Relational Quantitative Reasoning in Kindergarten Predicts Mathematical Achievement in Third Grade

Lennart Schalk, Henrik Saalbach, Roland H. Grabner, Elsbeth Stern


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.


mathematical achievement, quantitative reasoning, concept of order, general reasoning ability, longitudinal study

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Copyright (c) 2016 Schalk; Saalbach; Grabner; Stern