FoNS includes awareness of magnitude and of comparisons between different magnitudes (Clarke and Shinn 2004; Griffin 2004; Ivrendi 2011; Jordan et al. 2006; Jordan and Levine 2009; Yang and Li 2008) and deploys language like bigger than or smaller than (Gersten et al. 2005). Children understand that eight represents a quantity that is bigger than six but smaller than ten (Lembke and Foegen, 2009). In particular, children who are magnitude aware have moved beyond counting as “a memorized list and a mechanical routine, without attaching any sense of numerical magnitudes to the words” (Lipton and Spelke 2005, p. 979). Moreover, magnitude awareness has been shown to be a predictor, irrespective of ability or age, of more general mathematical achievement (Aunio and Niemivirta 2010; De Smedt et al. 2013; Desoete et al. 2012; Holloway and Ansari 2009; Nan et al. 2006; Stock et al. 2010).
References
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Clarke, B., & Shinn, M. (2004). A preliminary investigation into the identification and development of early mathematics curriculum-based measurement. School Psychology Review, 33(2), 234-248.
Desoete, A., Ceulemans, A., De Weerdt, F., & Pieters, S. (2012). Can we predict mathematical learning disabilities from symbolic and non-symbolic comparison tasks in kindergarten? Findings from a longitudinal study. British Journal of Educational Psychology, 82(1), 64-81.
De Smedt, B., Noël, M.-P., Gilmore, C., & Ansari, D. (2013). How do symbolic and non-symbolic numerical magnitude processing skills relate to individual differences in children's mathematical skills? A review of evidence from brain and behavior. Trends in Neuroscience and Education, 2(2), 48-55.
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Griffin, S. (2004). Building number sense with Number Worlds: A mathematics program for young children. Early Childhood Research Quarterly, 19(1), 173-180.
Holloway, I., & Ansari, D. (2009). Mapping numerical magnitudes onto symbols: The numerical distance effect and individual differences in children’s mathematics achievement. Journal of Experimental Child Psychology, 103(1), 17-29.
Ivrendi, A. (2011). Influence of self-regulation on the development of children’s number sense. Early Childhood Education Journal, 39(4), 239-247.
Jordan, N.., & Levine, S. (2009). Socioeconomic variation, number competence, and mathematics learning difficulties in young children. Developmental Disabilities Research Reviews, 15(1), 60-68.
Jordan, N., Kaplan, D., Nabors Oláh, L., & Locuniak, M. (2006). Number sense growth in kindergarten: A longitudinal investigation of children at risk for mathematics difficulties. Child Development, 77(1), 153-175.
Lembke, E., & Foegen, A. (2009). Identifying early numeracy indicators for kindergarten and first-grade students. Learning Disabilities Research & Practice, 24(1), 12-20.
Lipton, J., & Spelke, E. (2005). Preschool children's mapping of number words to nonsymbolic numerosities. Child Development, 76(5), 978-988.
Nan, Y., Knösche, T., & Luo, Y.-J. (2006). Counting in everyday life: Discrimination and enumeration. Neuropsychologica, 44(7), 1103-1113.
Stock, P., Desoete, A., & Roeyers, H. (2010). Detecting children with arithmetic disabilities from kindergarten: Evidence from a 3-year longitudinal study on the role of preparatory arithmetic abilities. Journal of Learning Disabilities, 43(3), 250-268.
Yang, D.-C., & Li, M.-N. (2008). An investigation of 3rd-grade Taiwanese students' performance in number sense. Educational Studies, 34(5), 443 - 455.