The Mahalonobis Blog has a great entry on using analogies to teach statistics. Here is part of their entry:

An educational experiment in 1989 pitted a group of students with high reading scores, selected especially for their lack of interest in baseball, against a group of low-scoring students who happened to be avid baseball fans. The two groups were asked to demonstrate their reading comprehension of a passage on baseball. Can you guess which team won? Answer: the baseball experts. The idea is that reading is primarily about analogies and metaphors, and so the more things you really know that are related to the subject under discussion, the easier it will be to understand what someone is saying about it. Stephen Pinker’s new book The Stuff of Thought emphasizes this point. A good analogy is meaningful if it resonates with one’s knowledge base, as opposed to those old 19th century writers who use phrases that have lost their meaning (eg, “long in the tooth”–very few people are up on horses today). So a vibrant speech contains many meaningful analogies because you know exactly what they are talking about when they say “it’s like rebooting your computer.” The more you know, the more meaningful the analogy and what it relates to, and so you know it’s strengths and limitations. Sure you have to know what analogies do (ie, process), but knowing the facts is perhaps more important. For example, say someone said that Microsoft’s Xbox strategy is like the Schlieffen plan? You need to know both facts, The Xbox strategy and the Schlieffen plan, to assess this statement. In fact, knowing the definition of an analogy is pretty superfluous in evaluating it if you know the facts.

It’s a simple point, but remember that most educators today emphasize learning to learn, and consider facts as less important than process.

I think this is where really mathematical people fail, in that without a good knowledge base about the subject in question, their ability to write down a partial differential equation or fancy algorithm is insufficient for the average problem that is really interesting. Sometimes these savants will have a neat problem fall into their lap, but many really smart mathematicians or programmers can’t prioritize because they don’t know the facts, so they can’t rank anything–they just connect things in often irrelevant ways.”