id: 06656050
dt: j
an: 2016f.01108
au: Mena-Lorca, Arturo; Parraguez, Astrid Morales Marcela
ti: Mental constructions for the group isomorphism theorem.
so: Math. Educ. (Ank.) 11, No. 2, 377-393 (2016).
py: 2016
pu: International Society of Educational Research (iSER), Ankara
la: EN
cc: H45 C35
ut: APOS theory; equivalence relation; genetic decomposition; group isomorphism
theorem
ci:
li: doi:10.12973/iser.2016.2112a
ab: Summary: 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.
rv: