Numerical magnitude understanding in kindergartners: A specific and sensitive predictor of later mathematical difficulties?

Abstract

Difficulties in mathematics are argued to stem from impairments of a specialized system of numerical magnitude representation. This study investigates whether different measures of numerical magnitude understanding in kindergarten uniquely predict mathematical achievement concurrently and 6 months later, and also examines the relative explanatory of each aspect of magnitude understanding. It also examines the utility of such tasks as sensitive and specific predictors of children at risk of mathematical learning difficulties. Kindergartners (N ϭ 215, M age ϭ 74 months) were administered a number-line estimation task, a nonsymbolic numerical discrimination task, and a nonsymbolic to word mapping task. Multiple measures of math achievement were administered concurrently and upon entering formal education (M age ϭ 80 months). Path analysis revealed that all 3 aspects of magnitude understanding had similar explanatory power in predicting concurrent and prospective math achievement; the only exception was that nonsymbolic numerical discrimination was not a significant predictor of concurrent mathematical reasoning. Of the 3 measures of magnitude understanding, number-line estimation was found to be the most accurate predictor of persistent mathematical difficulties. Approximately half of the children misclassified as having mathematical difficulties showed inconsistent mathematical achievement across the multiple measures. The implications for screening for mathematical difficulties and for designing interventions are discussed. Educational Impact and Implications StatementInsights into mechanisms that facilitate children's early quantitative learning are critical to the development of interventions that put at-risk children on the path to numeracy. The current findings suggest that these mechanisms may include an approximate sense of magnitude (numerical discrimination), the ability to map between nonsymbolic and symbolic quantities (numerical estimation) and the ability to explicitly operate on these numerical symbols and understand the logical relations among them (number-line estimation). Evidence is provided showing the utility of a short and simple measure of number-line estimation in kindergarten as a tool for identifying children at risk of persistent mathematical difficulties.

Heterogeneity in children at risk of math learning difficulties

“…Number line estimation skills, which are thought to capture the child's understanding of number order and symbol number magnitude, are less accurate in children with MLD. Recently, Bull et al (2021) found this skill to accurately discriminate between children with MLD and typical achievers. The ANS is responsible for representing non‐symbolic quantities and has been argued to support the acquisition of symbolic representations (cf.…”

Relational language influences young children’s number relation skills

“…Importantly, number line estimation performance by young children is one of the best predictors of later math achievement (Booth & Siegler, 2008; Schneider et al, 2018). It predicts kindergartners’ risk for future math learning difficulties (Bull et al, 2020) and differentiates intellectually precocious first graders from their peers with average math achievement (Hoard et al, 2008). Number lines provide a spatial representation of numerical magnitudes, with the direction and distance between numbers reflecting both ordinal and cardinal relations, and both types of knowledge influence the nature and precision of performance on the number line estimation task.…”

Working memory and numeracy training for children with math learning difficulties: Evidence from a large-scale implementation in the classroom.

“…Difficulties with numerical magnitude processing and the concept of number have also been found to characterize children with MLD (e.g., Geary, 2011). For instance, Bull et al (2021; see also, Swanson et al, 2018) found that poor number line estimation skills in kindergarten characterized children at risk of developing MLD in elementary school. Indeed, MLD screeners feature tasks that evaluate basic skills like numerical comparison and nonsymbolic-to-symbolic mapping (e.g., Butterworth & Laurillard, 2010; Nosworthy et al, 2013).…”

“…We used two measures that have been used widely in studies that have investigated core underlying skills that support the acquisition of mathematical abilities in school-age children. For instance, poor number line estimation skills are thought to characterize children at risk of developing MLD in elementary school(Bull et al, 2021). Similarly, numerical discrimination acuity of children with mathematical difficulties and dyscalculia is significantly poorer than that of their typically achieving peers(Skagerlund & Träff, 2016).In the Number-Line task, children were tasked to indicate on a line where a number at the top should go.…”