ERIC Number: ED443820
Record Type: Non-Journal
Publication Date: 1999
Reference Count: N/A
Quantifying Length: Children's Developing Abstractions for Measures of Linear Quantity in One-Dimensional and Two-Dimensional Contexts.
Barrett, Jeffrey E.; Clements, Douglas H.
The measurement and description of polygons and paths by elementary school students was studied from a constructivist point of view. A teaching experiment was devised to promote understanding of length based on the hypothesis that as children coordinate their number concept and their one-dimensional/two-dimensional spatial concepts they gain understanding of, and build more abstracted schemes for, length and perimeter. Four fourth graders were studied in the second semester of their academic year. Four themes were encountered in the study. Children quantified length by partitive operations and later by iterative operations, gradually restructuring their internal images. They coordinated their number sequence with their spatial images as they kept shifting from making visual comparisons between objects to quantifying the extent of partitioning operations. The children represented length when they curtailed their own movements through linear space, and they coordinated several linear quantities for an object by disembedding the linear aspects of the object in space. The children appeared to progress along four levels of strategy for length, and it is suggested that progress through these levels follows from increasing integration between conceptual knowledge and figural knowledge related to the measure of length. Children gained abstraction for length and perimeter concepts as they increased the correspondence between their counting scheme, their partitive scheme, and their iterative scheme. Six instructional strategies that supported the children in creating and recognizing relevant length structures and in reflecting on relations among measures of length taken along a complex figure are identified, and implications for instruction are discussed. (Contains 1 table, 8 figures, and 54 references.) (SLD)
Publication Type: Reports - Research
Education Level: N/A
Authoring Institution: N/A