The Linear Imperative: An Inventory and Conceptual Analysis of Students Overuse of Linearity

Autor/inn/en	Van Dooren, Wim; De Bock, Dirk; Janssens, Dirk; Verschaffel, Lieven
Titel	The Linear Imperative: An Inventory and Conceptual Analysis of Students Overuse of Linearity
Quelle	In: Journal for Research in Mathematics Education, 39 (2008) 3, S.311-342 (32 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0021-8251
Schlagwörter	Mathematics Instruction; Mathematical Logic; Problem Solving; Mathematical Concepts; Word Problems (Mathematics); Graphs; Probability; Algebra; Calculus; Number Concepts; Geometry + Suchen Sie Ihr Suchwort? Mathematics lessons; Mathematikunterricht; Mathematical logics; Mathematische Logik; Problemlösen; Textaufgabe; Grafische Darstellung; Wahrscheinlichkeitsrechnung; Wahrscheinlichkeitstheorie; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Number concept; Zahlbegriff; Geometrie
Abstract	The overreliance on linear methods in students' reasoning and problem solving has been documented and discussed by several scholars in the field. So far, however, there have been no attempts to assemble the evidence and to analyze it is a systematic way. This article provides an overview and a conceptual analysis of students' tendency to use linear methods beyond their applicability range. We start from an analysis of the linearity concept and its properties and representations. The main part consists of a summary and discussion of unwarranted applications of each of these properties and representations in various mathematical content domains in order to unravel similarities and differences. After that, we speculate on the factors that seem to be at the roots of the occurrence and persistence of the overreliance on linearity. Finally, we discuss educational implications and suggest perspectives for future research. (Contains 3 footnotes, 4 figures, and 1 table.) (Author).
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