Measures and References: Cardinality

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Numerous measures exist to gain a full picture of a student's learning strengths and challenges. Following are examples of measures used to assess this Learner Factor. These measures should be administered and interpreted by experienced professionals.

Give-Number Task (Negen, Sarnecka, & Lee, 2012): A measure to assess knower level during which students are told to give a certain number of items, generally one through six, to a puppet


Bialystok, E., & Codd, J. (1997). Cardinal limits: Evidence from language awareness and bilingualism for developing concepts of number. Cognitive Development, 12, 85-106.

Chu, F. W., & Geary, D. C. (2015). Early numerical foundations of young children's mathematical development. Journal of Experimental Child Psychology, 132, 205-212.

Geary, D. C., & vanMarle, K. (2016). Young children's core symbolic and nonsymbolic quantitative knowledge in the prediction of later mathematics achievement. Developmental Psychology, 52(12), 2130-2144.

Geary, D. C., vanMarle, K., Chu, F. W., Rouder, J., Hoard, M. K., & Nugent, L. (2018). Early conceptual understanding of cardinality predicts superior school-entry number-system knowledge. Psychological Science, 29(2), 191-205.

Moore, A. M., & Geary, D.C. (2016). Kindergartners' fluent processing of symbolic numerical magnitude is predicted by their cardinal knowledge and implicit understanding of arithmetic two years earlier. Journal of Experimental Child Psychology, 150, 31-47.

Negen, J., & Sarnecka, B.W. (2012). Number-concept acquisition and general vocabulary development. Child Development, 86(3), 2019-2027.

Negen, J., Sarnecka, B.W., & Lee, M. D. (2012). An Excel sheet for inferring children's number-knower levels from give-N data. Behavior Research Methods, 44(1), 57-66.

Sarnecka, B.W., & Carey, S. (2008). How counting represents number : What children must learn and when they learn it. Cognition, 108, 662-674.

Shusterman, A., Slusser, E., Halberda, J., & Odic, D. (2016). Acquisition of the cardinal principle coincides with improvement in approximate number system acuity in preschoolers. PLoS ONE, 11(4), 1-22.

Wagner, J. B., & Johnson, S.C. (2011). An association between understanding cardinality and analog magnitude representations in preschoolers. Cognition, 119(1), 10-22.

Wynn, K. (1989, April). Children's understanding of counting. In Proceedings of the Biennial Meeting of the Society for Research in Child Development Society for Research in Child Development (Vol. 36, pp. 155-193). Washington, D.C.: National Science Foundation.