I would add the following. Students actually find the idea of oral transmission of traditions pretty straightforward to grasp. They are familiar with the telling of stories in our culture, jokes, anecdotes, urban legends, and they are often inclined to think intuitively that this sort of thing provides a good analogy to the transmission of early Christian traditions. What students find harder to grasp, in my experience, is the notion that the Gospels are related on a literary level, that there is a lot of copying going on. They need to be shown the texts and to see that at least two of the evangelists are involved in some pretty serious copying. Our culture disdains this kind of copying, and avoidance of plagiarism is now a huge issue in universities and colleges. Students are sometimes shocked when they see the extent of agreement in the Gospels because their guess, before doing any study, is that they are independent witnesses to traditional material. This is especially the case for churchgoers, for whom the Synoptic Problem is rarely, if ever, taught.
I noticed this year on my Historical Jesus course a related failure of some students to grasp the idea of "multiple attestation". In spite of some introduction to the key issues in Gospel criticism, some of the weaker students would still treat the appearance of material in all three Synoptic Gospels as "multiple attestation", imagining a model in which the Synoptics were independently relating traditional materials.
Teaching students about oral tradition is an important and challenging element in the teaching of Christian origins, but I doubt that playing Chinese whispers helps anyone to understand it well, not least given the much larger task of explaining the inter-relations of the Gospels.