Abstract
Tremendous variation in elementary school children’s mathematical achievement can partly be traced back to differences in early domain-specific quantitative competencies. While previous research mainly focused on numerical magnitude representation and counting, we tested the long-term effects of relational quantitative reasoning. Before children (N = 51) entered school (i.e. at age 5-6), we assessed this competence with a test that required no knowledge about Arabic numerals. Two and a half years later, when children were in third grade of elementary school, we gauged mathematical achievement, general reasoning ability, and reading skills. A multiple regression analysis with mathematical achievement as outcome variable revealed a small but unique impact of children’s relational quantitative reasoning in kindergarten on their later mathematical achievement after controlling for general reasoning and reading abilities. Thus, a considerable amount of individual differences in mathematics achievement in elementary school results from differences in early relational quantity understanding that emerge before systematic instruction starts.
Highlights
Tremendous variation in elementary school children’s mathematical achievement can partly be traced back to differences in early domain-specific quantitative competencies
We investigated the predictive value of kindergarten children’s informally acquired understanding of relational quantitative reasoning and seriation skills on their later mathematical achievement in third grade
We administered an initial test of relational quantitative reasoning that does not require knowledge about Arabic numerals and assessed mathematical competencies controlling for children’s domain-general reasoning abilities in third grade
Summary
Tremendous variation in elementary school children’s mathematical achievement can partly be traced back to differences in early domain-specific quantitative competencies. We administered an initial test of relational quantitative reasoning that does not require knowledge about Arabic numerals and assessed mathematical competencies controlling for children’s domain-general reasoning abilities in third grade. Preferential looking studies in infants indicate that already few months old babies can discriminate between sets with different numbers of elements (Feigenson, Dehaene, & Spelke, 2004; Wynn, 1992; Xu & Spelke, 2000) This domain-specific ability is part of the universal roots of mathematical achievement, and seems to be an early source of individual differences: 6 months old infants’ ability to discriminate numerical changes predicts numerical discrimination abilities three months later (Libertus & Brannon, 2010). Children entering school without being able to count sets of different sizes, to recognize correct and incorrect counting, or to make numerical magnitude judgments run the risk of being disadvantaged in mathematics from the very beginning of their school career (e.g., Geary, 2011; Jordan, Kaplan, Ramineni, & Locuniak, 2009; Siegler, 2009)
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