The tl;dr version What successful strategies do you employ to teach the sampling distribution (of a sample mean, for example) at an introductory undergraduate level?
In September I'll be teaching an introductory statistics course for second year social science (mainly political science and sociology) students using The Basic Practice of Statistics by David Moore. It'll be the fifth time I've taught this course and one issue I've consistently had is that the students have really struggled with the notion of the sampling distribution. It's covered as the background for inference and follows a basic introduction to probability with which they don't seem to have trouble after some initial hiccups (and by basic, I mean basic -- after all, many of these students have been self-selected into a specific course stream because they were trying to avoid anything with even a vague hint of "math"). I would guess that probably 60% leave the course with no to minimal understanding, about 25% understand the principle but not the connections to other concepts, and the remaining 15% fully understand.
The main issue
The trouble students seem to have is with the application. It's difficult to explain what the precise issue is other than to say they just don't get it. From a poll I conducted last semester and from exam responses, I think that part of the difficulty is confusion between two related and similar sounding phrases (sampling distribution and sample distribution), so I've don't use the phrase "sample distribution" anymore, but surely this is something that, while confusing at first, is easily grasped with a little effort and anyway it can't explain the general confusion of the concept of a sampling distribution.
(I realize that it might be me and my teaching that's at issue here! However I think ignoring that uncomfortable possibility is reasonable to do since some students do seem to get it and overall everybody seems to do quite well...)
What I've tried
I had to argue with the undergraduate administrator in our department to introduce mandatory sessions in the computer lab thinking that repeated demonstrations might be helpful (before I started teaching this course there was no computing involved). While I think this helps overall understanding of the course material in general, I don't think it's helped with this specific topic.
One idea I've had is to simply not teach it at all or to not give it much weight, a position advocated by some (e.g. Andrew Gelman). I don't find this particularly satisfying since it has the whiff of teaching to the lowest common denominator and more importantly denies strong and motivated students who want to learn more about statistical application from really understanding how important concepts work (not only the sampling distribution!). On the other hand, the median student does seem to grasp p-values for example, so maybe they don't need to understand the sampling distribution anyway.
What strategies do you employ to teach the sampling distribution? I know there are materials and discussions available (e.g. here and here and this paper which opens a PDF file) but I'm just wondering if I can get some concrete examples of what works for people (or I guess even what doesn't work so I'll know not to try it!). My plan now, as I plan my course for September, is to follow Gelman's advice and "deemphasize" the sampling distribution. I'll teach it, but I'll assure the students that this is a sort of FYI-only topic and will not appear on an exam (except perhaps as a bonus question?!). However, I'm really interested in hearing other approaches people have used.