Having a child take things apart is not, in and of itself all that unusual. Nor is it unusual for a three year old to be defiant. I would hesitate to suggest that anyone could diagnose him just from what you have said here, and, from reading your answer, I would say that you are aware of that. Also, as I'm sure you are aware, it is extremely difficult to diagnose such a young child with ADD or ADHD, and I would get a second opinion if someone did.
Don't worry too much about traditional learning and set benchmarks. It sounds like he is picking up what he needs to, even if he isn't doing it the way that others would have him do it. Here are some things to try and sneak some 'learning' into your every day routine.
*Try having a 'sign in' sheet for activities that he likes to do. A favorite toy, or game on the computer or ipad, whatever. Have a clipboard and paper and he must sign in to use or do that activity with his name or whatever it is you would like him to do that day. To make it more engaging, have it a prerequisite for all the family members. If you want to watch a program on TV you have to sign in. If you want to play that game or surf the net, you have to sign in.
*Remove toys that are broken until they can be fixed. Explain to him that if you break your things, thats fine, its your choice, but now it has to go up until it gets fixed. Then do so, and don't make anymore of a big deal about it. Keep that consequence a natural one, don't punish or get upset (even if you are). To get the toys back he must help fix them.
*Keep 'screen time' to a minimum. TV, computer, ipad-all those things are fine in small doses, but if attention is a problem these things could make that problem worse. Turn on some music and have some quality time with quiet things like clay or wet sand. Let him use those taking apart skills in putting together. Have some letter cards that you can lay out clay onto to build the letters, or some molds of various sizes to make some sand castles (just recycled yogurt containers or the like). These sort of things can be remarkably soothing to young ones.
Anyway, don't panic. Every child is different and wonderful and I have never met a little one in twenty years of teaching that couldn't be reached, especially if the parents are engaged in their progress. Good luck!
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