Is this unusual, that he'd be able to do the computation without realizing how or why?
I wonder the same thing with my daughter! And then I think, does it matter now at age 4.5. if she can't explain how/why she arrives to correct solutions so consistantly, given that a) with homeschooling the chances we will circle back to it are high b) I'm the same way. I can solve complex equations because I can just "see" the answer.
On the note of the circling back, I do plan on covering math in depth, but often if I show it to my DD a handful of times at most, she understands it very well and can extrapolate upon whatever concept she is learning. Also, she's the type of kid that knowing the definition of a word, concept, etc. *IS* all the explaination she needs to internalize it on a deep level.
So, to *finally* answer your question: YES! It's normal for kids like ours. (Well, at least, I think it's normal and what you described above can apply to various and depending on the child several disciplines at once). I agree with Kriston, too that learning can present itself in spurts as she described in post further back in this thread. I see evidence of that frequently with my own children. I'm sure ND kids do this too, but at least with GT kids it's a deeper learning that happens much more quickly in comparison.
Mizzou
