Measures and References: Non-symbolic Number

Return to Non-symbolic Number factor page.


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.

Panamath (Psychophysical Assessment of Numerical Approximation) (Halberda et al., 2008): Assesses students' Non-symbolic Number understanding by comparing quantities of dots


Anobile, G., Pisa, U., & Stievano, P. (2013). Visual sustained attention and numerosity sensitivity correlate with math achievement in children. Journal of Experimental Child Psychology, 116, 380-391.

Chen, Q., & Li, J. (2014). Association between individual differences in non-symbolic number acuity and math performance : A meta-analysis. Acta Psychologica, 148, 163-172.

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.

Gilmore, C. K., McCarthy, S., & Spelke, E. S. (2010). Non-symbolic arithmetic abilities and achievement in the first year of formal schooling in mathematics. Cognition, 115(3), 394-406.

Halberda, J., Mazzocco, M. M., & Feigenson, L. (2008). Individual differences in non-verbal number acuity correlate with maths achievement. Nature, 455(7213), 665-668.

Hyde, D. C., Khanum, S., & Spelke, E. (2015). Brief non-symbolic, approximate number practice enhances subsequent exact symbolic arithmetic in children. Cognition, 131(1), 92-107.

Libertus, M. E., Feigenson, L., & Halberda, J. (2013). Is approximate number precision a stable predictor of math ability? Learning and Individual Differences, 25, 126-133.

Lyons, I. M., & Beilock, S. L. (2011). Numerical ordering ability mediates the relation between number-sense and arithmetic competence. Cognition, 121, 256-261.

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.

Xenidou-Dervou, L., Van Der Shot, M., & Van Lieshout, E. C. D. M. (2015). Working memory and number line representations in single-digit addition: approximate versus exact, nonsymbolic versus symbolic. Quarterly Journal of Experimental Psychology, 68(6), 1148-1167.

Zhou, X., Wei, W., Zhang, Y., Cui, J., & Chen, C. (2015). Visual perception can account for the close relation between numerosity processing and computational fluency. Frontiers in Psychology, 6, 1-13.