Cited References

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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.

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Baroody, A. J., & Wilkins, J. L. M. (1999). The development of informal counting, number, and arithmetic skills and concepts. In J. V. Copley (Ed.), Mathematics in the early years (pp. 48-65). Washington, DC, US: National Association for the Education of Young Children.

Li, X., & Baroody, A. J. (2014). Young children’s spontaneous attention to exact quantity and verbal quantification skills. European Journal of Developmental Psychology11, 608-623. 

Sophian, C. (2007). The origins of mathematical knowledge in childhood. New York, NY: Routledge.

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Wynn, K. (1992). Addition and subtraction by human infants. Nature, 358, 749–750

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Epstein, A. S. (2008). An early start on thinking. Educational Leadership, 65, 38-42.

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Wang, Z., Meltzoff, A. N., & Williamson, R. A. (2015). Social learning promotes understanding of the physical world: Preschool children’s imitation of weight sorting. Journal of Experimental Child Psychology, 136, 82–91. 


  • Cardinality
    is the concept that, when counting objects, the last number represents the total number of objects in the set
    includes size, length, height, weight, volume, distance, and time
    Number and operations
    refers to a set of math concepts related to understanding and representing numbers and operations (e.g., addition, subtraction, multiplication, and division) and the relationships between them
    is the ability to understand and reason with numbers
    One-to-one correspondence
    refers to matching one object to each number word when counting
    refers to the ability to identify the number of objects in a small group of objects without counting them
    is offering the right level of support to help a child achieve more than they would be able to on their own