Quantifying Path Length: Fourth-Grade Children's Developing Abstractions for Linear Measurement

This article describes how children build increasingly abstract knowledge of linear measurement, emphasizing ways they relate space and number. Assessments indicate children struggle to understand measurement, especially concepts related to complex paths as in perimeter tasks. This article draws on developmental accounts of children's knowledge of measurement to describe the coordination of cognitive processes as a progression through increasingly abstract layers of strategy (Clements, 2003; Lehrer, 2003) within a constructivist perspective (Steffe & Cobb, 1988; Steffe & Thompson, 2000). This article reports 4 case studies from a 6-month teaching experiment with Grade 4 students to examine ways of promoting their strategy development. Attending to children's understanding of length along straight objects alone proved inadequate in predicting and validating models of children's developing strategies and concepts for perimeter. Setting perimeter tasks that emphasized integral relations among unit of length, sides of polygons and perimeter, and prompting children to integrate partitive, iterative, and counting schemes appeared to promote increasingly abstract length measurement strategies. The researchers came to distinguish between a naïve use of units to find length (Level 2a) and a more abstract strategy for unitizing and iterating (Level 2b), extending an earlier framework (Clements, Battista, Sarama, Swaminathan, & McMillen, 1997). Finally, implications for instruction are drawn from the development of tasks and questioning sequences.