Went and saw the movie Sunday with some friends and so I searched out the story to see how close it was. They changed it quite a bit really, but it was a pretty good movie, sort of ET-ish, but it's a bit slow for a kids movie.
They happied up the ending of course, added some environmentalist aspects, and changed the mathematical aspect to a mental/psychic ability. The story is heavily psyhonalitical, and poses questions about children and learning. If you learnt non-Euclidean geometry, would you see the world differently than those whose minds have been conditioned to Euclid? In the movie they change it to mental capacity and sidestep the aspect of learning making the mind different. The character of the children was actually fairly similar, older brother with an annoying sister whom he loves and helps even when she's a bother, they aged them slightly in the movie, but it would have been difficult to really get a 2-year-old to act as the sister. The movie also gave away the AIW connection early, (of course the title implies a connection), but it was fun to see. The movie intro and outro were a bit overdone, and I could have done without the intro at least, or much less of one.