Jeffrey E. Barrett

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 childrens 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 childrens understanding of length along straight objects alone proved inadequate in predicting and validating models of childrens 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.

Surveying Current Research on Young Children's Mathematical Learning: A Review of Reconceptualizing Early Mathematics Learning

In Reconceptualizing Early Mathematics Learning, editors Lyn English and Joanne Mulligan present a widely varying collection of research and initiatives within the field of early mathematics education research, providing a thoughtful argument for further investment and work in this developing field of study. Among the diverse contributions to this volume, the editors have included (a) a narration of how the historical development of research in sociology, philosophy of education, mathematics, and the sciences contributes to the present perspectives and theoretical orientation of early childhood researchers, (b) a report of the use of iPad technology that provides interactive instruction for young children learning about number, and (c) a survey of several professional development programs that emphasize young learners’ awareness of structure in mathematical settings. The collection of research reported here provides a lively engagement with some important topics in early mathematics education research. One challenge for an edited collection of reports from a given field is organizing it along themes in a sequence that helps the reader understand the trends and issues. Rather than reading the book from cover to cover, we suggest reading groups of chapters identified by theme.