Not sure for 3 year olds, but our DD8 absolutely loves IMACS.
I think they have programs for younger kids but are only available
"live" in the Southeast, and of course everywhere online.
The program uses interactive games to teach math and logic
in a very engaging way that is fun for the kids, and they can
earn points to buy rewards (most significantly for DD, candy!)
So it is not the rote repetitive kind of thing that some kids would
just not put up with. We have had a hard time getting DD's
school to provide acceleration and so were very glad that a friend
told us about IMACS--I had not heard about it before that.
Good luck finding something that works for you!
