Scaling-Continuous Variation: Supporting Students' Algebraic Reasoning

Autor/inn/en	Ellis, Amy; Ely, Robert; Singleton, Brandon; Tasova, Halil
Titel	Scaling-Continuous Variation: Supporting Students' Algebraic Reasoning
Quelle	In: Educational Studies in Mathematics, 104 (2020) 1, S.87-103 (17 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-020-09951-6
Schlagwörter	Elementary School Students; Mathematics Skills; Thinking Skills; Algebra; Mathematical Logic + Suchen Sie Ihr Suchwort? Mathmatics achievement; Mathematics ability; Mathematische Kompetenz; Denkfähigkeit; Mathematical logics; Mathematische Logik
Abstract	This paper introduces a new mode of variational and covariational reasoning, which we call scaling-continuous reasoning. Scaling-continuous reasoning entails (a) imagining a variable taking on all values on the continuum at any scale, (b) understanding that there is no scale at which the continuum becomes discrete, and (c) re-scaling to any arbitrarily small increment for x and coordinating that scaling with associated values for y. Based on the analysis of a 15-h teaching experiment with two 12-year-old pre-algebra students, we present evidence of scaling-continuous reasoning and identify two implications for students' understanding of rates of change: seeing constant rate as an equivalence class of ratios, and viewing instantaneous rate of change as a potential rate. We argue that scaling-continuous reasoning can support a robust understanding of function and rates of change. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01