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

• 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
• ISSN: 0021-8251; 1945-2306
• DOI: 10.2307/30035058

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.