This study investigated whether young, poor, inner-city children are deficient in the mathematical skills and concepts necessary for later success in school arithmetic. Children of pre-kindergarten and kindergarten age, black or white, and lower class or middle class, were given a wide variety of mathematical tasks, including Piagetian measures, tasks assessing counting skills and the use and understanding of counting in problem solving, judgment of more, understanding of addition operations, and tasks involving written numbers. Results showed consistent differences on almost every task reflecting improved performance with age, but only minor social class or racial differences. The conclusion is that all children from all of the groups possess the cognitive competence necessary for later success in school arithmetic. (MP)