Transitional Points in Constructing the Preimage Concept in Linear Algebra

Autor/inn/en	Oktaç, Asuman; Vázquez Padilla, Rita; Ramírez Sandoval, Osiel; Villabona Millán, Diana
Titel	Transitional Points in Constructing the Preimage Concept in Linear Algebra
Quelle	In: International Journal of Mathematical Education in Science and Technology, 53 (2022) 5, S.1170-1189 (20 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Oktaç, Asuman) ORCID (Vázquez Padilla, Rita) ORCID (Ramírez Sandoval, Osiel) ORCID (Villabona Millán, Diana)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0020-739X
DOI	10.1080/0020739X.2021.1968523
Schlagwörter	Calculus; Mathematics Instruction; Introductory Courses; Schemata (Cognition); Task Analysis; Undergraduate Students; Mexicans; Intervention; Teaching Methods; Mathematical Concepts; Guidelines; Foreign Countries; Mexico + Suchen Sie Ihr Suchwort? Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Mathematics lessons; Mathematikunterricht; Einführungskurs; Cognition; Schema; Kognition; Aufgabenanalyse; Mexikaner; Teaching method; Lehrmethode; Unterrichtsmethode; Richtlinien; Ausland; Mexiko
Abstract	From an APOS (Action-Process-Object-Schema) theory perspective, learning mathematics involves construction of knowledge through mental mechanisms, which evolves between different mental structures or stages. The focus of this study is to explore how transition occurs from an Action to a Process conception, in the context of a task related to the learning of the concept of linear transformation in general, and the notion of preimage in particular. A questionnaire was designed and applied to 31 students from three different higher education institutions in Mexico, who were enrolled in an introductory linear algebra course. For the first time, transitional points known as "levels" are explicitly identified in the aforementioned context and empirical evidence is presented. Some difficulties resulting from the intervention of constructions related to the function concept are also pointed out. Discussion about the characteristics of levels in the APOS framework provides a theoretical contribution to the field. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01