I don't believe that small children have the speed of mental calculation to be able to handle being ignored because of their tantrum. Let me explain.....
The child is throwing a tantrum because he feels frustrated for whatever reason, and, like a new baby's only method of communication is
crying, the small child's natural method of expressing frustration is the tantrum. He is not being "naughty", he is feeling highly frustrated (rightly or wrongly), and is expressing that frustration instinctively - as he hasn't yet mastered handling such an overwhelming emotion in a more positive manner.
If his parent walks away and ignores him, the feeling of abandonment will overshadow the learning of the lesson that "when I do this, mummy walks away, therefore I shouldn’t do this – then mummy wouldn’t walk away/ ignore me". It compounds the feeling of frustration in the moment, and the feeling of being left is very strong.
Better than ignoring....
However, if you set your child up a couple of times specifically for this lesson, you have the control, and the opportunity to help the child learn the lesson with compassion, care and support. He can learn the lesson, and still feel your love, sincerity and care. Because you have designed the occasion especially for the tantrum - you are fully prepared, and therefore won't feel frustrated at the inconvenience/ embarrassment/ time wasted etc. You can calmly and sympathetically follow through with the consequence you have set up. (i.e. skipping a treat or outing)
Plan ahead, and choose a place she is bound to throw a tantrum. Make sure there is something in it for her. For example, if it's grocery shopping - make sure she's going to get something out of it in the end. Then... tell her that if she throws a tantrum (it's vital you make sure she knows what this means - explain to her exactly what constitutes "throwing a tantrum"), you will leave and go home immediately - skipping whatever her treat was.
The most important points here are:
1. that she knows exactly what "throwing a tantrum" involves, and therefore knows exactly how she needs to behave, and what she mustn’t do.
2. that the treat or benefit is something that means a lot to her - whether it's an ice-cream or a trip to the park, whatever it is, it needs to be something she cares about at the time, and is looking forward to.
3. that you follow through calmly, without hesitation, but with sincere compassion. It's important that it is not dealt out as a punishment - say something along the lines of: "I'm sorry sweetie, but I did say that if you did that, we would have to go straight home, and unfortunately, you did it, so we do have to go straight home now. But never mind, maybe next time you'll be able to do better, and then you can have the ice-cream/ go to the ...."
I really believe that a lot of good can be done by being on her side. Be genuinely sorry that she has to go without whatever it is, and that you have to go home. Feel sorry for her, rather than angry or frustrated. This will have two powerful effects in particular:
1. No matter how upset and frustrated she feels, she will feel you are on her side, and that you care. She won't feel a power-struggle.
2. It will help your own stress levels. You will feel calmer if you are just feeling sorry for her. Think of it as a trip to the dentist. It's unfortunate she has to go, but you do have to take her, and the best you can do is be sympathetic but still take her.
It's important you set it up so that you can leave the instant she throws her tantrum - regardless of whether you are finished shopping or not. Because you have set this up, you are expecting to leave, so do it when you don't reeeeeally need the shopping ; )
I believe you will only need to set this up a couple of times, and if you follow through without exception, and immediately, and with compassion and sympathy, it should work beautifully.