I'm a little suspicious of a site that "doesn't supply any ownership information" and "could not be verified by Yahoo" when I tried to sign in with my Yahoo ID, which they allow; has as an author a Japanese site, but has a domain of Micronesia (small S. Pacific island country).
Nonetheless, the site "worked" after temporarily allowing google-analytics.com and googleapis.com, as well as clicking "Recently blocked sites" and "Allow all from smart.fm".
But when I tried to play Brainspeed, the choices were blank squares, not words. Putting the cursor over them made reference to Adobe Flash Player, yet I saw no Flash objects (.swf, usually) anywhere on the page or in the menu. However,
RequestPolicy shows requests being made to Adobe, as well as to Googleapis. Scripts are trying to run from Twitter and Facebook.
I'm not sure I want to be able to make this site "work". Are you? ... If so, try continually opening the NoScript menu and allowing "Recently blocked", "Blocked Objects", etc., as each time you do this, more will try to load. So you may have to go through the menu several times. This is why "Allow scripts globally" failed, because it's more than just scripts, it's several generations of objects loading.
I would rather find another learning site than disable NoScript, but if you wish, try this out and let us know.
Mozilla/5.0 (Windows; U; Windows NT 5.1; en-US; rv:1.9.1.5) Gecko/20091102 Firefox/3.5.5