Coming in a little late on this, but your post could be my son. He does the work, and does well at it, but he's bored to tears and won't put any extra effort in because he sees it as a waste of time he could be spending on other things. Unfortunately, I haven't found a complete solution to this problem. But I have found that putting him in activities that teach him how to concentrate helped. My son started taekwondo when he was four, and violin when he was seven. Both force him to focus on one thing, and learn the value of practicing the same thing over and over. At school, he was not learning to focus because he didn't have to. Taekwondo and violin have given him a reason to do so, and to a certain extent the effects have spilled over into his school work. He still rushes through things and makes silly mistakes sometimes, but when he is told to write a five sentence paragraph, he doesn't limit it to that - if there is more to write, he writes it. He does his math work, not because he likes it, but because his teacher allows him to work on more accelerated assignments when he is finished.
Like I said, it's not a perfect solution, but it has helped.