ERIC Number: EJ1000940
Record Type: Journal
Publication Date: 2013-Jun
Abstractor: As Provided
Reference Count: 28
Making Sense by Measuring Arcs: A Teaching Experiment in Angle Measure
Moore, Kevin C.
Educational Studies in Mathematics, v83 n2 p225-245 Jun 2013
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.
Descriptors: Geometric Concepts, Measurement, Calculus, Comprehension, Students, Mathematics Instruction, Logical Thinking
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Publication Type: Journal Articles; Reports - Research
Education Level: N/A
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