International Electronic Journal of Mathematics Education

Mental Constructions for The Group Isomorphism Theorem
  • Article Type: Research Article
  • International Electronic Journal of Mathematics Education, 2016 - Volume 11 Issue 2, pp. 377-393
  • Published Online: 01 Mar 2016
  • Article Views: 765 | Article Download: 1059
  • Open Access Full Text (PDF)
AMA 10th edition
In-text citation: (1), (2), (3), etc.
Reference: Mena-Lorca A, Parraguez AMM. Mental Constructions for The Group Isomorphism Theorem. Int Elect J Math Ed. 2016;11(2), 377-393.
APA 6th edition
In-text citation: (Mena-Lorca & Parraguez, 2016)
Reference: Mena-Lorca, A., & Parraguez, A. M. M. (2016). Mental Constructions for The Group Isomorphism Theorem. International Electronic Journal of Mathematics Education, 11(2), 377-393.
Chicago
In-text citation: (Mena-Lorca and Parraguez, 2016)
Reference: Mena-Lorca, Arturo, and Astrid Morales Marcela Parraguez. "Mental Constructions for The Group Isomorphism Theorem". International Electronic Journal of Mathematics Education 2016 11 no. 2 (2016): 377-393.
Harvard
In-text citation: (Mena-Lorca and Parraguez, 2016)
Reference: Mena-Lorca, A., and Parraguez, A. M. M. (2016). Mental Constructions for The Group Isomorphism Theorem. International Electronic Journal of Mathematics Education, 11(2), pp. 377-393.
MLA
In-text citation: (Mena-Lorca and Parraguez, 2016)
Reference: Mena-Lorca, Arturo et al. "Mental Constructions for The Group Isomorphism Theorem". International Electronic Journal of Mathematics Education, vol. 11, no. 2, 2016, pp. 377-393.
Vancouver
In-text citation: (1), (2), (3), etc.
Reference: Mena-Lorca A, Parraguez AMM. Mental Constructions for The Group Isomorphism Theorem. Int Elect J Math Ed. 2016;11(2):377-93.

Abstract

The group isomorphism theorem is an important subject in any abstract algebra undergraduate course; nevertheless, research shows that it is seldom understood by students. We use APOS theory and propose a genetic decomposition that separates it into two statements: the first one for sets and the second with added structure. We administered a questionnaire to students from top Chilean universities and selected some of these students for interviews to gather information about the viability of our genetic decomposition. The students interviewed were divided in two groups based on their familiarity with equivalence relations and partitions. Students who were able to draw on their intuition of partitions were able to reconstruct the group theorem from the set theorem, while those who stayed on the purely algebraic side could not. Since our approach to learning this theorem was successful, it may be worthwhile to gather data while teaching it the way we propose here in order to check how much the learning of the group isomorphism theorem is improved. This approach could be expanded to other group homomorphism theorems provided further analysis is conducted: going from the general (e.g., sets) to the particular (e.g., groups) might not always the best strategy, but in some cases we may just be turning to more familiar settings.

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