In the first of three experiments, 132 students were found to gesture more often when they had difficulties solving mental rotation problems. In the second experiment, 22 students were encouraged to gesture, while 22 were given no such encouragement, and a further 22 were told to sit on their hands to prevent gesturing. Those encouraged to gesture solved more mental rotation problems.
Interestingly, the amount of gesturing decreased with experience with these spatial problems, and when the gesture group were given new spatial visualization problems in which gesturing was prohibited, their performance was still better than that of the other participants. This suggests that the spatial computation supported by gestures becomes internalized. The third experiment increased the range of spatial visualization problems helped by gesture.
The researchers suggest that hand gestures may improve spatial visualization by helping a person keep track of an object in the mind as it is rotated to a new position, and by providing additional feedback and visual cues by simulating how an object would move if the hand were holding it.
(2011). The nature of gestures' beneficial role in spatial problem solving..
Journal of Experimental Psychology: General. 140(1), 102 - 116.
Full text of the article is available at http://www.apa.org/pubs/journals/releases/xge-140-1-102.pdf