There is a great deal of research behind "brain-based" movement. If you’d like to know more, here are some resources to get you started.
Aerobic Fitness Boosts Memory and Learning:
http://www.medicalnewstoday.com/articles/265900.php
http://www.plosone.org/article/info:doi/10.1371/journal.pone.0072666
http://www.sciencedaily.com/releases/2013/09/130911184716.htm
Movement & Learning:
http://movementandlearning.wordpress.com/about/
http://moveplaythrive.com/images/pdf/Link_Movement_Learning.pdf
Rhythmic Movements to integrate primitive reflexes & improve self-regulation - 2022
https://qspace.library.queensu.ca/handle/1974/30352?show=full
Eric Jensen on Movement & Learning:
http://www.ascd.org/publications/books/104013/chapters/Movement-and-Learning.aspx
Eric Jensen, Carla Hannaford, & More
http://www.peopleoffaith.com/children-learning-fitness.htm
Carla Hannaford (“Smart Moves”) – The Importance of Moving:
http://www.teachingvalues.com/whymovement.html
Physical activity before trying to learn new material (“ideal” – Wikipedia):
http://en.wikipedia.org/wiki/Movement_in_learning
Importance of Play in Promoting Healthy Child Development (American Academy of Pediatrics):
http://pediatrics.aappublications.org/content/119/1/182.full
Play and Developmental Stages (Child Developmental Institute):
http://childdevelopmentinfo.com/child-development/play-work-of-children/pl2/