The Role of the Partitioning and Coset Algorithm Quotient Group Partial Meanings in Comprehending the First Isomorphism Theorem and Its Proof

Autor/inn/en	Melhuish, Kathleen; Guajardo, Lino; Dawkins, Paul C.; Zolt, Holly; Lew, Kristen
Titel	The Role of the Partitioning and Coset Algorithm Quotient Group Partial Meanings in Comprehending the First Isomorphism Theorem and Its Proof
Quelle	In: Educational Studies in Mathematics, 113 (2023) 3, S.499-517 (19 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Melhuish, Kathleen)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-023-10207-2
Schlagwörter	Algorithms; Comprehension; Mathematical Logic; Mathematical Concepts; Semiotics + Suchen Sie Ihr Suchwort? Algorithm; Algorithmus; Verstehen; Verständnis; Mathematical logics; Mathematische Logik; Semiotik
Abstract	In many advanced mathematics courses, comprehending theorems and proofs is an essential activity for both students and mathematicians. Such activity requires readers to draw on relevant meanings for the concepts involved; however, the ways that concept meaning may shape comprehension activity is currently undertheorized. In this paper, we share a study of student activity as they work to comprehend the First Isomorphism Theorem and its proof. We analyze, using an onto-semiotic lens, the ways that students' meanings for quotient group both support and constrain their comprehension activity. Furthermore, we suggest that the relationship between understanding concepts and proof comprehension can be reflexive: understanding of concepts not only influences comprehension activity, but engaging with theorems and proofs can serve to support students in generating more sophisticated understanding of the concepts involved. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01