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Tantrums have to be the most common issue that parents of 2 year olds face. Tantrums in children this age are common generally due to the fact of the child's communication abilities being limited. Just as adults get frustrated, so do children; and often this is because they are unable to efficiently communicate their wants and needs to those around them, and be understood, or simply because they do not get what they want.
Work through this by continuing to teach your daughter to use words and actions, instead of screaming and falling out to express herself. It can be easy to ignore this behavior at home, but in public, it is impossible. Take notice of the times when your daughter is likely to have a tantrum (perhaps because she is tired or hungry even), avoid taking her places during these times, and when you do have to, take along things that may help in distracting her when she tries to have a tantrum (a favorite toy, a book, or a snack). Just like with the potty, praise your daughter when she behaves as you want. Tell her how proud you are of her, and reward her with a little prize for her good behavior.
Definitely work not to yell at your daughter or get angry when she has a tantrum (I know this is much easier said than done), but it is necessary, and realistically, children learn by example, so if she sees you screaming or being angry, this is the kind of behavior she is learning. Always remain calm, and talk to her; when you are in public, take her away to a quiet place, bathroom, the car etc., where you can remove all other distractions, and work to get her attention one on one.
Here is a website that may help with more information on dealing with your daughter's tantrums: http://www.mayoclinic.com/health/tantrum/HQ01622
I also recommend that although the tantrums seem normal, that you bring this behavior up to your daughter's pediatrician at her next appointment to see if he or she has any further diagnosis or advice.
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