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There is a saying about Aspergers which I believe applies equally well to most, if not all, other special needs - to paraphrase; "if you've met one person with special needs, you've met ONE person needs".
Just as all special needs people are different, the calming techniques required are also quite different. Techniques which calm one person may simply infuriate another.
Trial and Error
In this post, I plan to cover a few approaches but the application of these is very much a matter of trial and error. If your actions seem to be worsening a situation then stop and try a different approach.
No technique is going to work unless you have attention. It doesn't have to be total attention, part attention is fine. Don't forget too that many special needs children have issues with eye contact, so "attention" doesn't necessarily mean "looking at you". In fact holding your hand out wide and saying "look at my hand" can often be more effective. In particular, if your child is holding an object which is causing an issue (Nintendo DS, I'm looking at you) then it's imperative that he puts it down before you try talking to them.
A Calming Influence
When my eldest son goes into a meltdown state, he responds best to a calm voice. I simply repeat reassuring phrases such as "it's alright" and "that's ok" in a quiet calm voice.
He'll usually try to shout over me but I won't engage him in conversation when he's melting down. Conversing with a melting down individuals will only bring insults and hurt which will be regretted later.
You may be tempted to pat the anxious or otherwise stressed individual on the back or arm. Be very sure before doing this as many individuals on the spectrum have issues with touch. Back off immediately if the child reacts badly and if possible, get them to come to you rather than approaching them. Putting your arms open wide and suggesting that a hug might help is a good way to do this.
If you're dealing with an adult, make sure that you ask them for permission first.
Some children react better to authority voices than to calm ones. An "authority voice" is always calm and mostly emotionless" but it has a stern edge to it and carries orders. For example; "Put that down - right now".
Some children react to a countdown, "three, two, one" but others will continually wait until the last number or will even worsen their misbehaviour as the countdown progresses knowing that so long as they stop before it ends, they'll be ok.
If your child is doing this, then the countdown method is not working and should be discontinued.
Shouting and Negative Reinforcement
Shouting almost never works unless perhaps your special needs child has a hearing loss. Seriously though, shouting can sometimes make you, the parent, feel better but most of the time it only worsens the issue.
Shouting at children only teaches them that shouting can be used to get others to do what you want. Shouting parents are more likely to have shouting children though of course, shouting behaviours can be learned in the playground too.
I'm not going to say much about violent methods of control here except that fear and violence usually bring the opposite of calm - and when they do produce calm, it's not a good kind of calm.
For some parents, calming times are "promise times" and parents will often promise their kids "the earth" for just a little calm.
If you promise your kids something, then follow through and deliver on it - good or bad. If you say "no dessert tonight" then don't give in later. Similarly, if you promise a toy for good behaviour, then you should provide it. Being consistent and predictable will lead to a much calmer life.
One thing to remember though, promise easy and inexpensive things like a walk in the park. It doesn't take much for these promises to become routine and I know parents who have to buy toys and/or sweets everytime they go out shopping.
When my kids are having a tough time, I'll often talk about my childhood. For example, if they're being bullied, I'll talk about when I was bullied at school. It's important to keep things positive but you shouldn't try to make out that things were tougher "in your day" or that you were a hero.
The object of the conversation is to relate - not make your kids feel more inadequate.
For the most part, reacting with humour to any meltdown, anxiety or stress event is a big "no no". While these outbursts may look like simple temper or "cry-baby" issues, the fears, anxieties and reactions of special needs children are very real to them. Not only is it impolite to laugh but it's also damaging to a child's self-esteem to reduce their issues to comedy. It is never ok to laugh at these children.
Of course, there are occasions during panic attacks and meltdowns where a bit of impromptu comedy can work wonders. In particular, where a distraction is needed to prevent fears from building up. For example, while waiting in a queue at an amusement park.
Out of Sight
If an object or a person is driving an issue, then it's important to get them/it out of sight as quickly as possible. If the child is having an issue with a computer game, then simply talking to them with the game playing in the background isn't going to help matters. Get them out of the house and onto outdoor play equipment. If their issue isn't staring them in the face, they'll get over it more quickly.
Keeping things out of sight is particularly important where meltdowns are concerned. I find, as an adult that if I'm overly stressed, the best thing to do is to be alone. If the child is too distressed to go into their room then it helps if those around him retreat to another area (or at least avoid looking at the him).
Don't be afraid to change plans. My eldest son recently went on a caves tour which ended in a boat ride. He became agitated about riding in a boat in the dark and refused to board. We changed plans to allow him to walk back through the caves with a guide. As a parent, you need to pick your battles. Sometimes you can convince a child to conquer their fears - and sometimes you can't. When you can't, you change the plan.
My last point is simply to be prepared. Try to see the danger signs before your child begins to stress out about them. If you can jump in and defuse the potential situation before it escalates into one, then you'll have saved everyone a great deal of trouble. For example, when eating at a friend's house, consider asking the friend to let you prepare your child's plate. That way you can ensure that it only has the things that they'll eat on it - and you can make sure that no foods are touching each other.
Being prepared is probably the best form of avoidance.