EDUCATOR’S PRACTICE GUIDE WHAT WORKS CLEARINGHOUSE™ 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 http://whatworks.ed.gov. 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 Educa- tion. Retrieved from the NCEE website: http://whatworks.ed.gov 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 http://whatworks.ed.gov. 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 ( iii ) Table of Contents (continued) Table 6. Using informal representations . 43 Table 7. Linking familiar concepts to formal symbols . 44 Table 8. Examples of open-ended questions . 45 Table 9. Integrating math across the curriculum . 51 Table 10. Examples of tools that can be useful in each math content area . 52 Table D.1. Summary of studies contributing to the body of evidence, by recommendation . 67 Table D.2. Studies of early math curricula that taught number and operations and contributed to the level of evidence rating . 72 Table D.3. Studies of comprehensive curricula with an explicit math component that taught number and operations and contributed to the level of evidence rating . 76 Table D.4. Studies of targeted interventions that taught number and operations and contributed to the level of evidence rating . 81 Table D.5. Studies of interventions that taught geometry, patterns, measurement, or data analysis and contributed to the level of evidence rating . 94 Table D.6. Studies of interventions that used a deliberate progress-monitoring process and contributed to the level of evidence rating . 104 Table D.7. Studies of interventions that incorporated math communication, math vocabulary, and linking informal knowledge to formal knowledge and contributed to the level of evidence rating . 112 Table D.8. Studies of interventions that included regular math time, incorporated math into other aspects of the school day, and used games to reinforce math skills and contributed to the level of evidence rating . 121 List of Examples Example 1. The Basic Hiding game . 16 Example 2. The Hidden Stars game . 18 Example 3. The Concentration: Numerals and Dots game . 22 Example 4. The Shapes game . 29 Example 5. Creating and extending patterns . 31 Example 6. The Favorites game . 34 Example 7. The flow of progress monitoring . 39 Example 8. Progress-monitoring checklist . 40 Example 9. Linking large groups to small groups . 49 Example 10. Snack time . 50 E x a m p l e 11. The Animal Spots game . 54 List of Figures Figure 1. Modeling one-to-one counting with one to three items . 17 Figure 2. Sample cardinality chart . 20 Figure 3. Sample number list . 21 Figure 4. Combining and separating shapes . 28 Figure 5. Moving from simple to complex patterns . 30 Figure 6. The repetitive nature of the calendar . 30 Figure 7. An example of a math-rich environment in the classroom . 53 ( iv )( ) Overview of Recommendations Recommendation 1. Teach number and operations using a developmental progression. • First, provide opportunities for children to practice recognizing the total number of objects in small collections (one to three items) and labeling them with a number word without needing to count them. • Next, promote accurate one-to-one counting as a means of identifying the total number of items in a collection. • Once children can recognize or count collections, provide opportunities for children to use number words and counting to compare quantities. • Encourage children to label collections with number words and numerals. • Once children develop these fundamental number skills, encourage them to solve basic problems. Recommendation 2. Teach geometry, patterns, measurement, and data analysis using a developmental progression. • Help children to recognize, name, and compare shapes, and then teach them to combine and separate shapes. • Encourage children to look for and identify patterns, and then teach them to extend, correct, and create patterns. • Promote children’s understanding of measurement by teaching them to make direct comparisons and to use both informal or nonstandard (e.g., the child’s hand or foot) and formal or standard (e.g., a ruler) units and tools. • Help children to collect and organize information, and then teach them to represent that infor- mation graphically. Recommendation 3. Use progress monitoring to ensure that math instruction builds on what each child knows. • Use introductory activities, observations, and assessments to determine each child’s existing math knowledge, or the level of understanding or skill he or she has reached on a develop- mental progression. • Tailor instruction to each child’s needs, and relate