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Amanda L. Miller and Jeffrey E. Barrett

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.

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Amanda L. Cullen, Cheryl L. Eames, Craig J. Cullen, Jeffrey E. Barrett, Julie Sarama, Douglas H. Clements, and Douglas W. Van Dine

We examine the effects of 3 interventions designed to support Grades 2–5 children's growth in measuring rectangular regions in different ways. We employed the microgenetic method to observe and describe conceptual transitions and investigate how they may have been prompted by the interventions. We compared the interventions with respect to children's learning and then examined patterns in observable behaviors before and after transitions to more sophisticated levels of thinking according to a learning trajectory for area measurement. Our findings indicate that creating a complete record of the structure of the 2-dimensional array—by drawing organized rows and columns of equal-sized unit squares—best supported children in conceptualizing how units were built, organized, and coordinated, leading to improved performance.