Are there moments in a child's development when he is particularly ready to make the transition from one knowledge state to another? Previous work by the investigator suggests that this is so -- a child in an unstable knowledge state with respect to a given concept is likely to be susceptible to input in that concept. The proposed studies will continue this line of research and implement two techniques for tapping this unstable knowledge state: (1) Gesture/Speech Discordance, which identifies a child as being in an unstable knowledge state if, in his explanations of a given concept, the information conveyed in his gestures is inconsistent with the information conveyed in his speech, and 2) Proximal Zone, which explores the breadth of the child's unstable knowledge state by observing the additional information expressed by the child when an adult structures a concept task versus when the child works on his own. The relationship between stability of knowledge and learning will be studied in two concepts: conservation and mathematical associativity. 120 boys and girls, 5-8 years old will participate in the conservation studies. Eighty boys and girls, 9-12 years old will participate in the conservation studies. Both populations will be drawn from a variety of ethnic and socio-economic backgrounds. A series of 6 videotaped experiments will be used: 1) to assess each child's basic level of understanding of the concept, 2) to assess the stability of the child's knowledge (via the Gesture/Speech Discordance measure) and to characterize the nature of that knowledge (via the Proximal Zone measure) and 3) to determine, in a training study, whether a child identified as unstable with respect to a given concept is more likely to benefit from input in that concept than a child identified as stable, and in a longitudinal study, whether a child in an unstable knowledge state will progress to the next level of understanding of the concept sooner than a child in a stable knowledge state. The techniques used in the proposed studies are designed to identify changing states of knowledge. The goal of these studies is to provide information about the role the child's own knowledge state might play in concept acquisition, and thus to contribute toward a general understanding of knowledge states, both static and in flux.