, Volume 48, Issue 7, pp 961–975 | Cite as

Psychometric analyses of the Birthday Party

  • Young-Sun Lee
Original Article


The present research focuses on the psychometric properties of the Birthday Party measure for ages 3–5. The Birthday Party was developed to provide a reliable, valid, and engaging measure of early mathematical content—Number and Operation, Shape, Space, and Pattern—that can be given in either a short or a long form to English and Spanish speakers. 522 preschoolers (147 for age three, 226 for age four, and 149 for age five) were tested with both the Birthday Party and a criterion measure: the mathematics portion of the Young Children’s Achievement Test to examine reliability and validity. Overall, the technical adequacy of the Birthday Party was established as follows: (1) the results indicated that the Birthday Party was reliable and showed evidence to support both criterion and construct validity, (2) the Spanish version of the Birthday Party displayed adequate reliability and validity results, as well as equivalence with the English version of the Birthday Party, and (3) a short version of the Birthday Party is available as a screening measure to help aid in the early identification of children who are weak in foundational mathematical skills and add to the Birthday Party’s practicality and usability.


Early mathematics assessment Reliability Validity 


  1. Allen, M. J., & Yen, W. M. (1979, reissued in 2002). Introduction to measurement theory. Waveland Press, Inc.Google Scholar
  2. Baker, F. B., & Kim, S.-H. (2004). Item response theory: Parameter estimation techniques (2nd ed.). New York: Dekker.Google Scholar
  3. Baroody, A. J. (1987). Children’s mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teachers College Press.Google Scholar
  4. Baroody, A. J., Cibulsksis, M., Lai, M., & Li, X. (2004). Comments on the use of learning trajectories in curriculum development and research. Mathematical Thinking and Learning, 6, 227–260.CrossRefGoogle Scholar
  5. Baroody, A. J., Lai, M., & 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. Saracho (Eds.), Handbook of research on the education of young children (Vol. 2). Mahwah, NJ: Erlbaum.Google Scholar
  6. Bowman, B. T., Donovan, M. S., & Burns, M. S. (Eds.). (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy Press.Google Scholar
  7. Brush, L. R. (1978). Preschool children’s knowledge of addition and subtraction. Journal for Research in Mathematics Education, 9, 44–54.CrossRefGoogle Scholar
  8. Casey, B., Kersh, J. E., & Young, J. M. (2004). Storytelling sagas: An effective medium for teaching early childhood mathematics. Early Childhood Research Quarterly, 19(1), 167–172.CrossRefGoogle Scholar
  9. Clements, D. H. (2004). Geometric and spatial thinking in early childhood education. In D. H. Clements, J. Sarama, & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 267–297). Mahwah, NJ: Lawrence Earlbam Associates, Publishers.Google Scholar
  10. Clements, D. H., Copple, C., & Hyson, M. (2002). Early childhood mathematics: Promoting good beginnings. A joint position statement of the National Association for the Education of Young Children (NAEYC) and the National Council of Teachers of Mathematics (NCTM) (revised ed.). Washington, DC: National Association for the Education of Young Children/National Council of Teachers of Mathematics.Google Scholar
  11. Clements, D. H., & Sarama, J. (Eds.). (2004). Hypothetical learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2).Google Scholar
  12. Clements, D. H., Swaminathan, S., Hannibal, M. A. Z., & Sarama, J. (1999). Young children’s concepts of shape. Journal for Research in Mathematics Education, 30(2), 192–212.CrossRefGoogle Scholar
  13. Crocker, L., & Algina, J. (1986, reprinted in 2006, 2008). Introduction to classical and modern test theory. Belmont, CA: Wadsworth.Google Scholar
  14. Denton, K., & West, J. (2002). Children’s reading and mathematics achievement in kindergarten and first grade. Washington, DC: National Center for Education Statistics.Google Scholar
  15. Ertle, B., Rosenfeld, D., Presser, A., & Goldstein, M. (2016). Preparing preschool teachers to use and benefit from formative assessment: the Birthday Party assessment professional development system. ZDM Mathematics Education, 48(7). doi: 10.1007/s11858-016-0785-9
  16. Garrick, R., Threlfall, J., & Orton, A. (1999). Pattern in the nursery. In A. Orton (Ed.), Pattern in the teaching and learning of mathematics (pp. 1–17). London: Cassell.Google Scholar
  17. Geary, D., Bow-Thomas, C., Fan, L., & Siegler, R. (1993). Even before formal instruction. Chinese children outperform American children in mental addition. Cognitive Development, 8, 517–529.CrossRefGoogle Scholar
  18. Gelman, R., & Gallistel, C. R. (1986). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
  19. Ginsburg, H. P., Cannon, J., Eisenband, J. G., & Pappas, S. (2005a). Mathematical thinking and learning. In K. McCartney & D. Phillips (Eds.), Handbook of early child development. Oxford, England: Blackwell.Google Scholar
  20. Ginsburg, A., Cooke, G., Leinwand, S., Noell, J., & Pollock, E. (2005b). Reassessing US international mathematics performance: New findings from the 2003 TIMSS and PISA. Washington, DC: American Institutes for Research.Google Scholar
  21. Ginsburg, H. P., Choi Y.E., Lopez, L.S., Netley, R., & Chao-Yuan, C. (1997). Happy birthday to you: Early mathematical thinking of Asian, South American, and U.S. children. In T. Nunes & P. Bryant (Eds.), Learning and teaching mathematics: An international perspective (pp. 163–207). Hove (UK): Psychology Press.Google Scholar
  22. Ginsburg, H. P., & Pappas, S. (2016). Invitation to the birthday party: Rationale and description. ZDM Mathematics Education, 48(7) (this issue).Google Scholar
  23. Griffin, S. (2004a). Building number sense with Number Worlds: a mathematics program for young children. Early Childhood Research Quarterly, 19(1), 173–180.CrossRefGoogle Scholar
  24. Griffin, S. (2004b). Number Worlds: A research-based mathematical program for young children. In D. H. Clements & A.-M. DiBiase (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 325–342). Mahweh, NJ: Lawrence Erlbaum Associates.Google Scholar
  25. Hresko, W., Peak, P., Herron, S., & Bridges, D. (2000). Young Children’s Achievement Test. Austin, TX: Pro-Ed, Incorporated.Google Scholar
  26. Hu, L.-T., & Bentler, P. M. (1995). Evaluating model fit. In R. H. Hoyle (Ed.), Structural equation modeling: Concepts, issues, and applications (pp. 76–99). Thousand Oaks, CA: Sage.Google Scholar
  27. Hu, L.-T., & Bentler, P. M. (1999). Cutoff criteria for fit indexes in covariance structure analysis: Conventional criteria versus new alternatives. Structural Equation Modeling: A Multidisciplinary Journal, 6, 1–55.CrossRefGoogle Scholar
  28. Huntley-Fenner, G. (2001). Why count stuff? Young preschoolers do not use number for measurement in continuous dimensions. Developmental Science, 4(4), 456–462.CrossRefGoogle Scholar
  29. Jimerson, S., Egeland, B., & Teo, A. (1999). A longitudinal study of achievement trajectories: Factors associated with change. Journal of Educational Psychology, 91, 116–126.CrossRefGoogle Scholar
  30. Kovalena, G. (2010). The TIMSS study: The quality of education in mathematics and natural sciences in Russia exceeds average international indicators. Russian Education and Society, 52, 72–89.CrossRefGoogle Scholar
  31. Manfra, L., Dinehart, L., & Sembiante, S. (2014). Associations between counting ability in preschool and mathematic performance in first grade among a sample of ethnically diverse, low-income children. Journal of Research in Childhood Education International, 28, 101–114.CrossRefGoogle Scholar
  32. Miura, I., Okamoto, Y., Kim, C., Chang, C., Steere, M., & Fayol, M. (1994). Comparisons of children’s cognitive representation of number: China, France, Japan, Korea, Sweden, and the United States. International Journal of Behavioral Development, 17, 401–411.CrossRefGoogle Scholar
  33. Mullis, I. V. S., Martin, M. O., Beaton, A. E., Gonzales, E. J., Kelly, D. L., & Smith, T. A. (1997). Mathematics and science achievement in the final year of secondary school: IEA’s third international mathematics and science study. Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational Policy, Boston College.Google Scholar
  34. Mullis, I. V. S., Martin, M. O., Gonzalez, D. L., Gregory, K. D., Garden, R. A., & O’Connor, K. M. (2000). TIMSS 1999 international mathematics report: Findings from IEA’s repeat of the Third International Mathematics and Science Study at the eighth grade. Boston, MA: International Study Center, Boston College.Google Scholar
  35. Muthén, L. K., & Muthén, B. O. (1998–2011). Mplus User’s Guide. Sixth Edition. Los Angeles, CA: Muthén & Muthén.Google Scholar
  36. National Center for Children in Poverty. (1996). Wake up America: Columbia University study shatters stereotypes of young child poverty. New York: Columbia University.Google Scholar
  37. Plake, B. S., Impara, J. C., & Spies, R. A. (2003). The fifteenth mental measurements yearbook (Eds.). Lincoln, NE: Buros Institute of Mental Measurements.Google Scholar
  38. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Chicago, IL: MESA Press.Google Scholar
  39. Reys, R. E., Lindquist, M., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics. Wiley.Google Scholar
  40. 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). Hillsdale, NJ: Erlbaum.Google Scholar
  41. Shaw, K., Nelsen, E., & Shen, Y. L. (2001, April). Preschool development and subsequent school achievement among Spanish-speaking children from low-income families. Paper presented at the annual meeting of the American Educational Research Association, Seattle, WA.Google Scholar
  42. Siegler, R., & Mu, Y. (2008). Chinese children excel on novel mathematics problems even before elementary school. Psychological Science, 19, 759–763.CrossRefGoogle Scholar
  43. Stevenson, H., Lee, S. S., & Stigler, J. (1986). The mathematics achievement of Chinese, Japanese, and American children. Science, 56, 693–699.CrossRefGoogle Scholar
  44. Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 1–10.CrossRefGoogle Scholar
  45. Wang, J., & Lin, E. (2009). A meta-analysis of comparative studies on Chinese and US students’ mathematics performance: Implications for mathematics education reform and research. Educational Research Review, 4, 177–195.CrossRefGoogle Scholar
  46. Zimowski, M. F., Muraki, E., Mislevy, R. J., & Bock, R. D. (1996). BILOG-MG: Multiple-group IRT analysis and test maintenance for binary items [Computer software]. Chicago: Scientific Software International.Google Scholar
  47. Zur, O., & Gelman, R. (2004). Young children can add and subtract by predicting and checking. Early Childhood Research Quarterly, 19(1), 121–137.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  1. 1.Teachers CollegeColumbia UniversityNew YorkUSA

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