Good points by tschock. Kids with ADHD can focus on things they like. You might want to get the book, "The ADD/ ADHD Answer book," by Susan Ashley. It will not only help you figure out if he has something like ADHD, it will give you many ways to help him if he does.
He's 3 1/2...they do that. Toddlers do not sit still! They ALL appear hyper...well, maybe not all...some are like zombies.
I have ADD...had it all my life. When I was a child my mom knew that I was "special". I was a very quick learner, smart as a whip, and knew how to read by the time I was 4.
It wasn't until grade 1 that I started to "act" strangely. I couldn't focus...and that is what ADD/ADHD is all about...concentration. When a child is bored they will doodle or read to themselves...children with ADD/ADHD sometimes do a little more "disruptive" things in class...but not always. I always sat there...read to myself, got ahead of the others in our readers while reading out loud, and then I had no idea where in the story we were when it was my turn to read.
A child of three is used to, and meant to, run around exploring...not sitting at a stuffy old desk. I hate that children nowadays are considered "hyper" by the age of 5 if they aren't zombie-like. I also think that most of these children that are now being forced to go to Kindergarten full days are going to be labeled with ADHD.
I wish that all adults over the age of 40 would try to remember what it was like when they were kids.
We went to Kindergarten to play, not to memorize times tables. We ran around, out on the streets until dinner time. We ran!!!! We skipped!!! We had fun!!!
Kids now are expected to sit like good little zombies and not be heard from.
Unless your child is a "gamer" he isn't considered "normal".
"Normal kids" sit and do nothing. "Hyper kids" play hockey, baseball, etc.
Hyper kids play with toys and have good imaginations...normal kids are the ones that are obedient and don't fart until you tell them to.
Seriously, what is this world coming to? We want babies to be adults. 3 year olds need to run and explore, not sit at a table being quiet. There are some children who prefer to sit and read ( I was one of them), but if they don't want to do that before the age of 5 then we shouldn't force them.
If it was me, and my child being discussed, I would bring him to a different nursery/play school. If they expect a 3 1/2 year old to sit still for long periods of time then they need to have thier heads examined.
IF your son was 16...I would be worried.