When I taught Kindergarten I was very firm on whining and screaming will NOT get you your way. I would let kids tantrum all they wanted (under my terms) but they quickly realized that it did not mean I would give in and let them do what they wanted to do. So, for the most part it stopped because they realized it wasn't getting the reaction they wanted and / or the results they wanted.
Well, being a mom of a strong willed, independent toddler... I've had to start this already with Blake. I have not given him a time-out yet, as I feel it would not be effective (I would if I needed a break more than he needed a time-out, but we haven't got there yet). I do not give in to him, and usually walk away and do something else if he starts screaming or such.
Today we went for a walk around the block, as we do every morning. Part way around he banged himself in the head with the toy he was play with in the carriage. I stopped an picked him up (stupid me!). When he calmed down I put him back in, but he did NOT want that. This I should have thought of ahead of time... once he's out he does not go back in willingly. So that meant for the next oh 20 houses or so Blake was screaming. I kept telling him that he was fine and needed to calm down. I knew all he wanted was to be carried, but I can not carry him, push the carriage and walk Abby all at the same time... sorry not going to happen!
Oh well, he finally settled down, and I was glad that I didn't give in and pick him up again. In the past when we've dealt with situations like this, the next time it happened he cried for a shorter time and then shorter and shorter. So yep, he's getting it, but it's still hard to watch your child scream in public and not give in. I am a mean mommy.... and proud of it!