Transitional knowledge in the acquisition of concepts

These studies explore children's conceptual knowledge as it is expressed through their verbal and gestural explanations of concepts. We build on previous work that has shown that children who produce a large proportion of gestures that do not match their verbal explanations are in transition with respect to the concept they are explaining. This gesture/speech mismatch has been called "discordance." Previous work discovered this phenomenon with respect to 5- to 7-year-old children's explanations of conservation problems. Study 1 shows: (1) that older children (10 to 11 years old) exhibit gesture/speech discordance with respect to another concept, understanding the equivalence relationship in mathematical equations, and; (2) that children who produce many discordant responses in their explanations of mathematical equivalence are more likely to benefit from instruction in the concept than are children who produce few such responses. Studies 2 and 3 explore the properties and usefulness of discordance as an index of transitional knowledge in a child's acquisition of mathematical equivalence. Under any circumstance in which new concepts are acquired, there exists a mental bridge connecting the old knowledge state to the new. The studies reported here suggest that the combination of gesture and speech may be an easily observable and significantly interpretable reflection of knowledge states, both static and in flux.