Identifying the cognitive predictors of early counting and calculation skills: Evidence from a longitudinal study

Abstract

The extent that phonological, visual-spatial STM and non-symbolic quantitative skills support the development of counting and calculation skills was examined in this 14-month longitudinal study of 125 children. Initial assessments were made when the children were 4:8. Phonological awareness, visual-spatial STM and non-symbolic approximate discrimination predicted growth in early calculation skills. These results suggest that both the approximate number system and domain-general phonological and visual-spatial skills support early calculation. In contrast, only performance on a small non-symbolic quantity discrimination task (where the presented quantities were always within the subitising range) predicted growth in cardinal counting skills.These results suggest that the development of counting and calculation are supported by different cognitive abilities.

Does the Approximate Number System Serve as a Foundation for Symbolic Mathematics?

“…In the first study to show this relationship, Halberda and colleagues demonstrated that Weber fraction measured at 14 years of age retroactively predicted standardized math scores at age 5, even after controlling for verbal IQ (Halberda, Mazzocco, & Feigenson, 2008). This positive correlation has since been found in adults (Agrillo, Piffer, & Adriano, 2013; DeWind & Brannon, 2012; Halberda, Ly, Wilmer, Naiman, & Germine, 2012; Libertus, Odic, & Halberda, 2012; Lourenco, Bonny, Fernandez, & Rao, 2012); in school-aged children (Geary, Hoard, Nugent, & Rouder, 2015; Pinheiro-Chagas et al, 2014); in children just beginning formal math education (Gilmore et al, 2010; Keller & Libertus, 2015; Mundy & Gilmore, 2009); and in preschool aged children before they begin formal math education (Chu, vanMarle, & Geary, 2015; Libertus, Feigenson, & Halberda, 2011, 2013; Mazzocco, Feigenson, & Halberda, 2011b; Soto-Calvo, Simmons, Willis, & Adams, 2015; Starr, Libertus, & Brannon, 2013; van Marle, Chu, Li, & Geary, 2014). Three meta-analyses have concluded there is a significant correlation between ANS and math ability (Chen & Li, 2014; Fazio, Bailey, Thompson, & Siegler, 2014; Schneider et al, 2016).…”

“…(Starr, Libertus & Brannon, 2013). Recent longitudinal studies that follow children in the preschool years have revealed a nuanced relationship between the ANS and early symbolic math skills (Purpura & Logan, 2015; Soto-Calvo et al, 2015). Soto-Calvo and colleagues measured preschoolers’ ANS ability, a variety of symbolic math skills, phonological awareness, and visual-spatial short term memory at age 4 and then again 14 months later (Soto-Calvo et al, 2015).…”

Early numeracy skills in preschool-aged children: a review of neurocognitive findings and implications for assessment and intervention

“…Phonological awareness predicted individual differences in learning the number sequence; but not individual differences on tasks where the number sequence is mapped onto quantity (e.g., deciding which of two number words represented “more” or “less”; matching quantities to the corresponding Arabic numerals and vice versa). Along these lines, Soto-Calvo and colleagues (2015) found that phonological awareness assessed in the first year of pre-kindergarten (at 4 years, 8 months on average) no longer predicted sequential counting skills 14-months later after including the autoregressor (sequential counting skills from the previous year). If a cognitive predictor remains significant when autoregressor effects are controlled, it can be concluded that the cognitive predictor predicts growth in the outcome measure.…”

“…Phonological awareness, more so than measures of vocabulary or word meaning, tap the quality of lexical representations (perhaps because they require fine distinctions between phonological representations such as cat vs. car or cat vs. rat) and is related to young children’s sequential counting skills (Barnes et al, 2011; Koponen, Salmi, Eklund, & Aro, 2013; Krajewski & Schneider, 2009; Soto-Calvo, Simmons, Willis, & Adams 2015). A longitudinal study conducted by Krajewski and Schnieder (2009) followed children from preschool to third grade and examined the relation of phonological awareness to the development of early numeracy skills.…”

“…Moreover, the role of phonological awareness in learning the counting sequence may be rather circumscribed: Phonological awareness may influence the rate at which children acquire the first few number words, but later extension of the number sequence may depend to a greater extent on other conceptual factors, such as knowledge of the base 10 (Soto-Calvo et al, 2015). For example, it is likely that conceptual number knowledge, rather than phonological awareness is important for understanding that 20 follows 19 and comes before 21.…”