Kindergartners’ fluent processing of symbolic numerical magnitude is predicted by their cardinal knowledge and implicit understanding of arithmetic 2 years earlier

Abstract

Fluency in first graders’ processing of the magnitudes associated with Arabic numerals, collections of objects, and mixtures of objects and numerals predicts current and future mathematics achievement. The quantitative competencies that support the development of fluent processing of magnitude are not fully understood, however. At the beginning and end of preschool (M = 3 years, 9 months at first assessment; range 3 years, 3 months to 4years, 3 months), 112 (51 boys) children completed tasks measuring numeral recognition and comparison, acuity of the approximate number system, and knowledge of counting principles, cardinality, and implicit arithmetic, and completed a magnitude processing task (number sets test) in kindergarten. Use of Bayesian and linear regression techniques revealed that two measures of preschoolers’ cardinal knowledge and their competence at implicit arithmetic predicted later fluency of magnitude processing, controlling domain general factors, preliteracy skills, and parental education. The results help to narrow the search for the early foundation of children’s emerging competence with symbolic mathematics and provide direction for early interventions.

Explaining early moral hypocrisy: Numerical cognition promotes equal sharing behavior in preschool‐aged children

“…Prior work points to several correlates of cardinality that may be most relevant to active resource distribution: acquiring knowledge of the cardinal principle may increase the precision through which children perform intuitive division operations on the resources (McCrink & Spelke, ), provide a tool through which children can count out equal sets (Sarnecka & Wright, ) or help participants identify when sharing errors occur (Muldoon, Lewis, & Berridge, ). Consistent with our findings, in the latter two cases, cardinality, rather than subitizing or knower‐level knowledge, relates to these developments (see also Chernyak et al., ; Jara‐Ettinger et al., ; Moore, vanMarle, & Geary, ).…”

Prevention: Necessary But Insufficient? A 2‐Year Follow‐Up of an Effective First‐Grade Mathematics Intervention

“…In any event, the similar impacts on the number sets test and addition fact retrieval are consistent with Moore et al. 's () finding that fluency on the number sets test is related to children's understanding of addition and subtraction. The results here suggest that fluency in these operations facilitates fluency in combining symbolic and nonsymbolic quantities (core skills assessed by the number sets test; Geary et al., ), although the results could also emerge because some number‐set items involve comparison of pairs to numerals (e.g., “3 4”) to the target (e.g., “5”).…”

“…Transfer distance from the intervention differed across measures. In order of proximity, measures were Arithmetic Combinations (Fuchs, Hamlett, & Powell, 2003; adding and subtracting through sets of 12); Double-Digit Calculations (Fuchs et al, 2003; two-digit adding and subtracting with and without regrouping); Addition Strategy Assessment-Facts Correctly Retrieved (Geary, Hoard, Byrd-Craven, Nugent, & Numtee, 2007; simple addition problems answered quickly and correctly without indication of counting); Number Sets Test (Geary et al, 2009;Moore, vanMarle, & Geary, 2016; an integrative task of cardinality, subitizing, counting, numeral identification, symbolic and nonsymbolic quantity understanding, number decomposition, arithmetic principles), and Story Problems (Jordan & Hanich, 2000;combine, compare, and change word problems involving simple arithmetic). See Supporting Information for explanation of transfer distance.…”

Developmental change in the influence of domain-general abilities and domain-specific knowledge on mathematics achievement: An eight-year longitudinal study.

“…The adjustment enabled us to maintain the sensitivity of the test, despite faster processing times across grades. The d-prime score appears to capture the speed and accuracy with which children can access the magnitudes associated with whole numbers and their implicit or explicit understanding of arithmetic (Moore, vanMarle, & Geary, 2016), and is highly reliable in all grades; the Spearman-Brown reliability estimates ranged from .89 to .92 (median =.90), based on the correlation between performance on the 5 and 9 target sums.…”