We haven't read any research on the particular brain-embiggening
properties of Big Brain Academy: Wii Degree,
and we're also quite certain that playing it won't result in an actual degree conferral (which is too bad, because we could use some more of those!) Whatever health or brain-bigness benefits it may have, the game certainly looks cute and fun.
Siliconera has posted some impressions of the Japanese version, with plenty of screenshots and explanation of the various minigames
involved. We suggest you check it out and dramatically increase the size of the area of your brain that holds Big Brain Academy