Student Understanding of Linear Combinations of Eigenvectors

Autor/inn/en	Wawro, Megan; Watson, Kevin; Zandieh, Michelle
Titel	Student Understanding of Linear Combinations of Eigenvectors
Quelle	In: ZDM: The International Journal on Mathematics Education, 51 (2019) 7, S.1111-1123 (13 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Wawro, Megan)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-018-01022-8
Schlagwörter	Mathematics Instruction; Mathematical Logic; Multiple Choice Tests; Abstract Reasoning; Advanced Courses; Geometric Concepts; Algebra; Equations (Mathematics); Concept Formation; Mathematical Concepts; Mathematics Tests + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Multiple choice examinations; Multiple-choice tests, Multiple-choice examinations; Multiple-Choice-Verfahren; Abstraktes Denken; Denken; Fortgeschrittenenunterricht; Elementare Geometrie; Equations; Mathematics; Gleichungslehre; Concept learning; Begriffsbildung
Abstract	To contribute to the sparse educational research on student understanding of eigenspace, we investigated how students reason about linear combinations of eigenvectors. We present results from student reasoning on two written multiple-choice questions with open-ended justifications involving linear combinations of eigenvectors in which the resultant vector is or is not an eigenvector of the matrix. We detail seven themes that analysis of our data revealed regarding student responses. These themes include: determining if a linear combination of eigenvectors satisfies the equation A\varvec{x}=\lambda \varvec{x} reasoning about a linear combination of eigenvectors belonging to a set of eigenvectors; conflating scalars in a linear combination with eigenvalues; thinking eigenvectors must be linearly independent; and reasoning about the number of eigenspace dimensions for a matrix. In the discussion, we explore how themes sometimes cut across questions and how looking across questions gives insight into individuals' conceptions of eigenspace. Implications for teaching and future research are also offered. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2020/1/01