But (not sure if I'm getting this right) some others, such as kiskidee, seemed to say those kids could not then function when they got to school and had to obey a teacher just because they're in the position of authority. (Is that what was meant?)"
The explanation thing is not a straightforward thing. Remember i am talking with a teacher head here because I am the parent of a 3.5yo.
Don't give explanations when a child is challenging your authority. At this time, the child is treating you as an equal and they most certainly are not. It is better to break off contact, remove the child or yourself from the room before losing your cool or getting shouty. You losing control is a sign to kids that they are
controlling you. As early as you can identify that the outcome is heading down an familiar negative path, break off the contact by sending child to his room etc. At home you may find that you leaving the room for a few minutes may give the child time to 'save face', and they may comply in that time. Or say something like, when that song finishes, the next commercial break starts, etc, you should do X or Y. It gives the child a few minutes to cool down and a 'save face' in which to follow instruction.
Only have a discussion with a child after they have shown by body language, not necessarily words, or have followed an instruction. It doesn't have to be right away but only when you are sure they are being compliant mode, not necessarily when they are doing the job, maybe sometime later. But keep it brief. It is after they are complaint that you can discuss reasons for your expectations, appeal to their empathy or even say embarrassing things like if I didn't care, I would not punish you / expect you to follow rule X because I would not care how other people see you/ how you turned out when you are older, etc.
If you are trying to break a cycle of established bad behaviour, it is beneficial to lay out certain defined sanctions for not complying with basic household rules. This way, when a child breaks the rule, they already know what will happen. You can only briefly remind the existence of that rule when a child is not being compliant and if they defy it, the sanction has to be followed. Hopefully you have another half (at school it is a colleague who you can send the child to be supervised with) to whom the child may resort for appeal, only to find that your other half backs up the rule rather than undermine it. Having a partner there gives you relief. The child also has relief from the situation but the child also finds someone who will reinforce the rule. (the rule! not take your side).
There are some children who are experts at playing off one parent figure off another and come to school and try to play one member of staff off another. These are the kids who are problematic because they the most difficult to accept that they are not your equal. For them, explanation really is room for negotiating a more equal footing with you, ie get their way. Unfortunately they can be unhappy for a long time before tehy 'get it' and I can't say that there are easy ways breaking their expectations. The change if you are in this problem has to start with the parents cooperating with each other which may have its own set of issues why this problem occurred in the first instance.
There are some kids who accept your authority and you find that over time you can discuss the whys of a rule but be careful when you hold this discussion. Not when a child is not in the mood to follow the rule. These are the same kids however who least need to have rules and sanctions - and they bring this behaviour from home. When I find myself punishing these children, they accept that they are wrong anyway and accept their punishment without whinging.
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as I said, Blessthismess, I have not read AK so I don't know how he fits the explanation thing into the picture.
This was a long ramble but hopefully it makes sense to some of you.