George Mason University professors Thomas and Collier in their longitudinal research in North Carolina public schools found that students in dual language classrooms achieved significantly higher test scores regardless of race, socioeconomic status, special needs and language spoken at home. Interestingly, they also found increased attendance and fewer behavioral referrals in dual language classes.
The most recent rigorous longitudinal study conducted in Portland Oregon by Rand Corporation and American University finds much the same
Here is a collection of research on how Language Immersion affects cognitive development by ACTFL, the American Council on the Teaching of Foreign Languages.
Or you can just look at the central part of this awesome infographic.