Sometimes all you can do is stand by, try to keep the child and others safe, and wait until it's over...which means:
You stay close.
You get them away from other people/get other people away from them.
You move fragile and potentially dangerous objects out of the child's reach.
If the child is at risk of injury from self-harm you try to estrain them or you try to redirect their aggression (e.g. old phone books to rip and claw at, punching bag or pillows or foam safety mats to hit and kick and smack your head against).*
You wait for the child to calm down.
Some children can be calmed during meltdowns (e.g. with restraining bear hugs or being wrapped tightly in a blanket, and/or hearing a calm/soothing voice). For others, this is either impossible (they are too strong/too big) or would simply escalate their feelings of panic and rage, prolonging the meltdown and/or worsening behavior over the long-term via traumatizing them. (I suppose that calming like this technically does, from a developmental perspective, have the potential to teach self-soothing, but I doubt this is what you mean by "discipline").
What would you do? Tell them to stop? Threaten consequences? Try to reason with them? Hit them? My parents did all that during meltdowns and all they ever accomplished was to make those meltdowns worse, and actually to make future meltdowns worse because I would instinctively expect to be hurt during meltdowns.
A child having a meltdown (at least what I define as a meltdown) is not able to think rationally -- you can't reason with them. Some people lose language processing abilities under stress (and a meltdown involves the most extreme levels of stress a person can experience), which complicates things even more. Many can't even remember most of what happens during meltdowns -- how are you supposed to learn from something you can't even remember?
A child having a meltdown is operating on basic instinct, in a state of extreme fight or flight where any attempt to intervene may be registered as an extreme threat -- the same level of fear as if the intervening person was an axe-weiling maniac attempting to chop off their head. The more aggressive the intervention (angry voice, shouting, physical discipline, threats) the more likely the child's out-of-control emotions and behavior will escalate and that they will simply be traumatized rather than learning anything.
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*Thinking about this, redirecting aggression counts as discipline, as it would hopefully (over time) become automatic/instinct.
You lived with these meltdowns, and learned plenty. Do you also have a child that went through this? It would be awesome if we all had this awareness, coping skill, and understanding, but 99.9 % of the population does not. This is why we keep hearing in the news about caregivers, school and police personnel, and bus drivers behaving badly with autistic children having meltdowns. No one knows what to do, but reverts to what they were brought up- which is discipline, restraint, yelling, and more. Or utter fear and helpless terror.
It takes a special person to understand, engage, and have the patience to endure all this. Only families and or specially trained people who work with Autism are taught to recognize, understand, and safely engage with the child prone to these negative behaviors.
Although I don’t condone this father’s behavior, it seems to be the culture he comes from, and he is doing what comes as his response to something he knows nothing about. He is clearly fearful, frustrated, uneducated, and enraged. So I can understand how he copes by beating his kid.
I see teenage “baby mamas” beating their kids all the time, and it’s due to lack of education, awareness, maturity, and cultural upbringing. That old saying “Spare the rod, and spoil the child” is still very much in action. It’s difficult to witness when I walk down the street, or ride the transit system.
People don’t care why a child is behaving badly, they want it to stop and stop immediately. It’s an instant gut reaction, just like when a car alarm keeps going off and no one shuts the damn thing off. Or stops their barking dog. It’s a sensory issue. It’s a fight or flight mechanism- in this case the parent “fights” his child.
Meltdowns can be so shocking to witness to the casual observer- sounds, actions, words, violence. Truly, one wants to run away, or call the police, or do something. But what? Interfering brings on potential violence but not interfering is potentially as bad.