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Problematic and Supportive Aspects of Indirect Proof in Afghan Undergraduate Students' Proofs of the Irrationality of [square root]3 and [square root]5/8

Artigo2023

Ahmad Khalid Mowahed; Jawed Ahmad Mayar

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Resumo

In this study, we aimed to find problematic and supportive issues in Afghan undergraduate students' proofs of the irrationality of [square root]3 and [square root]5/8 while using the indirect proof method. Collecting and analyzing produced proofs of 30 sophomore and 48 senior undergraduate students on the irrationality of [square root]3 and [square root]5/8, respectively, revealed that the majority were not able to extend indirect proof beyond showing the irrationality of [square root]2 due to not being able to apply the supportive 'multiples of an integer' notion in their reasoning process of the irrationality of [square root]3, and this notion was not supportive in the case of showing irrationality of [square root]5/8, and finally we propose the method of finding nonzero integral solutions to the resulted Diophantine equation and using the rational roots theorem to prove that [square root]p/q is irrational.

Dados da obra

Tipo
Artigo
Periódico
Mathematics Teaching Research Journal
Ano
2023
Idioma
en
Palavras-chave
Foreign Countries; Undergraduate Students; Mathematical Logic; Validity; Mathematics Education; Algebra
Temas
Álgebra, Cálculo
Acesso
Download disponível
Fontes
ERIC — Education Resources Information Center
Na Biblioteca desde
01/10/2026 · verificada em 03/10/2026

Como citar

ABNT
MOWAHED, Ahmad Khalid; MAYAR, Jawed Ahmad. Problematic and Supportive Aspects of Indirect Proof in Afghan Undergraduate Students' Proofs of the Irrationality of [square root]3 and [square root]5/8. Mathematics Teaching Research Journal, 2023. Disponível em: https://eric.ed.gov/?id=EJ1409364. Acesso em: 5 nov. 2026.

APA

Mowahed, A. K., & Mayar, J. A. (2023). Problematic and Supportive Aspects of Indirect Proof in Afghan Undergraduate Students' Proofs of the Irrationality of [square root]3 and [square root]5/8. Mathematics Teaching Research Journal. https://eric.ed.gov/?id=EJ1409364

BibTeX
@article{mowahed2023,
  author = {Mowahed, Ahmad Khalid and Mayar, Jawed Ahmad},
  title = {Problematic and Supportive Aspects of Indirect Proof in Afghan Undergraduate Students' Proofs of the Irrationality of [square root]3 and [square root]5/8},
  year = {2023},
  journal = {Mathematics Teaching Research Journal},
  url = {https://eric.ed.gov/?id=EJ1409364},
  language = {en}
}
RIS
TY  - JOUR
AU  - Mowahed, Ahmad Khalid
AU  - Mayar, Jawed Ahmad
TI  - Problematic and Supportive Aspects of Indirect Proof in Afghan Undergraduate Students' Proofs of the Irrationality of [square root]3 and [square root]5/8
PY  - 2023
JO  - Mathematics Teaching Research Journal
UR  - https://eric.ed.gov/?id=EJ1409364
LA  - en
ER  -

Referência gerada automaticamente a partir dos metadados das fontes; confira com o documento original. Baixar BibTeX · Baixar RIS

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