Effects of Three Interventions on Children's Spatial Structuring and Coordination of Area Units

Author:
Amanda L. Cullen Illinois State University

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Cheryl L. Eames Southern Illinois University Edwardsville

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Craig J. Cullen Illinois State University

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Jeffrey E. Barrett Illinois State University

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Julie Sarama University of Denver

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Douglas H. Clements University of Denver

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Douglas W. Van Dine Marzano Research

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Volume/Issue:
Volume 49: Issue 5
Page(s):
533–574
DOI:
https://doi.org/10.5951/jresematheduc.49.5.0533
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Subjects:
Grade(s) or Audience, All grades PK-12, Grades 3-5, Third, Fourth, Grades PK-2, Second, Math Topic, Algebra, Algebraic Thinking/Pre-algebra Concepts, Algebraic Thinking, Geometry, Measurement, Perimeter/Area/Volume, Number, Number & Operations in Base Ten
Keywords:
Elementary grades; Geometric measurement; Learning trajectory; Spatial structuring; CCSS.Math.Content.4.MD.A.3; CCSS.Math.Content.4.NBT.B.5; CCSS.Math.Content.3.MD.C.7b; CCSS.Math.Content.3.MD.C.7a; CCSS.Math.Content.3.MD.C.6; CCSS.Math.Content.3.MD.C.5b; CCSS.Math.Content.3.MD.C.5a; CCSS.Math.Content.2.OA.C.4; CCSS.Math.Content.2.G.A.2

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.

Contributor Notes

Amanda L. Cullen, Department of Mathematics, Illinois State University, Campus Box 4520, Normal, IL 61790; almille@ilstu.edu

Cheryl L. Eames, Department of Mathematics and Statistics, Southern Illinois University Edwardsville, Campus Box 1653; 40 Hairpin Dr., Edwardsville, IL 62026; ceames@siue.edu

Craig J. Cullen, Department of Mathematics, Illinois State University, Campus Box 4520, Normal, IL 61790; cjculle@ilstu.edu

Jeffrey E. Barrett, Department of Mathematics, Illinois State University, Campus Box 4520, Normal, IL 61790; jbarrett@ilstu.edu

Julie Sarama, Morgridge College of Education, Marsico Institute for Early Learning and Literacy, Katherine A. Ruffatto Hall 154, 1999 East Evans Avenue, University of Denver, Denver, CO 80208-1700; Julie.Sarama@du.edu

Douglas H. Clements, Morgridge College of Education, Marsico Institute for Early Learning and Literacy, Katherine A. Ruffatto Hall 154, 1999 East Evans Avenue, University of Denver, Denver, CO 80208-1700; Douglas.Clements@du.edu

Douglas W. Van Dine, Marzano Research, 12577 East Caley Avenue, Centennial, CO 80111-6432; douglas.vandine@marzanoresearch.com

(Corresponding author is Cullen almille@ilstu.edu)
(Corresponding author is Eames ceames@siue.edu)
(Corresponding author is Cullen cjculle@ilstu.edu)
(Corresponding author is Barrett jbarrett@ilstu.edu)
(Corresponding author is Sarama Julie.Sarama@du.edu)
(Corresponding author is Clements Douglas.Clements@du.edu)
(Corresponding author is Van Dine douglas.vandine@marzanoresearch.com)
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Journal for Research in Mathematics Education
Cover Journal for Research in Mathematics Education
Copyright:
The National Council of Teachers of Mathematics, Inc. All rights reserved. 2018
Page Count:
42
Article Category:
Research Article
Print Publication Date:
01 Nov 2018
Online Publication Date:
Nov 2018
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