I'm trying to teach my kids to take ownership for themselves. I want to teach them to be responsible and independent people. There are many different situations which provide me the opportunity to turn a mistake into a teachable moment.
One technique for teaching that I've had some success with is the "You can fix it, or I can fix it" approach. It's very simple and I've found it very effective. It doesn't work in every scenario, but when it's an option, it's one I tend to favor. Here's how it works:
I've had to "clean" the room a couple times, but the whole process takes me maybe 5 minutes.
The technique can be applied in many situations where the kid needs to take some corrective action that perhaps they don't want to take. Offering them the opportunity to take that action and solve the problem in a way that they prefer gives them ownership in the solution and teaches them how to solve problems. If they don't take you up on your offer, then you get to solve the problem however you see fit.