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It sounds like your daughter is experimenting with her voice and, at the same time, with her place in the family. She certainly wants to be noticed! Having ruled out a medical cause, approach this like any other 3-year-old behavior and ask yourself, what is she getting out of this? In this case, it is likely a way of seeking attention. She gets attention when people look at her, when they respond to what she is shouting and when you remind her to be quiet. Don't forget, negative attention is better than no attention at all!
So, the way to manage this is to NOT give her attention when she shouts - only when she uses an appropriate voice. Start by listing examples of good times to yell and good times to speak in an indoor voice. Then, practice. Go outside and shout with her. Encourage her to shout more. Then, come inside and speak almost in a whisper. Once she gets the hang of this game, tell her that the game is going to continue all day. When she shouts, "MOMMY, I WANT MILK," just respond calmly and in a regular tone of voice, "I'll be happy to give it to you when you speak with an indoor voice." Say it once, maybe twice, and that's it. Then, go about your business until she modulates her voice. Even if she tantrums, don't give in! If you wait her out a few times, she'll get the message that she can only get what she wants when she speaks appropriately. When you are out somewhere that requires her to be quiet, such as the grocery store, let her know that you will have to leave if she is speaking too loudly and disturbing the people around her. After one warning, follow through. When she sees that you're consistent and calm about it, she'll slowly learn to use an indoor voice.
The answers from our experts are for educational purposes only. Please always refer to your child's pediatrician and mental health expert for more in-depth advice.