It is often taken for granted that young children know very little, if anything, about the abstract conceptual domains of causality and mathematics, that they focus on perceptual learning and only turn to abstract concepts around 6 or 7 years of age. Gelman and others have shown in their research that even very young children, in some cases infants, are interested in rather abstract materials. For example, 6-8 month-old infants choose to look at a picture with the same number of objects as they hear in a sequence of drumbeats. Three-year-olds can already use information in pictures of unfamiliar statues of animals to decide which of these can move on their own. This suggests that people spontaneously form some classes of abstract concepts at very early ages. This research pursues this hypothesis by focussing on early knowledge and learning about number and cause. The research targets preschoolers' development and understanding of the principles of counting and arithmetic, as well as how these support their ability and interest in acquiring more sophisticated concepts, e.g., infinity, as older children. It also includes work on what information preschool children use to learn the different principles which govern the causality of animate and inanimate objects, for instance that animate objects have intentions and move on their own, obeying the laws of biology, while inanimate objects are moved by agents and are controlled solely by the laws of physics. The research will document the sensitivity of humans to the kinds of perceptual information that distinguish animate and inanimate objects, e.g., that the former are made of malleable and the latter of rigid substance, that the movements of machines are stereotyped, while those of animals are coordinated to respond to variations in the environment. It will also test the hypothesis that young children honor the constraint to associate statements about things they cannot see (e.g., it has a brain, a heart, etc.) with objects that project appropriate perceptual information, a bias which aids their efforts to build the correct class of theories about the two different kinds of object classes. This work is governed by a working theory which confronts the variability and fragility of the abilities of young children. Tests of the theory will help shape an account of conceptual competence and provide information about mechanisms of learning. Although the work on mechanisms is embedded in the context of studies of arithmetic and casual knowledge, it is likely that it will bear on a more general theory of learning and development. The research has implications for the conduct of the educational enterprise, most particularly early childhood education. If we know what young children are capable of, we can design their educational experiences to capitalize on those capabilities.
