Motor skills as mental lubricant?

Over at the Boston Globe today, there's an interesting story about the buzz surrounding "embodied cognition." As in, when squirming helps you solve that quadratic equation.
A series of studies, the latest published in November, has shown that children can solve math problems better if they are told to use their hands while thinking. Another recent study suggested that stage actors remember their lines better when they are moving. And in one study published last year, subjects asked to move their eyes in a specific pattern while puzzling through a brainteaser were twice as likely to solve it.
I'm a good example of this...I mean, if you make me sit on my hands, whole areas of my brain seize. If we're having a tête-à -tête, you're going to need a generous radius, because my hands will be underlining everything I say. A lot of women open their mouths while putting on eye makeup, and when I was a gymnast there were the girls who were chastised for sticking their tongues out while on the balance beam. There was typically a "But I can't help it!" in response, and now it seems, in fact, you wouldn't want her to help it: it's keeping her balanced...So what do you think: do motor skills help you solve certain problems?