A Method for Using Adjacency Matrices to Analyze the Connections Students Make within and between Concepts: The Case of Linear Algebra

Autor/inn/en	Selinski, Natalie E.; Rasmussen, Chris; Wawro, Megan; Zandieh, Michelle
Titel	A Method for Using Adjacency Matrices to Analyze the Connections Students Make within and between Concepts: The Case of Linear Algebra
Quelle	In: Journal for Research in Mathematics Education, 45 (2014) 5, S.550-583 (34 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-8251
Schlagwörter	Mathematics Instruction; Algebra; Mathematical Concepts; Concept Formation; Matrices; Introductory Courses; Teaching Methods; Interviews; College Mathematics; Mathematics Skills; Video Technology; Mathematical Logic + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Concept learning; Begriffsbildung; Matrizenrechnung; Einführungskurs; Teaching method; Lehrmethode; Unterrichtsmethode; Interviewing; Interviewtechnik; Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Mathematical logics; Mathematische Logik
Abstract	The central goals of most introductory linear algebra courses are to develop students' proficiency with matrix techniques, to promote their understanding of key concepts, and to increase their ability to make connections between concepts. In this article, we present an innovative method using adjacency matrices to analyze students' interpretation of and connections between concepts. Three cases provide examples that illustrate the usefulness of this approach for comparing differences in the structure of the connections, as exhibited in what we refer to as dense, sparse, and hub adjacency matrices. We also make use of mathematical constructs from digraph theory, such as walks and being strongly connected, to indicate possible chains of connections and flexibility in making connections within and between concepts. We posit that this method is useful for characterizing student connections in other content areas and grade levels. (As Provided).
Anmerkungen	National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191-1502. Tel: 800-235-7566; Tel: 703-620-3702; Fax: 703-476-2970; e-mail: orders@nctm.org; Web site: http://www.nctm.org/publications/
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10