Reinventing Solutions to Systems of Linear Differential Equations: A Case of Emergent Models Involving Analytic Expressions

Autor/inn/en	Rasmussen, Chris; Blumenfeld, Howard
Titel	Reinventing Solutions to Systems of Linear Differential Equations: A Case of Emergent Models Involving Analytic Expressions
Quelle	In: Journal of Mathematical Behavior, 26 (2007) 3, S.195-210 (16 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0732-3123
DOI	10.1016/j.jmathb.2007.09.004
Schlagwörter	Instructional Design; Mathematics Education; Heuristics; Equations (Mathematics); Educational Environment; Mathematical Formulas; Calculus; Higher Education + Suchen Sie Ihr Suchwort? Lesson concept; Lessonplan; Unterrichtsentwurf; Mathematische Bildung; Heuristik; Equations; Mathematics; Gleichungslehre; Lernumgebung; Pädagogische Umwelt; Schulumwelt; Mathematische Formel; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Hochschulbildung; Hochschulsystem; Hochschulwesen
Abstract	An enduring challenge in mathematics education is to create learning environments in which students generate, refine, and extend their intuitive and informal ways of reasoning to more sophisticated and formal ways of reasoning. Pressing concerns for research, therefore, are to detail students' progressively sophisticated ways of reasoning and instructional design heuristics that can facilitate this process. In this article we analyze the case of student reasoning with analytic expressions as they reinvent solutions to systems of two differential equations. The significance of this work is twofold: it includes an elaboration of the Realistic Mathematics Education instructional design heuristic of emergent models to the undergraduate setting in which symbolic expressions play a prominent role, and it offers teachers insight into student thinking by highlighting qualitatively different ways that students reason proportionally in relation to this instructional design heuristic. (Author).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10