Previous work has shown that, when asked to explain a concept they are acquiring, children often convey one procedure in speech and a different procedure in gesture. Such children, whom we label "discordant," have been shown to be in a transitional state in the sense that they are particularly receptive to instruction--indeed more receptive to instruction than "concordant" children, who convey the same procedure in speech and gesture. This study asks whether the discordant state is transitional, not only in the sense that it predicts receptivity to instruction, but also in the sense that it is both preceded and followed by a concordant state. To address this question, children were asked to solve and explain a series of problems instantiating the concept of mathematical equivalence. The relationship between gesture and speech in each explanation was monitored over the series. We found that the majority of children who learned to correctly solve equivalence problems did so by adhering to the hypothesized path: They first produced a single, incorrect procedure. They then entered a discordant state in which they produced different procedures--one in speech and another in gesture. Finally, they again produced a single procedure, but this time a correct one. These data support the notion that the transitional state is characterized by the concurrent activation of more than one procedure, and provide further evidence that gesture can be a powerful source of insight into the processes involved in cognitive development.