Many eggs, and a comically messy counter later, I figured there had to be a better way to teach a kid how to break a few eggs.
Rap the egg firmly against the inside wall of the bowl.
☆ Use an especially large bowl. The high walls of the bowl act as a splash-guard.
Turn the egg about a quarter turn around the dotted line around the center of the egg, and rap it again. Repeat around the egg until there's a nice clean(ish) break.
Pull the halves of the shell apart.
Ker-plunk! Mission accomplished.