The "build a big log cabin and watch it burn" technique is too finicky and prone to failure for my taste (or at, least, I don't have the right skill set to make it work). Keeping tinder/burning small stuff close together and gradually expanding the fire by adding wood of the right size (at the right time) seems to be a more fool-proof way to proceed, in my humble experience.
I've played with different arrangements to start campfires a lot, and I've observed others a lot too. There are lots of ways to set them up that work good, and most don't require as much fussing around as that one.
The advantages I've found with this arrangement are that once the tinder is burning you shouldn't have to mess with it at all, the fire should take off fast, get hot fast, burn hot a long time, and have a good bed of coals that will last awhile before it flames out.
The disadvantages are you have to sort by size, and break to length, a lot of sticks to set it up, and then you have to build it.
But sorting your fuel supply is something I've found pretty important to getting a fire going quickly anyway. You don't want to be futzing around trying to find more good tinder while what little flame you have is dying out.
This one takes some fiddling to build before you light it, but I think it's worth learning and practicing because it has consistent good results and it fairly well demonstrates the basic rules of making a fire, Tinder-Kindling-Fuel-Airspace. It sort of forces them in the building process too. If you try and stuff too many sticks in your log cabin it will fall apart
I take the time to do it because I can light it easily when I'm ready and then sit back and relax awhile.
I guess another tip worth mentioning and teaching the kids would be to mix your wet wood and dry wood while you keep your fire going. Once I have a fire going I'll often switch to adding fuel in a tepee arrangement. That works really good with damp fuel because you can tepee the bigger wetter sticks in the coals and keep the flames up with smaller sticks under them until they dry out enough to start burning. Once you have a good bed of coals you can burn some pretty wet wood doing that. I've had big billows of steam coming off my fires doing that