Here's the thing. Whenever a kid gets hurt there are a few things that must be done. In order.

**Assess the damage**

You want to be careful not to scare the child in this phase, but before anything else (even comforting) you need to asses. This can be done very fast. All fingers still attached, yep. Anything broken, nope. Move on.

**Calm the child**

Kids are kids, and haven't developed the means to cope with pain like we adults have. They get scared. They are scared that they will get in trouble, or that they did something wrong. They are scared of the pain. They just get scared. You should take a moment and make sure to calm them down. How you do this is different for every kid and every parent. Some times for every situation. Maybe it's a hug, maybe a "Hey, your ok! Listen! Your O! K!" It just depends. As long as the child is calm now, your did good.

**Teach The lesson**

"I told you to be careful around doors. This is why. If you don't want to get hurt again, then be more careful around doors." Some times it won't stick. Some times it will. You need to make sure that your response is measured and not angry, but that doesn't mean it shouldn't me firm. 

"Don't mess with the chain saw or you'll get a boo boo." Is not going to help anyone. "Do NOT TOUCH THAT CHAIN SAW OR Y O U - W I L L - G E T - H U R T!!!!" even though a bit scary will make  a lasting impression. At the same time getting that "loud" over a door or something trivial is just silly. (side note IRL, move the chain saw.)

Keep in mind that in order to teach that their actions had this painful outcome they have to be calm. 

**Treat the issue**

Yep last, normally. You want to get in the association really fast. So when the injury is minor you make your point first and then treat the injury. But remember that all this takes place in a matter of seconds, not hours. If you can't, for example, calm the child, then skip that step. Also remember to use a bit of common sense. If a finger has been removed, then you still need to calm the child, to make treatment better, but your first priority becomes stopping blood loss, and preventing further damage. 

**Notes on sympathy**

You don't need to be sympathetic every time. You need to be you. You need to make sure everything is ok, and that the child knows that action leads to result. That said, sympathy is a great way to calm a child, and overall makes people feel better. It's also great for "treating" an injury.

That said, reacting to every scrape and bruise with this big fountain of attention  and activity, will only teach that getting hurt leads to attention. Not really a good lesson. Small injuries like this one are normal and every day, and should be treated as such.  There's nothing wrong with a hug and a little sympathy, but at the very same time, an over reaction can cause problems too. 

**What I do**

Access the damage, "Hey, listen! Can you wiggle them like this? Let me see." Calm the child, "It's ok, look like you just smashed them really good. It will be ok. It might hurt now but that will pass." Teach the lesson, "This is why we say it's important to watch your finders around doors. If you don't you get hurt." Treat the issue, "Here, lets put some ice on it. It will make it feel better." Then while were sitting around with ice on hands, Tell a story, "You know I was forever getting my fingers smashed, but I learned. If I just watch where I put my hands I could avoid that."

As to hugs, to each their own, some families and huggy, some rarely touch.  

**The important part**

You don't have to be super emotional and talk all weird and squishy to show sympathy. Heck even "See! Don't be a dumb ass! (that one would be my grandfather)" is a fine response. Though in fairness "don't be a dumb ass" always turned into him making me feel better, by telling me about times where he was being a dumb ass and ended in the same result. There are many way's to show sympathy. The key is to keep interacting, and show that you too faced like problems.