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Students' Development of Length Concepts in a Logo-Based Unit on Geometric Paths

Douglas H. Clements, Michael T. Battista, Julie Sarama, Sudha Swaminathan, Sue McMillen 

January 1997, Volume 28, Issue 1, Page 70

Abstract:
We investigated the development of linear measure concepts within an instructional unit on paths and lengths of paths, part of a large-scale curriculum development project funded by the National Science Foundation (NSF). We also studied the role of noncomputer and computer interactions in that development. Data from paper-and-pencil assessments, interviews, and case studies were collected within the context of a pilot test of this unit with 4 third graders and field tests with 2 third-grade classrooms. Three levels of strategies for solving length problems were observed: (a) apply general strategies such as visual guessing of measures and naive guessing of numbers or arithmetic operations; (b) draw hatch marks, dots, or line segments to partition lengths to serve as perceptible units to quantify the length; (c) no physical partitioning--use an abstract unit of length, a "conceptual ruler," to project onto unsegmented objects. Those students who had connected numeric and spatial representations evinced different and more powerful problem-solving strategies in geometric situations than those who had forged fewer such connections.

Keywords:
Qualitative
Grades 3-5
Curriculum Developer
Conceptual Development
Connections / Applications
Higher Education
Geometry & Measurement
Teacher
Problem Solving / Problem Posing
Technology
Representation