With each one, I need to find a balance. Believe it or not, very few of my students have studied a single story from Greek myth (most were stunned to find out that Disney's Hercules had little resemblance to the original story, since that was their only previous encounter with Greek myth), and while more of them have experience with some Native American stories (since we live in the Northwest), virtually none have read any stories from Africa or China.
And I find myself researching each system to the nth degree, reading reams of books on geography, typical community values, beliefs, monetary systems, and other associated elements, but I don't want to overload the students with too much information so that they end up drowning in it instead of digesting any of it. I also don't want to stereotype cultural assumptions, especially since different tribal and geographical communities had different ideals and accepted precepts.
At the same time, an understanding of major belief or cultural systems is necessary for deciphering some of the tales. In fact, the stories themselves serve as good examples for illustrating some major ideas. For instance, several stories in our Chinese myth text explain and contrast Confucianism with Taoism, allowing students to see both major tenets of each belief system and how the two philosophies compare and in some ways argue with each other. I only have a few weeks to let students explore all of this, however, so I have to balance dealing with the stories fully and giving background so that students can see each story's cultural significance.
Perhaps, at this point, my goal should be meaningful exposure. Let the students read, research, and find what they can, while (hopefully) encouraging them to continue their reading once class is over. I find, with each set, though, that I wish I could spend the whole semester on it. I love each one, for different reasons, and I am always sorry when a particular section must come to an end.
I only hope this dabbling into myth inspires students to examine their own mythic system, examining it for its sources and influences... and even assumptions. That might be the most meaningful exploration of all.