Making sense by measuring arcs: a teaching experiment in angle measure View Full Text


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Article Info

DATE

2013-06

AUTHORS

Kevin C. Moore

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. More... »

PAGES

225-245

References to SciGraph publications

  • 2005-10. Students’ understanding of trigonometric functions in MATHEMATICS EDUCATION RESEARCH JOURNAL
  • 2007-12. The design of tasks in support of teachers’ development of coherent mathematical meanings in JOURNAL OF MATHEMATICS TEACHER EDUCATION
  • 2000-03. Development of angle concepts by progressive abstraction and generalisation in EDUCATIONAL STUDIES IN MATHEMATICS
  • 1994-03. Images of rate and operational understanding of the fundamental theorem of calculus in EDUCATIONAL STUDIES IN MATHEMATICS
  • 2000-01. Students' Development of Strategies for Turn and Angle Measure in EDUCATIONAL STUDIES IN MATHEMATICS
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    http://scigraph.springernature.com/pub.10.1007/s10649-012-9450-6

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