One of the finest features of National Parks in the US is the Park Ranger program: knowledgeable park rangers give free lectures, lead hikes, and offer free (or low-cost) programs at visitors' centers. Some parks -- including Yellowstone-- also have a "Junior Ranger" program for kids.
Any visitor to Yellowstone National Park will want to learn about geology and wildlife, and fortunately, learning is easy due to an abundance of free or low-cost Park Ranger programs.
Above, a Park Ranger gives a group of kids an introduction into how the game of life is played, by Yellowstone's animals
If you enter the park from the north, Head to the Visitor's Center at Mammoth Hot Springs, and sign up the kids for the "Junior Ranger" program (for a modest fee.) Kids get takeaway material about wildlife, and if they complete certain activities they can return to the Center and earn a patch (badge)*. Read about the Junior Ranger program at the Yellowstone National Park site.
*Always check for updates!