Skip to main content

Advertisement

Log in

Psychometric analyses of the Birthday Party

  • Original Article
  • Published:
ZDM Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Allen, M. J., & Yen, W. M. (1979, reissued in 2002). Introduction to measurement theory. Waveland Press, Inc.

  • Baker, F. B., & Kim, S.-H. (2004). Item response theory: Parameter estimation techniques (2nd ed.). New York: Dekker.

  • 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 

  • 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.

    Article  Google Scholar 

  • 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 

  • Bowman, B. T., Donovan, M. S., & Burns, M. S. (Eds.). (2001). Eager to learn: Educating our preschoolers. Washington, DC: National Academy Press.

    Google Scholar 

  • Brush, L. R. (1978). Preschool children’s knowledge of addition and subtraction. Journal for Research in Mathematics Education, 9, 44–54.

    Article  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(1), 167–172.

    Article  Google Scholar 

  • 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 

  • 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.

  • Clements, D. H., & Sarama, J. (Eds.). (2004). Hypothetical learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2).

  • 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.

    Article  Google Scholar 

  • Crocker, L., & Algina, J. (1986, reprinted in 2006, 2008). Introduction to classical and modern test theory. Belmont, CA: Wadsworth.

  • 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 

  • 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

  • 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 

  • 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.

    Article  Google Scholar 

  • Gelman, R., & Gallistel, C. R. (1986). The child’s understanding of number. Cambridge, MA: Harvard University Press.

    Google Scholar 

  • 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 

  • 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 

  • 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.

  • Ginsburg, H. P., & Pappas, S. (2016). Invitation to the birthday party: Rationale and description. ZDM Mathematics Education, 48(7) (this issue).

  • Griffin, S. (2004a). Building number sense with Number Worlds: a mathematics program for young children. Early Childhood Research Quarterly, 19(1), 173–180.

    Article  Google Scholar 

  • 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 

  • Hresko, W., Peak, P., Herron, S., & Bridges, D. (2000). Young Children’s Achievement Test. Austin, TX: Pro-Ed, Incorporated.

    Google Scholar 

  • 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 

  • 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.

    Article  Google Scholar 

  • Huntley-Fenner, G. (2001). Why count stuff? Young preschoolers do not use number for measurement in continuous dimensions. Developmental Science, 4(4), 456–462.

    Article  Google Scholar 

  • Jimerson, S., Egeland, B., & Teo, A. (1999). A longitudinal study of achievement trajectories: Factors associated with change. Journal of Educational Psychology, 91, 116–126.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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.

  • 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 

  • Muthén, L. K., & Muthén, B. O. (1998–2011). Mplus User’s Guide. Sixth Edition. Los Angeles, CA: Muthén & Muthén.

  • 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 

  • Plake, B. S., Impara, J. C., & Spies, R. A. (2003). The fifteenth mental measurements yearbook (Eds.). Lincoln, NE: Buros Institute of Mental Measurements.

  • Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Chicago, IL: MESA Press.

    Google Scholar 

  • Reys, R. E., Lindquist, M., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2014). Helping children learn mathematics. Wiley.

  • 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 

  • 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.

  • Siegler, R., & Mu, Y. (2008). Chinese children excel on novel mathematics problems even before elementary school. Psychological Science, 19, 759–763.

    Article  Google Scholar 

  • Stevenson, H., Lee, S. S., & Stigler, J. (1986). The mathematics achievement of Chinese, Japanese, and American children. Science, 56, 693–699.

    Article  Google Scholar 

  • Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38, 1–10.

    Article  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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 

  • Zur, O., & Gelman, R. (2004). Young children can add and subtract by predicting and checking. Early Childhood Research Quarterly, 19(1), 121–137.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Young-Sun Lee.

Appendix

Appendix

See Tables 13, 14, 15 and 16.

Table 13 Item statistics and indication of DIF detection of Number and Operation
Table 14 Item statistics and indication of DIF detection of Pattern
Table 15 Item Statistics and indication of DIF detection of Shape
Table 16 Item statistics and indication of DIF detection of Space

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Lee, YS. Psychometric analyses of the Birthday Party. ZDM Mathematics Education 48, 961–975 (2016). https://doi.org/10.1007/s11858-016-0801-0

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11858-016-0801-0

Keywords

Navigation