Presented are the results of an investigation of stimulus integration capabilities of three- and four-year-old children in judgments of small and large numbers. There is much evidence that suggested young children have a concept of number for small numbers, but not for large ones. A concept of number was hypothesized by Piaget to rest on the child's ability to correctly integrate two stimulus dimensions, length and density. Piaget's analysis predicts that young children's judgments will obey the correct Length x Density Integration rule, whereas large number judgments would obey a one-dimensional rule. The study reveals that children's judgments of small numbers did follow the correct Length x Density rule, while the children used an incorrect Length + Density rule for large numbers. These results show that a concept of number is present for small numbers but not for large numbers, in line with previous work. Contrary to Piaget's analysis of previous work, the absence of a concept of number does not imply the absence of stimulus integration. (MP)