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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.
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.
Decarli, G., Sella, F., Lanfranchi, S., Gerotto, G., Gerola, S., Cossu, G., & Zorzi, M. (2022). Severe developmental dyscalculia is characterized by core deficits in both symbolic and non-symbolic number sense. Psychological Science.
Fazio, L. K., Bailey, D. H., Thompson, C. A., & Siegler, R. S. (2014). Relations of different types of numerical magnitude representations to each other and to mathematics achievement. Journal of Experimental Child Psychology, 123, 53-72.
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.
Moeller, K., Neuburger, S., Kaufmann, L., Landerl, K., & Nuerk, H. C. (2009). Basic number processing deficits in developmental dyscalculia: Evidence from eye tracking. Cognitive Development, 24(4), 371-386.
Piazza, M., Facoetti, A., Trussardi, A. N., Berteletti, I., Conte, S., Lucangeli, D., ... & Zorzi, M. (2010). Developmental trajectory of number acuity reveals a severe impairment in developmental dyscalculia. Cognition, 116(1), 33-41.
Rousselle, L., & Noel, M. P. (2007). Basic numerical skills in children with mathematics learning disabilities: A comparison of symbolic vs non-symbolic number magnitude processing. Cognition, 102(3), 361-395.
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.