Number Sense Growth in Kindergarten: A Longitudinal Investigation of Children at Risk for Mathematics Difficulties

Abstract

Number sense development of 411 middle‐ and low‐income kindergartners (mean age 5.8 years) was examined over 4 time points while controlling for gender, age, and reading skill. Although low‐income children performed significantly worse than middle‐income children at the end of kindergarten on all tasks, both groups progressed at about the same rate. An exception was story problems, on which the low‐income group achieved at a slower rate; both income groups made comparable progress when the same problems were presented nonverbally with visual referents. Holding other predictors constant, there were small but reliable gender effects favoring boys on overall number sense performance as well as on nonverbal calculation. Using growth mixture modeling, 3 classes of growth trajectories in number sense emerged.

Individual variance in responsiveness to early computerized mathematics intervention

“…Differences between low-and typically-performing children can already be seen in the pre-primary year (recently Aunio, Heiskari, van Luit, & Vuorio, 2015). Weaknesses in early number skills likely contribute to lowperforming children's inability to benefit from instruction to the same extent as their age-peers (e.g., Jordan, Kaplan, Nabors Oláh, & Locuniak, 2006). Similar findings have been documented among Finnish children in pre-primary education (e.g., .…”

“…Older children tend to show more improvement than younger children (DiPerna, Lei, & Reid, 2007;Jordan et al, 2007, Jordan et al, 2006 and perform better in some numerical sub-skills (e.g., verbal counting skills; and domain-general skills associated with later mathematics achievement (cf. Kurdek & Singlair, 2001).…”

“…3). Evidence indicates that children with low socio-economic status (SES) exhibit lower spontaneous development during the kindergarten year (Jordan et al, 2006) and that the growth rate of their math skills decreases in first grade (Jordan et al, 2007) and later grades . Children from low SES families tend to be over-represented among those diagnosed as having MD (Jordan & Levine, 2009).…”

“…However, according to several longitudinal studies, the differences in the early number skills between low-and typically-performing children is notable, and this gap tends to grow in the following years (the Matthew-effect) (e.g., Jordan et al, 2007;Kohli et al, 2015). Children with low early number skills at the beginning of kindergarten (pre-primary education in the Finnish context) do not seem to benefit from instruction in the same way as their age-peers Jordan et al, 2006). Two risk-groups have been identified based on developmental growth-rates in early mathematics achievement (e.g., Morgan et al, , 2011.…”

Defective number module or impaired access? Numerical magnitude processing in first graders with mathematical difficulties

“…Moreover, structural (Isaacs, Edmonds, Lucas, & Gadian, 2001;Rotzer et al, 2008) and functional (Mussolin et al, 2010;Price, Holloway, Rasanen, Vesterinen, & Ansari, 2007) There exists considerable evidence that representations of magnitude are impaired in children with mathematical difficulties (De Smedt, Reynvoet, et al, 2009;Geary et al, 2007Geary et al, , 2008Iuculano et al, 2008;Jordan, Kaplan, Olah, & Locuniak, 2006;Landerl et al, 2004Passolunghi & Siegel, 2004;Rousselle & Noël, 2007). However, the majority of these studies only relied on tasks with a symbolic processing requirement and do not allow us to clarify whether difficulties in mathematics result from difficulties in representing numerical magnitudes, as postulated in the defective number module hypothesis, or from difficulties in the ability to access numerical magnitudes from formal symbols, such as Arabic numerals, as assumed in the access deficit hypothesis.…”