While it's true that developmentally it's not as simple at 3 to say something and expect them to just do it (is that really reasonable to expect at any age?? LOL!), when I read your post OP I wondered whether you ever have any consequences for your child when they act like that.
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To me, watching your child not listen again and again and not experimenting with consequences... well there's no reason to think they're going to do differently unless parents try something different.
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I related to the longer post above about consequences. My dd turned 3 last month, but I have been using consequences since she was early 2. And it works! She has favorite foods, treats, and activities that we do most days, and on a day when she's not listening/purposefully doing things she knows she's not supposed to do, I explain that she knows she's not supposed to do that, I ask her not to do it again. If she does it again, I tell her that if she doesn't stop or she does it again, the consequence will be she won't get any _____ or won't get to do ________. I try to pick the thing she was most likely to get/do next, so that it will be more immediate. I explain that she wont get it, or won't be able to do it, and then if she does it again, it's not a big conversation, it's a simple "Ok, now you can't do/get _____". Then, whenever she asks for it or it's the time we usually would do it, I calmly get down to her level, ask her if she remembers before when she did _______, asks her if she remembers me telling her she can't have it now because she did it again. She often will start to cry, but I explain that that's what happens when you don't listen, and I hold her and I'm not mad and I don't make a big deal, but I hold firm on the consequence.
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Now, at 3, we almost always can get her to listen and stop doing it, whatever it is. And if she does it anyway, she is used to getting the consequence, and she'll still make a fuss sometimes but mostly she just moves on now. NOW she's starting to try to talk her way out of it, which is hysterical and makes me smile, but I try to keep a straight face.
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Lastly, it's really important to not wait until your exasperated to try consequences. That's been one of my biggest learnings. I do them early on, when I'm still calm and it hasn't gotten too far yet. Because if I wait until I'm really frustrated, I've learned I just need to ride out her tantrum and not even talk about anything, because she can't hear and I"m too frustrated to deliver the consequences calmly and fairly.
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One more thing, I also really really have started making a point of coming back to GOOD behavior and reminding her of it and complimenting her for it or rewarding her. The other night we pulled up and I noticed that my neighbor's car hadn't been there for a few days and there was another car there instead, and I said out loud but to myself "I hope she's ok, hope nothing happened to her car..." and dd said "We have to go talk to her! If Melissa and Marnie's mommy has a problem, we have to help!" I was so proud of her, after we checked on the neighbor (she was fine), I took dd home and rewarded her with extra treats for "being kind and thoughtful".