Predicting First‐Grade Math Achievement from Developmental Number Sense Trajectories

Abstract

Number sense development was tracked from the beginning of kindergarten through the middle of first grade, over six time points. Children (n = 277) were then assessed on general math achievement at the end of first grade. Number sense performance in kindergarten, as well as number sense growth, accounted for 66 percent of the variance in first-grade math achievement. Background characteristics of income status, gender, age, and reading ability did not add explanatory variance over and above growth in number sense. Even at the beginning of kindergarten, number sense was highly correlated with end of first-grade math achievement (r = 0.70). Clarifying the observed slope effect, general growth mixture modeling showed that children who started kindergarten with low number sense but made moderate gains by the middle of kindergarten had higher first-grade math achievement than children who started out with similarly low number sense with flat growth. The majority of children in the low/flat growth class were from low-income families. The findings indicate that screening early number sense development is useful for identifying children who will face later math difficulties or disabilities.

Exploring the impact of phonological awareness, visual–spatial working memory, and preschool quantity–number competencies on mathematics achievement in elementary school: Findings from a 3-year longitudinal study

“…In a first step of analysis, we were able to replicate core findings of previous longitudinal studies that found substantial correlations not only between early quantity-number competencies and math performance in school (see Aunola et al, 2004;Gersten et al, 2005;Jordan et al, 2007;Koponen, Aunola, Ahonen, & Nurmi, 2007;Krajewski & Schneider, in press;Passolunghi, et al, 2007;Stern, 1997Stern, , 1999, but also between early phonological awareness and math school performance (e.g., Alloway et al, 2005;Bradley & Bryant, 1985;Hecht et al, 2001;Koponen, Aunola, Ahonen, & Nurmi, 2007;Leather & Henry, 1994;Simmons, Singleton, & Horne, 2008). The latter were comparable in size with correlations between phonological awareness and subsequent literacy achievement in school found in studies on literacy development (e.g., Schneider & Näslund, 1999).…”

“…The phonological loop and central executive were not included in the latent variable model because only one indicator each was available to represent these variables. According to our assumptions, QNC Level-I competencies should predict QNC at higher levels (when number words are linked with quantity; see Krajewski, 2008;Passolunghi et al, 2007), and these should predict later mathematical achievement in Grade 3 (see Gersten et al, 2005;Jordan et al, 2007;Koponen et al, 2007;Stern, 1999). We expected early phonological awareness (measured at T 1 ) to predict the development of QNC Level-I competencies (at T 2 ), but not to predict higher levels of QNC (isolated number-words hypothesis).…”

“…There is empirical evidence demonstrating that the described early quantity-number competencies predict later mathematical school achievement (Aunola, Leskinen, Lerkkanen, & Nurmi, 2004;Koponen, Aunola, Ahonen, & Nurmi, 2007;Krajewski & Schneider, in press;Jordan, Kaplan, Locuniak, & Ramineni, 2007;Passolunghi, Vercelloni, & Schadee, 2007;Stern, 1997Stern, , 1999von Aster, Schweiter, & Weinhold-Zulauf, 2007;Weißhaupt, Peucker, & Wirtz, 2006; see also Gersten, Jordan, &Flojo, 2005, andOkamoto &Case, 1996 for the special importance of Levels I and II). Moreover, in studies focusing on children with mathematical learning disabilities, school children showed deficits in these quantity-number competencies (Gaupp, Zoelch, & Schumann-Hengsteler, 2004;Geary, Hamson, & Hoard, 2000;Geary, Hoard, Byrd-Craven, & DeSoto, 2004;Landerl, Bevan, & Butterworth, 2004).…”

Individual variance in responsiveness to early computerized mathematics intervention

“…At that age, Finnish children do not receive diagnoses for either math or reading difficulties. 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).…”

“…Inter-individual differences in early number skills performance appears to be highly stable from kindergarten (called pre-primary education in the Finnish context) to later primary grades in both international (Jordan, Kaplan, Locuniak, & Ramineni, 2007;Kohli, Sullivan, Sadeh, & Zopluoglu, 2015; and national research (e.g., for review see also Mazzocco & Räsänen, 2013). Differences between low-and typically-performing children can already be seen in the pre-primary year (recently Aunio, Heiskari, van Luit, & Vuorio, 2015).…”