"Simple tasks he turns into something completely different and does them incorrectly."

My big question is, is it an incorrect way? Or just his way?

Like other posters, your first comment that "he does not seem to understand directions very well" took me straight to auditory processing, which itself has significant overlap with ADHD-I symptoms. Both will leave a kid missing a lot of instructions. Auditory processing issues can also make it hard to develop good phoneme awareness, and therefore can also impede early phonetics/ reading. (We've just finished an auditory assessment BTW; happy to share details if of any possible relevance).

But other than the teacher's comment, virtually everything you mention does seem explainable as his likely HG+. Especially if you throw in a heavy dose of visual spatial. So I would wonder about your own experience: in every day life, do you also feel like he doesn't *understand* instructions? Or that he hears something different than what was actually said? Or that he isn't able to pay enough attention to the instructions? Or - the $20,000 question - that he actively chooses to go his own way, regardless of the instructions?

Your description rings a lot of bells with my extremely visual-spatial DS10. Very out-of-the-box. He thrives on teachers he calls "eccentric, like me", and has had a lot of trouble with the more linear, conventional thinkers. He will never take a straight line to do anything, and even when very young, would chose incredibly hard, convoluted routes to get from A to B (simple example - with a toddler counting book, he'd jump all over the place counting the 20 fish, and never systematically work his way across, down, or through clusters. He was never wrong, though.) He avoids doing things the way everyone else does, on principle: his art was never recognizable because "I made it interesting, so it doesn't look like everyone else's." I can still instantly find his work on the classroom wall, as his will be ten times more complex than anyone else's - and unusually unfinished ("complexity" was his favourite word for several years). His clothes and long hair set him out from the other kids, on purpose. Even as a toddler, he was noticeably impervious to peer pressure (even when you wished he would, just this once, try something just because all his friends were doing it.)

There were a lot of things we thought he couldn't do, simply because he wasn't interested in doing what everyone else did. Then he'd do it once, you'd realize he was perfectly capable - but you'd never see it again, and sometimes we'd think we just imagined it. A seriously divergent thinker can be rather bewildering to live with at times. A teacher-pleaser he ain't.

Worksheets and repetition make his anxiety levels go through the roof. He never finishes the simple tasks at school, so his grades are so-so, regardless of his knowledge of the material (he got his first-ever real differentiation in math this year - and his first-ever As). He too desperately needs that big picture, or the material just doesn't mean much or engage him. He thinks in visuals and concepts, and putting those into words for other people can be slow (and writing them down veeeerrrrrry slow.)

But given our school is generally a very bad fit for a divergent, math-y thinker, I couldn't begin to tease out how much of his school challenges are simply boredom/ bad fit vs. learning challenges. He does have slow processing speed. It's highly likely that he is ADHD-I like his sister (but much more so!). These surely contribute to his being slow/ off-task, but we don't see them much when he's doing something exciting, like programming (but then, LDs are notoriously inconsistent). And maybe there's also something going on in expressive language that's impeding his writing (we're still struggling to tease all this out), or maybe it's really just the visual-spatial thing a la Linda Silverman (she may be pretty skimpy on evidence, but she sure can describe the men in my house - and a recent STB suggests we were not wrong in suspecting that DS is a pretty extreme example of the VS species).

So this isn't too helpful, I know! First I tell you its all just giftedness, then I throw all these possible LDs into the mix. Your own intuition is probably the best starting guide. Do you feel like he's struggling with certain things? Do you sense that some stuff is actually too hard for him, or just harder than it seems like it ought to be? Or does it feel more like he's actively seeking out ways to make simple things harder, in order to liven up an otherwise tedious task, or simply to exert his own very sideways approach on it?