If it's happening in the middle of the night, I wonder if this is night terrors and not tantrums. Usually a tantrum is in response to something -- a protest so to speak -- where ignoring might work. (I recommend the Happiest Toddler on the Block book or dvd since it really helped us).
Night terrors will wake the baby up and make them scream. I pulled this information off of Dr Sear's website for you:
Characteristics of night terrors:
Your child seems frightened, but cannot be awakened or consoled.
Your child may sit up in bed, or walk around the room, screaming or talking senselessly.
Your child doesn't acknowledge you, his eyes may be open but he seems to stare right through you.
Objects or persons in the room might be mistaken for dangers.
Episodes usually last between 10 and 30 minutes.
Usually occur in children 1 to 8 years old.
Your child cannot remember the episode in the morning.
Usually happens within 2 hours of falling asleep.
Night terrors are harmless and each episode will end on its own.
Why does a child get night terrors?
Night terrors are an inherited problem and occur in about 2% of children. It is as if the child is having a bad dream during deep sleep and cannot wake up. Night terrors are not caused by psychological stress, but they seem to be associated with being overtired.
Will my child outgrow this problem?
Yes, most children with night terrors will stop having them by age 12, usually sooner.
What should I do when my child is having a night terror?
1. Help child go back to sleep.
Do not try to awaken your child. Turn on the lights so that your child won't be confused by shadows. Remain calm, talk in a soothing tone, "you are okay, you are at home, you are in your own bed, you can go back to sleep". Again, speak calmly, and keep repeating these soothing comments. You can try holding his hand or snuggling him, but if he pulls away don't persist. Don't try to wake him with shaking or shouting, this will only agitate him more and prolong the attack.
2. Protect him from getting hurt.
Keep you child away from stairs, windows or sharp objects. Try to gently direct him back to bed.
3. Educate your caregivers.
Be sure to warn babysitters, family members, or others who might be caring for him at night. Explain to them what to do in case of an attack, so that they don't overreact.
Can night terrors be prevented?
The following exercise has been shown to stop night terrors in 90% of children. For several nights, keep track of the time between falling asleep and the onset of the night terror. Then, wake him up 15 minutes prior to the expected time of the episode, get him out of bed and fully awake for 5 minutes. Do this for seven consecutive nights. If the night terrors recur, repeat the seven nights of awakenings.