She's Not Stubborn,
Your little darling is at the playground and accidentally whaps a playmate in the head with a shoe. The playmate is crying, the moms come running, and the other mom and child are looking at you like, "Well, what are you going to do about it?" So you turn to your child and say, "Say sorry." But she won't. At all. Instead her waterworks start, and the afternoon at the playground turned into a whiny, blubbery mess. With perhaps a time out or two, too. What the heck happened?
It seems like such a simple scenario. All your child had to do was apologize and it would have been fine. Instead, with no apology and the stares and expectations of other parents at the playground, the situation just escalated.
Why couldn't your child apologize? Maybe she was struggling to manage another emotion often associated with such unintentional play events. Maybe she was embarrassed. And then frustrated, and then mad, and then...well, lots of things.
Kids have emotions, too
Kids are both simple and complex creatures. Yes, they can be happy and sad, but they can also be shy and angry and even mortified. Some emotions are more complex to describe to kids, so perhaps we don't as early as we could - but that doesn't mean kids don't feel those things.
Each child has his or her own unique personality, and as such, you can never be quite sure how a child's emotions will come into play at a given age or in any situation - but dismissing complex emotions all together would be a mistake.
Put a name on it and talk about it
A situation doesn't have to be as dramatic as a (minor) injury for a child to feel a wide range of emotions. It could be mistaking a stranger for a relative, or forgetting her library book, or any number of scenarios that makes a child feel embarrassed or something else. Put a name on various emotions and describe them. Describe what they feel like to you - and that everyone feels these things, not just your child. That not feeling alone can go a long way to helping to manage the emotions, and hopefully move on.
Apologies still need to happen
Manners and etiquette are, among other things, how we show people we respect them and care about them. Helping a child to understand this -- in parallel with helping to name and manage emotions - can help you to help your child to move beyond the embarrassment factor. In these little faux pas of everyday life, apologies still need to happen.
With understanding and coaching, you can help your child move beyond the feeling of being embarrassed about making a mistake so the apology can happen and play can continue. Next time, the whack won't be the end of the afternoon.
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