Advertisement

ZDM

, Volume 48, Issue 7, pp 947–960 | Cite as

Invitation to the birthday party: rationale and description

  • Herbert P. Ginsburg
  • Sandra Pappas
Original Article

Abstract

Educators in many countries around the world have a strong interest in improving early childhood mathematics education, one component of which is formative assessment. Unlike summative assessment, this approach can provide teachers with information useful for understanding and teaching individual children. This paper describes the rationale for and the development of the birthday party (BP), a mathematics assessment system appropriate for investigating the mathematical thinking and learning of young children, 3-, 4-, and 5-years of age. The BP uses computer technology to help teachers administer the assessment. The system also provides professional development to help teachers understand the results of the assessment and determine how to promote individual children’s learning. The ultimate goal of the system is to nurture thoughtful teachers who can conduct inventive formative assessments on a daily basis without the guidance of the BP software.

Keywords

Mathematics Formative assessment Computer technology Early childhood education Professional development 

Notes

Acknowledgments

This work was supported by the National Institute of Child Health and Human Development, Grant Number 1 R01 HD051538-01, to Herbert Ginsburg, principal investigator.

Supplementary material

11858_2016_818_MOESM1_ESM.pdf (3.2 mb)
Supplementary material 1 (PDF 3226 kb)

References

  1. Administration for Children & Families. (2015). Head start early learning outcomes framework ages birth to five. Washington, DC: Author.Google Scholar
  2. Anderson, A. (1993). Wondering–One child’s questions and mathematics learning. Canadian Children, 18(2), 26–30.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. Bertelli, R., Joanni, E., & Martlew, M. (1998). Relationship between children’s counting ability and their ability to reason about number. European Journal of Psychology of Education, 13(3), 371–384.CrossRefGoogle Scholar
  5. Binet, A. (1969). The perception of lengths and numbers. In R. H. Pollack & M. W. Brenner (Eds.), Experimental psychology of Alfred Binet (pp. 79–92). New York: Springer Publishing Co.Google Scholar
  6. Bloom, L. (1970). Language development: Form and function in emerging grammars. Cambridge, MA: MIT Press.Google Scholar
  7. Bosch, C., Álvarez Díaz, L., Correa, R., & Druck, S. (2010). Mathematics education in Latin America and the Caribbean: A reality to be transformed (Vol. 4). Rio de Janeiro and Mexico City: ICSU-LAC/CONACYT.Google Scholar
  8. Burger, W., & Shaughnessy, J. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 17, 31–48.CrossRefGoogle Scholar
  9. 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
  10. Center for Universal Education at Brookings and UNESCO Institute for Statistics. (2013). Toward universal learning: What every child should learn. Retrieved from Washington, DC.Google Scholar
  11. Clements, D. H. (2004a). 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
  12. Clements, D. H. (2004b). Major themes and recommendations. In D. H. Clements & J. Sarama (Eds.), Engaging Young Children in Mathematics (pp. 7–72). Mahwah, New Jersey and London: Lawrence Erlbaum Associates, Publishers.Google Scholar
  13. 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
  14. Clements, D. H., Sarama, J. H., & Liu, X. H. (2008). Development of a measure of early mathematics achievement using the Rasch model: The research-based early maths assessment. Educational Psychology, 28(4), 457–482.CrossRefGoogle Scholar
  15. 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
  16. Cross, C. T., Woods, T. A., & Schweingruber, H. (Eds.). (2009). Mathematics learning in early childhood: Paths toward excellence and equity. Washington, DC: National Academy Press.Google Scholar
  17. CTB, McGraw-Hill. (1976). Comprehensive tests of basic skills. Monterey, Calif: McGraw-Hill.Google Scholar
  18. 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
  19. Duncan, G. J., Dowsett, C. J., Claessens, C., Magnuson, K., Huston, A. C., Klebanov, P., et al. (2007). School readiness and later achievement. Developmental Psychology, 43(6), 1428–1446.CrossRefGoogle Scholar
  20. Duncan, G. J., & Magnuson, K. (2011). The nature and impact of early achievement skills, attention skills, and behavior problems. In G. J. Duncan & R. J. Murnane (Eds.), Whither opportunity: Rising inequality, schools, and children’s life chances (pp. 47–69). New York, NY: Russell Sage.Google Scholar
  21. Durkin, K., Shire, B., Riem, R., Crowther, R. D., & Rutter, D. R. (1986). The social and linguistic context of early number word use. British Journal of Developmental Psychology, 4, 269–288.CrossRefGoogle Scholar
  22. Economo Poulos, K. (1998). What comes next? The mathematics of pattern in kindergarten. Teaching Children Mathematics, 5(4), 230–233.Google Scholar
  23. Fuson, K. C. (1991). Children’s early counting: Saying the number word sequence, counting objects, and understanding cardinality. In K. Durkin & B. Shire (Eds.), Language in mathematical education: Research and practice (pp. 27–39). Milton Keynes, England: Open University Press.Google Scholar
  24. 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
  25. Gelman, R., & Gallistel, C. R. (1986). The child’s understanding of number. Cambridge, MA: Harvard University Press.Google Scholar
  26. Ginsburg, H. P. (1989). Children’s arithmetic: How they learn it and how you teach it (2nd ed.). Austin, TX: Pro Ed.Google Scholar
  27. Ginsburg, H. P. (2003). Assessment probes and instructional activities for the Test of Early Mathematics Ability-3. Austin, TX: Pro Ed.Google Scholar
  28. Ginsburg, H. P., & Baroody, A. J. (2003). The test of early mathematics ability: Third edition. Austin, TX: Pro Ed.Google Scholar
  29. 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
  30. Ginsburg, H. P., Greenes, C., & Balfanz, R. (2003). Big math for little kids. Parsippany, NJ: Dale Seymour Publications.Google Scholar
  31. Ginsburg, H. P., Lee, J. S., & Boyd, J. S. (2008). Mathematics education for young children: What it is and how to promote it. Society for Research in Child Development Social Policy Report: Giving Child and Youth Development Knowledge Away, 22(1), 1–24.Google Scholar
  32. 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
  33. 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
  34. Griffin, S. (2007). Number worlds: A mathematics intervention program for grades prek-6. Columbus, OH: SRA/McGraw-Hill.Google Scholar
  35. Irwin, K., & Burgham, D. (1992). Big numbers and small children. The New Zealand Mathematics Magazine, 29(1), 9–19.Google Scholar
  36. Jordan, N. C., Glutting, J., C., R., & 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(2), 181–195, 39(2), 181–195.Google Scholar
  37. Jordan, N. C., Hanich, L. B., & Uberti, H. Z. (2003). Mathematical thinking and learning difficulties. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 359–383). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
  38. Jordan, N. C., Huttenlocher, L., & 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.CrossRefGoogle Scholar
  39. Kadosh, R. C., & Dowker, A. (Eds.). (2015). The Oxford handbook of numerical cognition. Oxford, UK: Oxford University Press.Google Scholar
  40. Kagan, S. L., & Gomez, R. (2014). One, two, buckle my shoe: Early mathematics education and teacher professional development. In H. P. Ginsburg, T. A. Woods, & M. Hyson (Eds.), Preparing early childhood educators to teach math: Professional development that works (pp. 1–28). Baltimore, MD: Paul H. Brookes Publishing Co.Google Scholar
  41. Klein, A., & Starkey, P. (2004). Fostering preschool children’s mathematical knowledge: Findings from the Berkeley Math Readiness Project. In D. H. Clements & J. Sarama (Eds.), Engaging young children in mathematics: Standards for early childhood mathematics education (pp. 343–360). Mahwah, NJ: Lawrence Earlbam Associates.Google Scholar
  42. Lee, Y.-S. (2016). Psychometric analyses of the Birthday Party. ZDM Mathematics Education, 48(7) (this issue).Google Scholar
  43. Lehrer, R., Jenkins, M., & Osana, H. (1998). Longitudinal study of children’s reasoing about space and geometry. In R. Lehrer & D. Chazan (Eds.), Designing learning environments for developing understanding of geometry and space (pp. 137–167). Mahwah, NJ: Lawrence Earlbam Associates.Google Scholar
  44. Lillemyr, O. F., Fagerli, O., & Søbstad, F. (2001). A global perspective on early childhood care and education: A proposed model. Retrieved from Paris.Google Scholar
  45. Love, J. M., & Xue, Y. (2010). How early care and education programs 0–5 prepare children for Kindergarten: Is it enough? Paper presented at the Head Start’s 10th National Research Conference. DC: Washingon.Google Scholar
  46. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.Google Scholar
  47. National Governors Association Center for Best Practices & Council of Chief State School Officers. (2010). Common Core State Standards for Mathematics. Washington, DC: Author.Google Scholar
  48. Newcombe, N., & Huttenlocher, J. (1992). Children’s early ability to solve perspective-taking problems. Developmental Psychology, 28(4), 635–643.CrossRefGoogle Scholar
  49. Newcombe, N., & Learmonth, A. (1999). Change and continuity in early spatial development: claiming the radical middle. Infant Behavior and Development, 22(4), 457–474.CrossRefGoogle Scholar
  50. Nunes, T., & Bryant, P. (2015). The development of mathematical reasoning. In L. S. Liben & U. Mueller (Eds.), Handbook of child psychology and developmental science (7th ed., Vol. 2 Cognitive Processes, pp. 715–762). Hoboken, NJ: Wiley.Google Scholar
  51. Papic, M. (2007). Promoting repeating patterns with young children—More than just alternating colours. Australian Primary Mathematics Classroom, 12(3), 8–13.Google Scholar
  52. 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(3), 431–450.CrossRefGoogle Scholar
  53. Pieraut-Le Bonniec, G. (1982). From rhythm to reversibility. In G. E. Forman (Ed.), Action and thought: From sensorimotor schemes to symbolic operations (pp. 235–263). London: Academic Press.Google Scholar
  54. Platas, L. M., Ketterlin-Geller, L. R., & Sitabkhan, Y. (2016). Using an assessment of early mathematical knowledge and skills to inform policy and practice: Examples from the early grade mathematics assessment. International Journal of Education in Mathematics, Science and Technology, 4(3), 163–173.CrossRefGoogle Scholar
  55. Sarama, J., & Clements, D. H. (2004). Building blocks for early childhood mathematics. Early Childhood Research Quarterly, 19(1), 181–189.CrossRefGoogle Scholar
  56. Sarama, J., & Clements, D. H. (2009). Early childhood mathematics education research: Learning trajectories for young children. New York: Routledge.Google Scholar
  57. 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
  58. Serow, P., Callingham, R., & Tout, D. (2016). Assessment of mathematics learning: What are we doing? In K. Makar, S. Dole, M. Goos, J. Visnovska, A. Bennison, & K. Fry (Eds.), Research in mathematics education in Australasia 2012–2015 (pp. 1–19). Dordrecht: Springer.Google Scholar
  59. Sophian, C. (2004). Mathematics for the future: Developing a Head Start curriculum to support mathematics learning. Early Childhood Research Quarterly, 19(1), 59–81.CrossRefGoogle Scholar
  60. Sophian, C., & Adams, N. (1987). Infants’ understanding of numerical transformations. British Journal of Developmental Psychology, 5, 257–264.CrossRefGoogle Scholar
  61. Starkey, P., Klein, A., & Wakeley, A. (2004). Enhancing young children ‘s mathematical knowledge through a pre-kindgarten mathematics intervention. Early Childhood Research Quarterly, 19(1), 99–120.CrossRefGoogle Scholar
  62. Teppo, A. (1991). Van Hiele levels of geometric thought revisited. Mathematics Teacher (March), 210–221.Google Scholar
  63. University of Chicago. (2013). Getting on track early for school success: Project overview. http://www.norc.org/gettingontrack.
  64. U.S. Department of Health and Human Services. (2002). Children’s early learning, development, and school readiness: Conceptual frameworks, constructs, and measures.Google Scholar
  65. Wagner, S. H., & Walters, J. (1982). A longitudinal analysis of early number concepts: From numbers to number. In G. E. Forman (Ed.), Action and thought: From sensorimotor schemes to symbolic operations (pp. 137–161). NY: Academic Press.Google Scholar
  66. Walkerdine, V. (1988). The mastery of reason: Cognitive development and the production of rationality. London: Routledge.Google Scholar
  67. Weiland, C., Wolfe, C. B., Hurwitz, M. D., Clements, D. H., Sarama, J. H., & Yoshikawa, H. (2012). Early mathematics assessment: Validation of short form of a prekindergarten and kindergarten mathematics measure. Educational Psychology, 32(3), 311–333.CrossRefGoogle Scholar

Copyright information

© FIZ Karlsruhe 2016

Authors and Affiliations

  1. 1.Department of Human DevelopmentTeachers College, Columbia UniversityNew YorkUSA

Personalised recommendations