-1-83-91
Аннотация
В статье описан опыт применения нового математического языка (методология гроссуана) в работе со старшими школьниками. В эксперименте приняли участие одиннадцать учащихся 12 класса средней школы в Ливане. Им было предложено решить классические парадоксы бесконечности двумя способами: традиционным и новым (методология гроссуана).
На первом этапе школьники, которые учатся по традиционной программе, предложили интуитивные решения трех парадоксов бесконечности. На втором этапе они изучили новый математический термин (гроссуан), после чего (на третьем этапе) разрешили те же парадоксы, используя новую методологию. Затем учащиеся сравнили результаты своих решений письменно.
Результаты этого эксперимента показали, что, используя гроссуан, школьники смогли решить парадоксы бесконечности (полностью или частично), а интуитивные решения учащихся были аналогичны решениям трех рассматриваемых парадоксов с применением гроссуана (поэтому школьники сочли их убедительными). Новый математический язык показал свою эффективность не только в решении вопросов бесконечности, но и в попытках шагнуть за пределы освоения математических понятий по теории APOS.
Данное исследование показывает актуальность использования альтернативного метода объяснения парадоксов бесконечности, которым является использование гроссуана, для школьников и студентов младших курсов.
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Рецензия
Для цитирования:
Наср Л. Разрешение студентами некоторых парадоксов бесконечности в объективе методологии гроссуана. Информатика и образование. 2023;38(1):83-91. https://doi.org/10.32517/0234-0453-2023-38-1-83-91
For citation:
Nasr L. Students’ resolutions of some paradoxes of infinity in the lens of the grossone methodology. Informatics and education. 2023;38(1):83-91. https://doi.org/10.32517/0234-0453-2023-38-1-83-91