A study of 9 and 10 year olds in the journal, Brain Research found an association between brain size, cognitive ability, and exercise. You can find an online article about the study, written for a lay audience, at the website of Science Today magazine:
When they analyzed the MRI data, the researchers found that the physically fit children tended to have bigger hippocampal volume -- about 12 percent bigger relative to total brain size -- than their out-of-shape peers.
The children who were in better physical condition also did better on tests of relational memory -- the ability to remember and integrate various types of information -- than their less-fit peers.
The new findings suggest that interventions to increase childhood physical activity could have an important effect on brain development
The study, conducted by researchers at the University of Illinois, Ohio State University, and the University of Pittsburgh, was serious enough to warrant notation in the December issue of Pediatrics magazine, published by the American Academy of Pediatrics. The study provides further evidence that a built environment creating walkable and bikeable schools could improve academic performance. Other studies examined by the Centers for Disease Control and Prevention have linked physical activity and academic performance.
We have engineered incidental exercise out of our lives. Sprawl development patterns, using dangerous highways to connect schools to subdivisions, have reduced the percentage of children walking and biking to school from over 40% in the late 1960's to around 13% today. Partly as a result, childhood obesity is reaching epidemic proportions--at about 17% of the pediatric population--with about a third of children overweight. Instead of self-reliance, we are instilling in our children a culture of dependency.
A properly built, smart growth environment can induce up to 80% of children to walk to school. I suspect additional research in coming years will show that smart growth can make kids smarter.