infojournalИнформатика и образованиеInformatics and education0234-04532658-7769Publishing House Education and Informatics10.32517/0234-0453-2023-38-1-83-91infojournal-924Research ArticleЗАРУБЕЖНЫЙ ОПЫТFOREIGN EXPERIENCEРазрешение студентами некоторых парадоксов бесконечности в объективе методологии гроссуанаStudents’ resolutions of some paradoxes of infinity in the lens of the grossone methodologyhttps://orcid.org/0000-0002-1314-5992НасрЛ.NasrL.

Наср Лейла, аспирант, педагогический факультет

Бейрут

Layla Nasr, Ph.D. student, Faculty of Education

Beirut

Laylanasr1@hotmail.comЛиванский университетЛиванLebanese UniversityLebanon2023160420233818391Copyright © Наср Л., 20232023Наср Л.Nasr L.This work is licensed under a Creative Commons Attribution 4.0 License.https://info.infojournal.ru/jour/article/view/924

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.

In the article, students’ responses to some classical paradoxes related to infinity were investigated by considering the traditional methods and later by considering a new methodology for dealing with infinity (grossone methodology) which was introduced to them briefly. Eleven students of grade 12 participated in this study.

In phase 1, the students (who study in the traditional methods) provided their intuitive resolutions to three paradoxes of infinity. In phase 2, the students were introduced to the grossone methodology after which they were asked to resolve the same paradoxes using this methodology in phase 3. After being presented by the normative and the grossone-based resolutions, the students reflected on them inwriting.

Results of this study showed that students’ intuitive solutions were similar to grossone-based solutions of the three considered paradoxes. Therefore, the students accepted those solutions.

This study shows the relevance of using an alternative method, which is the grossone methodology, in order to simplify resolutions of some paradoxical situations with infinity for undergraduate students.

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The authors declare that there are no conflicts of interest present.