Teaching Math to Young Children

EDUCATOR'S PRACTICE GUIDE

WHAT WORKS CLEARINGHOUSETM

Teaching Math to Young Children

NCEE 2014-4005 U.S. DEPARTMENT OF EDUCATION

The Institute of Education Sciences (IES) publishes practice guides in education to bring the best available evidence and expertise to bear on current challenges in education. Authors of practice guides combine their expertise with the findings of rigorous research, when available, to develop specific recommendations for addressing these challenges. The authors rate the strength of the research evidence supporting each of their recommendations. See Appendix A for a full description of practice guides.

The goal of this practice guide is to offer educators specific, evidence-based recommendations that address the challenge of teaching early math to children ages 3 to 6. The guide provides practical, clear information on critical topics related to teaching early math and is based on the best available evidence as judged by the authors.

Practice guides published by IES are available on our website at .

IES Practice Guide

Teaching Math to Young Children

November 2013

Panel

Douglas Frye (Chair) University of Pennsylvania Arthur J. Baroody University of Illinois at Urbana-Champaign and University of Denver Margaret Burchinal University of North Carolina Sharon M. Carver Carnegie Mellon University Children's School Nancy C. Jordan University of Delaware Judy McDowell School District of Philadelphia

Staff

M. C. Bradley Elizabeth Cavadel Julia Lyskawa Libby Makowsky Moira McCullough Bryce Onaran Michael Barna Mathematica Policy Research Marc Moss Abt Associates

Project Officers

Joy Lesnick Diana McCallum Institute of Education Sciences

NCEE 2014-4005 U.S. DEPARTMENT OF EDUCATION

This report was prepared for the National Center for Education Evaluation and Regional Assistance, Institute of Education Sciences under Contract ED-IES-13-C-0010 by the What Works Clearinghouse, which is operated by Mathematica Policy Research.

Disclaimer The opinions and positions expressed in this practice guide are those of the authors and do not necessarily represent the opinions and positions of the Institute of Education Sciences or the U.S. Department of Education. This practice guide should be reviewed and applied according to the specific needs of the educators and education agency using it, and with full realization that it represents the judgments of the review panel regarding what constitutes sensible practice, based on the research that was available at the time of publication. This practice guide should be used as a tool to assist in decisionmaking rather than as a "cookbook." Any references within the document to specific education products are illustrative and do not imply endorsement of these products to the exclusion of other products that are not referenced.

U.S. Department of Education Arne Duncan Secretary

Institute of Education Sciences John Q. Easton Director

National Center for Education Evaluation and Regional Assistance Ruth Neild Commissioner

November 2013 This report is in the public domain. Although permission to reprint this publication is not necessary, the citation should be:

Frye, D., Baroody, A. J., Burchinal, M., Carver, S. M., Jordan, N. C., & McDowell, J. (2013). Teaching math to young children: A practice guide (NCEE 2014-4005). Washington, DC: National Center for Education Evaluation and Regional Assistance (NCEE), Institute of Education Sciences, U.S. Department of Education. Retrieved from the NCEE website:

What Works Clearinghouse practice guide citations begin with the panel chair, followed by the names of the panelists listed in alphabetical order.

This report is available on the IES website at .

Alternate Formats On request, this publication can be made available in alternate formats, such as Braille, large print, or CD. For more information, contact the Alternate Format Center at (202) 260-0852 or (202) 260-0818.

Table of Contents

Teaching Math to Young Children

Table of Contents

Overview of Recommendations . . . . . . . . . . . . . . . . . . . . . . . . 1 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Institute of Education Sciences Levels of Evidence for Practice Guides . . . . . . . 4 Introduction to the Teaching Math to Young Children Practice Guide . . . . . . 7 Recommendation 1. Teach number and operations using a developmental progression . . 12 Recommendation 2. Teach geometry, patterns, measurement, and data analysis

using a developmental progression . . . . . . . . . . . . . . . . . . . . . . . . 25

Recommendation 3. Use progress monitoring to ensure that math instruction

builds on what each child knows . . . . . . . . . . . . . . . . . . . . . . . . . 36

Recommendation 4. Teach children to view and describe their world mathematically . . . 42 Recommendation 5. Dedicate time each day to teaching math, and integrate

math instruction throughout the school day . . . . . . . . . . . . . . . . . . . . 47

Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 Appendix A. Postscript from the Institute of Education Sciences . . . . . . . . . . . . 59 Appendix B. About the Authors . . . . . . . . . . . . . . . . . . . . . . . . 61 Appendix C. Disclosure of Potential Conflicts of Interest . . . . . . . . . . . . . . . 64 Appendix D. Rationale for Evidence Ratings . . . . . . . . . . . . . . . . . . . 65 Endnotes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

List of Tables

Table 1. Institute of Education Sciences levels of evidence for practice guides. . . . . . . 5 Table 2. Recommendations and corresponding levels of evidence . . . . . . . . . . .11 Table 3. Examples of a specific developmental progression for number knowledge . . . 13 Table 4. Common counting errors . . . . . . . . . . . . . . . . . . . . . . 19 Table 5. Examples of vocabulary words for types of measurement. . . . . . . . . . 32

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