Richard Gilder wrote a wonderful, cogent post about the relationship between the mind and body -- the topic explicitly was the Olympics.
However, it's the same in school. When we present abstract concepts to Years 4, 5, and 6 in State schools across London, we always involve the body to engage the mind more fully.
I can't sing (trust me), but last year I taught a song about case endings to 25 classes. I asked them to stand up, use hand movements, and use their voices in different ways while singing.
After a long summer, the kids have forgot a lot. But they still know their case endings.
More important even that children learn the material with which they are presented, they are learning how to learn. Simple strategies such as standing up, or creating gestures, creates a legacy of understanding how they think. We've seen that this works both for pupils who are considered high achievers and low.
In other words, CAGSE is working to efface this distinction between pupils.
Now THAT would be a legacy.