The Development of Quantitative Competencies in Preschool Children

Principal Investigator: 
Project Overview
Background & Purpose: 

This project seeks to identify the preschool quantitative competencies that predict risk for later learning disability in mathematics and to determine how young children's inherent sense of quantity influences their learning of formal quantitative competencies and mathematics achievement.


Columbia, Missouri

Research Design: 

The project uses a longitudinal research design and will generate evidence that is both associative/correlational [quasi-experimental] and causal [quasi-experimental, statistical modeling]. Original data are being collected on 3-year-olds, who will be followed for five years, using assessments of learning and behavioral responses to experimental tasks, reaction time, and psychophysical methods. Instruments or measures being used include standard intelligence and achievement tests, experimental tasks for effortful control/executive functions, and a battery of 12 basic quantitative tasks. A variety of analytic methods will be used, including psychophysical models, logistic regression, multi-level models, and multiple mediation analyses.


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.