The study assessed the relations among acuity of the potentially inherent approximate number system (ANS), performance on other measures of early quantitative knowledge, and mathematics achievement for a sample of 68 (35 boys) preschoolers at risk for school failure. ANS acuity was significantly correlated with mathematics achievement, and predicted performance on measures of children’s explicit knowledge of Arabic numerals, number words, and cardinal value, as well as sensitivity to ordinal relations, controlling for intelligence, executive control, preliteracy knowledge, and parental education. The relation between ANS acuity and mathematics achievement was fully mediated by children’s explicit number knowledge and sensitivity to ordinal relations. Thirty-four of these children were at high risk for later mathematical learning disability and, relative to their typically achieving peers, were less accurate on the ANS task, did not understand ordinal relations, and had slower learning of Arabic numerals, number words, and their cardinal values. The overall pattern suggests ANS acuity facilitates the early learning of explicit numerical knowledge and relations, and indirectly influences individual and group differences in mathematics achievement through this explicit knowledge.
