The following is from How our hands help us learn, by Susan Goldin-Meadow and Susan Wagner Cook:

Gesture is based on a different representational format from speech. Whereas speech is segmented and linear, gesture can convey several pieces of information all at once. At a certain point in acquiring a concept, it might be easier to understand, and to convey, novel information in the visuospatial medium offered by gesture than in the verbal medium offered by speech.

Gesture is not specifically acknowledged. As a result, gesture can allow speakers to introduce into their repertoires novel ideas not entirely consistent with their current beliefs, without inviting challenge from a listener--indeed, without inviting challenge from their own self-monitoring systems. Gesture might allow ideas to slip into the system simply because it is not the focus of attention. Once in, those new ideas could catalyze change.

Gesture helps to ground words in the world. Deictic gestures point out objects and actions in space and thus provide a context for the words they accompany. Gestures might, as a result, make it easier to understand words and also to produce them.

Whatever the process, there is ample evidence that the spontaneous gestures we produce when we talk reflect our thoughts -- often thoughts not conveyed in our speech. Moreover, evidence is mounting that gesture goes well beyond reflecting our thoughts, to playing a role in shaping them.

The point of this is of course, that the hands, even when they are not engaged in directly shaping materials, are still engaged in the creative shaping of ideas. That is why sitting at desks with hands stilled is a really dumb notion unless your purpose in schooling is to restrain creativity and train students to conformity, lethargy, and compliance. If our purpose was for children to learn, our schools would look more like Froebel Kindergartens with children working with blocks and planting gardens.