I don't know. My son was trained before that age (he was done around 30 months?), and I have often wondered if late training boys have simply "missed the window" as your son's preschool teacher has suggested. I didn't have any drama with my son. No tantrums. No refusal. No nothing.
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Oh, and as for ideas? What I did was simply bribe him.
No, not some big something he wanted that he had to earn through some randomly assigned number of checks or stickers or what have you. Not a prize for 10 stickers. Not a prize for anything at the end of the week. But something for RIGHT NOW and something that involved him getting a choice.
It was simple really, but it may not work for your son. I don't know. But I bought a big bag of multicolored/fruit flavored lifesavers candies (individually wrapped). I dumped the candies into a clear ziploc bag and kept it on the kitchen counter, where he could see it but not reach it (at least not without scaling the front of the cabinets, which he could do if I wasn't watching).
Every time he used the potty successfully, after washing hands, he got to chose a candy out of the bag for immediate consumption. Every time. Didn't matter if it was bedtime. Didn't matter if it was right before dinner. It was a lifesaver. It wasn't going to spoil his meal. And if it was bedtime, we just brushed teeth again.
He LOVED getting to CHOOSE. In a way, it was an exchange of control. He went to the potty when I expected him to and in exchange, he got to choose what color/flavor candy.
After a couple of bags, I stopped buying "refills" and left only the candies that he had declined to choose (I think they were the pineapple ones, that are rather plain looking). He could still choose a candy after pottying, so I wasn't removing the reward... but he began to choose skipping the reward. And eventually, he just didn't bother to ask about it anymore.
I did the same thing with my daughter. She had a tendency to like the purple (grape) ones, while our son had liked the green (apple?) and red (cherry?) ones the best.
And I don't recall (it's been over 10 years now...) making a big deal about the bag of candies, either. Just said, hey, this is what we are going to do. He was a smart kid. And he didn't have access to a lot of candy (well, almost NONE to be exact)... and this was his ticket.
No pee, no poop, no candy. Really simple. But it isn't punitive. An accident where they run but just don't make it in time? Your call. If they really made a legit effort, I gave them candy anyway, but only AFTER they helped clean up whatever mess there was.