Big Math for Little Kids: The Effectiveness of a Preschool and Kindergarten Mathematics Curriculum

REFERENCES

• Arnold, D. H., & Doctoroff, G. L. (2003). The early education of socioeconomically disadvantaged children. Annual Review of Psychology, 54, 517–545.
   PubMed Web of Science ®Google Scholar
• Baroody, A. J., Lai, M.-L., & Mix, K. S. (2006). The development of young children's early number and operation sense and its implications for early childhood education. In B. Spodek & O. N. Saracho (Eds.), Handbook of research on the education of young children (2nd ed., pp. 187–221). Mahwah, NJ: Erlbaum.
   Google Scholar
• Bloom, H. S., Hill, C. J., Black, A. R., & Lipsey, M. W. (2008). Performance trajectories and performance gaps as achievement effect-size benchmarks for educational interventions (MDRC Working Papers on Research Methodology). New York, NY: MDRC.
   Google Scholar
• Bowman, B. T., Donovan, M. S., & Burns, M. S. (Eds.). (2000). Eager to learn: Educating our preschoolers. Washington, DC: National Academies Press.
   Google Scholar
• Brown, E. T. (2005). The influence of teachers’ efficacy and beliefs regarding mathematics instruction in the early childhood classroom. Journal of Early Childhood Teacher Education, 26, 239–257.
   Google Scholar
• Brush, L. R. (1978). Preschool children's knowledge of addition and subtraction. Journal for Research in Mathematics Education, 9, 44–54.
   Google Scholar
• Burkam, D. T., Ready, D. D., Lee, V. E., & LoGerfo, L. F. (2004). Social-class differences in summer learning between kindergarten and first grade: Model specification and estimation. Sociology of Education, 77, 1–31.
   Web of Science ®Google Scholar
• Campbell, F. A., Pungello, E. P., Miller-Johnson, S., Burchinal, M., & Ramey, C. T. (2001). The development of cognitive and academic abilities: Growth curves from an early childhood educational experiment. Developmental Psychology, 37, 231–242.
   PubMed Web of Science ®Google Scholar
• Casey, B., Kersh, J. E., & Young, J. M. (2004). Storytelling Sagas: An effective medium for teaching early childhood mathematics. Early Childhood Research Quarterly, 19, 167–172.
   Web of Science ®Google Scholar
• Chau, M. M., Thampi, K., & Wight, V. R. (2010, October). Basic facts about low-income children, 2009: Children under age 6. New York, NY: Columbia University, Mailman School of Public Health.
   Google Scholar
• Clements, D. H. (1999). Geometric and spatial thinking in young children. In J. V. Copley (Ed.), Mathematics in the early years (pp. 66–79). Reston, VA: National Council of Teachers of Mathematics.
   Google Scholar
• Clements, D. H., & Sarama, J. (2007). Early childhood mathematics learning. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 461–555). Charlotte, NC: Information Age.
   Google Scholar
• Clements, D. H., & Sarama, J. (2011, August 19). Early childhood mathematics intervention. Science, 333, 968–970.
   PubMed Web of Science ®Google Scholar
• Cross, C. T., Woods, T. A., & Schweingruber, H. (Eds.). (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington, DC: National Academies Press.
   Google Scholar
• Dodge, D. T., Colker, L. J., & Heroman, C. (2002). Connecting content, teaching, and learning: The Creative Curriculum for preschool (Rev. ed.). Washington, DC: Teaching Strategies.
   Google Scholar
• Douglas-Hall, A., Chau, M., & Koball, H. (2006). Basic facts about low-income children: Birth to age 18. New York, NY: National Center for Children in Poverty, Columbia University, Mailman School of Public Health.
   Google Scholar
• Dowker, A. (2005). Individual differences in arithmetic: Implications for psychology, neuroscience and education. New York, NY: Psychology Press.
   Google Scholar
• Duncan, G. J., Dowsett, C. J., Claessens, A., Magnuson, K., Huston, A. C., Klebanov, P. …Japel, C. (2007). School readiness and later achievement. Developmental Psychology, 43, 1428–1446.
   PubMed Web of Science ®Google Scholar
• Early, D. M., Iruka, I. U., Ritchie, S., Barbarin, O. A., Winn, D-M. C., Crawford, G. M. …Pianta, R. C. (2010). How do pre-kindergarteners spend their time? Gender, ethnicity, and income as predictors of experiences in pre-kindergarten classrooms. Early Childhood Research Quarterly, 25, 177–193.
   Web of Science ®Google Scholar
• Enders, C. K. (2010). Applied missing data analysis. New York, NY: Guilford Press.
   Google Scholar
• Entwisle, D. R., & Alexander, K. L. (1989). Early schooling as a “critical period” phenomenon. In K. Namboodiri & R. G. Corwin (Eds.), Sociology of education and socialization (Vol. 8, pp. 27–55). Greenwich, CT: JAI Press.
   Google Scholar
• Ertle, B. B., Ginsburg, H. P., Cordero, M. I., Curran, T. M., Manlapig, L., & Morgenlander, M. (2008). The essence of early childhood mathematics education and the professional development needed to support it. In A. Dowker (Ed.), Mathematical difficulties: Psychology and interventions (pp. 59–83). San Diego, CA: Elsevier.
   Google Scholar
• Gelman, R., & Gallistel, C. R. (1986). The child's understanding of number. Cambridge, MA: Harvard University Press.
   Google Scholar
• Ginsburg, H. P. (2006). Mathematical play and playful mathematics: A guide for early education. In D. G. Singer R. M. Golinkoff & K. Hirsh-Pasek (Eds.), Play = learning: How play motivates and enhances children's cognitive and social-emotional growth (pp. 145–165). New York, NY: Oxford University Press.
   Google Scholar
• Ginsburg, H. P., Cannon, J., Eisenband, J., & Pappas, S. (2006). Mathematical thinking and learning. In K. McCartney & D. Phillips (Eds.), Blackwell handbook of early child development (pp. 208–229). Malden, MA: Blackwell.
   Google Scholar
• Ginsburg, H. P., Greenes, C. E., & Balfanz, R. (2003). Big Math for Little Kids. Parsippany, NJ: Dale Seymour Publications, Pearson Learning Group.
   Google Scholar
• Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Social Policy Report—Giving Child and Youth Development Knowledge Away, 22(1), 1–24.
   Google Scholar
• Ginsburg, H., & Pappas, S. (2004). SES, ethnic, and gender differences in young children's informal addition and subtraction: A clinical interview investigation. Journal of Applied Developmental Psychology, 25, 171–192.
   Web of Science ®Google Scholar
• Ginsburg, H. P., Pappas, S., & Seo, K.-H. (2001). Everyday mathematical knowledge: Asking young children what is developmentally appropriate. In S. L. Golbeck (Ed.), Psychological perspectives on early childhood education: Reframing dilemmas in research and practice (pp. 180–216). Mahwah, NJ: Erlbaum.
   Google Scholar
• Gonzales, P., Williams, T., Jocelyn, L., Roey, S., Kastberg, D., & Brenwald, S. (2008). Highlights from TIMSS 2007: Mathematics and science achievement of US fourth- and eighth-grade students in an international context (NCES 2009–001 Rev.). Washington, DC: National Center for Education Statistics.
   Google Scholar
• Gormley, W. T. (2007). Early childhood care and education: Lessons and puzzles. Journal of Policy Analysis and Management, 26, 633–671.
   Web of Science ®Google Scholar
• Greenes, C., Ginsburg, H. P., & Balfanz, R. (2004). Big Math for Little Kids. Early Childhood Research Quarterly, 19, 159–166.
   Web of Science ®Google Scholar
• Griffin, S. (2007). Number Worlds: A mathematics intervention program for Grades preK–6. Columbus, OH: SRA/McGraw-Hill.
   Google Scholar
• Heckman, J. J. (2000). Policies to foster human capital. Research in Economics, 54, 3–56.
   Google Scholar
• Jordan, N. C., Glutting, J., Ramineni, C., & Watkins, M. W. (2010). Validating a number sense screening tool for use in kindergarten and first grade: Prediction of mathematics proficiency in third grade. School Psychology Review, 39, 181–195.
   Web of Science ®Google Scholar
• Jordan, N. C., Huttenlocher, J., & Levine, S. C. (1994). Assessing early arithmetic abilities: Effects of verbal and nonverbal response types on the calculation performance of middle- and low-income children. Learning and Individual Differences, 6, 413–432.
   Web of Science ®Google Scholar
• Kilpatrick, J., Swafford, J., & Findell, B. (Eds.). (2001). Adding it up: Helping children learn mathematics. Washington, DC: National Academies Press.
   Google Scholar
• Klein, A., Starkey, P., & Ramirez, A. B. (2002). Pre-K mathematics curriculum: Early childhood. Glenview, IL: Scott Foresman.
   Google Scholar
• Klibanoff, R. S., Levine, S. C., Huttenlocher, J., Vasilyeva, M., & Hedges, L. V. (2006). Preschool children's mathematical knowledge: The effect of teacher “math talk.” Developmental Psychology, 42, 59–69.
   PubMed Web of Science ®Google Scholar
• Kontos, S. (1999). Preschool teachers’ talk, roles, and activity settings during free play. Early Childhood Research Quarterly, 14, 363–382.
   Web of Science ®Google Scholar
• Kuhn, D. (2000). Metacognitive development. Current Directions in Psychological Science, 9, 178–181.
   Web of Science ®Google Scholar
• Layzer, J., Goodson, B., & Moss, M. (1993). Life in preschool: Volume one of an observational study of early childhood programs for disadvantaged four-year-olds. Cambridge, MA: Abt Associates.
   Google Scholar
• Lemke, M., & Gonzales, P. (2006). US student and adult performance on international assessments of educational achievement: Findings from “The Condition of Education, 2006” (NCES 2006–073). Washington, DC: National Center for Education Statistics.
   Google Scholar
• Ludwig, J., & Phillips, D. A. (2007, March). The benefits and costs of Head Start (National Bureau of Economic Research Working Paper No. w-12973). Retrieved from http://www.nber.org/papers/w12973.pdf
   Google Scholar
• Miller, K. F., & Parades, D. R. (1996). On the shoulders of giants: Cultural tools and mathematical development. In R. J. Sternberg & T. Ben-Zeev (Eds.), The nature of mathematical thinking (pp. 83–117). Mahwah, NJ: Erlbaum.
   Google Scholar
• Mullis, I. V. S., Martin, M. O., Beaton, A. E., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1997). Mathematics achievement in the primary school years: IEA's Third International Mathematics and Science Study (TIMSS). Chestnut Hill, MA: Boston College, Center for the Study of Testing, Evaluation, and Educational Policy.
   Google Scholar
• Mullis, I. V. S., Martin, M. O., Beaton, A. E., Gonzalez, E. J., Kelly, D. L., & Smith, T. A. (1998). Mathematics and science achievement in the final year of secondary school: IEA's Third International Mathematics and Science Study (TIMMS). Chestnut Hill, MA: Boston College, Center for the Study of Testing, Evaluation, and Educational Policy.
   Google Scholar
• Muthén, B., & Muthén, L. (2007). Mplus (Version 5) [Computer software]. Los Angeles, CA: Authors.
   Google Scholar
• Najarian, M., Snow, K., Lennon, J., & Kinsey, S. (2010). Early Childhood Longitudinal Study, Birth Cohort (ECLS-B), preschool–kindergarten 2007 psychometric report (NCES 2010–009). Washington, DC: National Center for Education Statistics.
   Google Scholar
• National Assessment of Educational Progress. (2011). The nation's report card: Mathematics 2011 (NCES 2012–458). Washington, DC: National Center for Education Statistics.
   Google Scholar
• National Association for the Education of Young Children and National Council of Teachers of Mathematics. (2010). Early childhood mathematics: Promoting good beginnings. Retrieved from www.naeyc.org/files/naeyc/file/positions/psmath.pdf
   Google Scholar
• National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
   Google Scholar
• National Governors Association Center for Best Practices and Council of Chief State School Officers. (2010). Common Core State Standards: Mathematics standards. Retrieved from http://www.corestandards.org/the-standards
   Google Scholar
• National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.
   Google Scholar
• Organisation for Economic Co-operation and Development. (2013). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know. Paris, France: Author.
   Google Scholar
• Pappas, S., Ginsburg, H. P., & Jiang, M. (2003). SES differences in young children's metacognition in the context of mathematical problem solving. Cognitive Development, 18, 431–450.
   Web of Science ®Google Scholar
• Pianta, R. C., Barnett, W. S., Burchinal, M., & Thornburg, K. R. (2009). The effects of preschool education: What we know, how public policy is or is not aligned with the evidence base, and what we need to know. Psychological Science in the Public Interest, 10, 49–88.
   PubMedGoogle Scholar
• Pianta, R. C., & La Paro, K. (2003). Improving early school success. Educational Leadership, 60, 24–29.
   Web of Science ®Google Scholar
• Rathbun, A., West, J., & Hausken, E. G. (2004). From kindergarten through third grade: Children's beginning school experiences (NCES 2004–007). Washington, DC: National Center for Education Statistics.
   Google Scholar
• Raudenbush, S. W., Spybrook, J., Congdon, R., Liu, X. F., Martinez, A., & Bloom, H. (2011). Optimal design software for multi-level and longitudinal research (Version 3.01) [Software]. Retrieved from www.wtgrantfoundation.org
   Google Scholar
• Reynolds, A. J., & Ou, S. (2003). Promoting resilience through early childhood intervention. In S. S. Luthar (Ed.), Resilience and vulnerability: Adaptation in the context of childhood adversities (pp. 436–459). New York, NY: Cambridge University Press.
   Google Scholar
• Rudd, L. C., Lambert, M. C., Satterwhite, M., & Zaier, A. (2008). Mathematical language in early childhood settings: What really counts? Early Childhood Education Journal, 36, 75–80.
   Google Scholar
• Schafer, J. L. (1999). Multiple imputation: A primer. Statistical Methods in Medical Research, 8, 3–15.
   PubMed Web of Science ®Google Scholar
• Schafer, J., & Graham, J. W. (2002). Missing data: Our view of state of the art. Psychological Methods, 7, 147–177.
   PubMed Web of Science ®Google Scholar
• Seo, K.-H., & Ginsburg, H. P. (2004). What is developmentally appropriate in early childhood mathematics education? Lessons from new research. In D. H. Clements J. Sarama & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 91–104). Mahwah, NJ: Erlbaum.
   Google Scholar
• Siegler, R. L. (2010, March). Teaching the meaning of numbers. Paper presented at the Annual Tisch Lecture, Teachers College, Columbia University, New York, NY.
   Google Scholar
• Sophian, C. (2004). Mathematics for the future: Developing a Head Start curriculum to support mathematics learning. Early Childhood Research Quarterly, 19, 59–81.
   Web of Science ®Google Scholar
• Starkey, P., & Klein, A. (2008). Sociocultural influences on young children's mathematical knowledge. In O. N. Saracho & B. Spodek (Eds.), Contemporary perspectives on mathematics in early childhood education (pp. 253–276). Charlotte, NC: Information Age.
   Google Scholar
• Stevenson, H., Lee, S. S., & Stigler, J. (1986, February 14). Mathematics achievement of Chinese, Japanese, and American children. Science, 231, 693–699.
   PubMed Web of Science ®Google Scholar
• Stipek, D. (2004). Teaching practices in kindergarten and first grade: Different strokes for different folks. Early Childhood Research Quarterly, 19, 548–568.
   Web of Science ®Google Scholar
• Young-Loveridge, J. M. (2004). Effects on early numeracy of a program using number books and games. Early Childhood Research Quarterly, 19, 82–98.
   Web of Science ®Google Scholar