Making Sense by Measuring Arcs: A Teaching Experiment in Angle Measure

Autor/in	Moore, Kevin C.
Titel	Making Sense by Measuring Arcs: A Teaching Experiment in Angle Measure
Quelle	In: Educational Studies in Mathematics, 83 (2013) 2, S.225-245 (21 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0013-1954
DOI	10.1007/s10649-012-9450-6
Schlagwörter	Geometric Concepts; Measurement; Calculus; Comprehension; Students; Mathematics Instruction; Logical Thinking + Suchen Sie Ihr Suchwort? Elementare Geometrie; Messverfahren; Analysis; Differenzialrechnung; Infinitesimalrechnung; Integralrechnung; Verstehen; Verständnis; Student; Schüler; Schülerin; Studentin; Mathematics lessons; Mathematikunterricht
Abstract	I discuss a teaching experiment that sought to characterize precalculus students' angle measure understandings. The study's findings indicate that the students initially conceived angle measures in terms of geometric objects. As the study progressed, the students formed more robust understandings of degree and radian measures by constructing an arc length image of angle measures; the students' quantification of angle measure entailed measuring arcs and conceiving multiplicative relationships between a subtended arc, a circle's circumference, and a circle's radius. The students leveraged these quantitative relationships to transition between units with a fixed magnitude (e.g., an arc length's measure in feet) and various angle measure units, while maintaining invariant meanings for angle measures in different units. These results suggest that quantifying angle measure, regardless of unit, through processes that involve measuring arc lengths can support coherent angle measure understandings. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10