Great question. Frankly, based upon your description he sounds quite ADHD to me. Almost always, the adults around the ADHD child share a universal "gut reaction:" they typically say things like "He's a great kid... he's bright and creative... but HOLY COW - he wears everyone out!" Too, these kiddos often get into trouble not because they are bad kids, but rather because they cannot seem to contain themselves. So, they blurt out stuff, knock things off the counter, break things, act inappropriately... all in the name of being a little nutty.
And the teacher may well have taught an ADHD student in the past, but not all ADHD looks the same. Honestly, I would take him for an evaluation. And here's the nice thing from your perspective as a parent: if your boy is prescribed a trial of medicine to see if it will work, two things are for certain - (a) we will be able to tell within a few days (or less!)if the medicine is right or not, and (b) if it is not, no harm no foul. The medicine is very water soluble, and will clear his system in either about 4 hours (for the standard meds), or about 8 hours (if he is given the sustained release). So, nothing hangs around in his system.
I hear the frustration in your question, but I also hear the admiration you have for your son. And believe me, even the best, XXXXX XXXXX and well-intentioned parents get pushed to their limits when they have one of these high-impact, high-energy, high-maintenance kiddos in their home. It is tough, but hang in there. If the medicine works, it will be like some one finally turned up the inner light in your child - all of the good will shine through without the crazy noise around it!
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