When asked to explain their solutions to a problem, both adults and children gesture as they talk. These gestures at times convey information that is not conveyed in speech and thus reveal thoughts that are distinct from those revealed in speech. In this study, we use the classic Tower of Hanoi puzzle to validate the claim that gesture and speech taken together can reflect the activation of two cognitive strategies within a single response. The Tower of Hanoi is a well-studied puzzle, known to be most efficiently solved by activating subroutines at theoretically defined choice points. When asked to explain how they solved the Tower of Hanoi puzzle, both adults and children produced significantly more gesture-speech mismatches-explanations in which speech conveyed one path and gesture anotherat these theoretically defined choice points than they produced at non-choice points. Even when the participants did not solve the problem efficiently, gesture could be used to indicate where the participants were deciding between alternative paths. Gesture can, thus, serve as a useful adjunct to speech when attempting to discover cognitive processes in problem-solving.

Children frequently gesture when they explain what they know, and their gestures sometimes convey different information than their speech does. In this study, we investigate whether children's gestures convey knowledge that the children themselves can recognize in another context. We asked fourth-grade children to explain their solutions to a set of math problems and identified the solution procedures each child conveyed only in gesture (and not in speech) during the explanations. We then examined whether those procedures could be accessed by the same child on a rating task that did not involve gesture at all. Children rated solutions derived from procedures they conveyed uniquely in gesture higher than solutions derived from procedures they did not convey at all. Thus, gesture is indeed a vehicle through which children express their knowledge. The knowledge children express uniquely in gesture is accessible on other tasks, and in this sense, is not tied to the hands.

Children in transition with respect to a concept, when asked to explain that concept, often convey one strategy in speech and a different one in gesture. Are both strategies activated when that child solves problems instantiating the concept? While solving a math task, discordant children (who produced different strategies in gesture and speech on a pretest) and concordant children (who produced a single strategy) were given a word recall task. All of the children solved the math task incorrectly. However, if discordant children are activating two strategies to arrive at these incorrect solutions, they should expend more effort on this task than concordant children, and consequently have less capacity left over for word-recall and perform less well on it. This prediction was confirmed, suggesting that the transitional state is characterized by dual representations, both of which are activated when attempting to explain or solve a problem.