Students' Coordination of Geometric Reasoning and Measuring Strategies on a Fixed Perimeter Task: Developing Mathematical Understanding of Linear Measurement

This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, w...

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Bibliographic Details
Published in:Journal for research in mathematics education 2006-05, Vol.37 (3), p.187-221
Main Authors: Barrett, Jeffrey E., Clements, Douglas H., Klanderman, David, Pennisi, Sarah-Jean, Polaki, Mokaeane V.
Format: Article
Language:English
Subjects:
Age Differences
Children
Cognition & reasoning
Comprehension
Coordinate systems
Elementary School Students
Geometric Concepts
Geometric shapes
Geometry
Grade 10
Grade 2
Identification
Logical Thinking
Mathematical Aptitude
Mathematical Logic
Mathematics education
Mathematics Instruction
Measurement
Measurement Techniques
New York
Observation
Reasoning
Rectangles
Secondary School Students
Straw
Student Development
Students
Triangles
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Summary:This article examines students' development of levels of understanding for measurement by describing the coordination of geometric reasoning with measurement and numerical strategies. In analyzing the reasoning and argumentation of 38 Grade 2 through Grade 10 students on linear measure tasks, we found support for the application and elaboration of our previously established categorization of children's length measurement levels: (1) guessing of length values by nai've visual observation, (2) making inconsistent, uncoordinated reference to markers as units, and (3) using consistent and coordinated identification of units. We elaborated two of these categories. Observations supported sublevel distinctions between inconsistent identification (2a) and consistent yet only partially coordinated identification of units (2b). Evidence also supported a distinction between static (3a) and dynamic (3b) ways of coordinating length; we distinguish integrated abstraction (3b) from nonintegrated abstraction (3a) by examining whether students coordinate number and space schemes across multiple cases, or merely associate cases without coordinating schemes.
ISSN:0021-8251
1945-2306
DOI:10.2307/30035058