Solution:
Here’s the paraphrased version I learned from the brilliant folks at Boutell.com. Create a page (in Dreamweaver, or wherever) with the following:
<?php
header('Content-disposition: attachment; filename=yourmovietitle.mov');
header('Content-type: video/mov');
readfile('yourmovietitle.mov');
?>

Save that file as movielink.php, or something more specific. Add that to the same folder (on your host) that your movie is in. Change the name from movie.mpg to the actual name of your file. Finally, write the link as <a href="movielink.php">Download me</a>.
You create a file that forces your browser to save, not open.

Here is my solution:
I created an empty folder on my server (inside public.html) named educ515, and simply installed another Wordpress account inside that folder. Now, I can log in to my main Wordpress, or my 515 Wordpress. Once I’m logged into my 515 account, I created one (static) page for each week of class, with directions, reminders, and notes from that class session. Disclaimer: I’m not sure if this is how you’re supposed to do it, but it’s working really well so far.

This is yet another reason I’m happy to pay for my own hosting service. So much more control than the free wordpress.com blog, so less hassle (and work) than a web site built from scratch.

After much consideration, I decided to use WordPress to power my site. WordPress recommends BlueHost as a hosting solution. And let me say, I have been nothing but pleased with BlueHost. Installing WordPress on to the server (hosted by bluehost.com) was really easy. Check out this simple, straightforward how-to video if you’re interested in why BlueHost and WordPress rock:

http://tutorials.bluehost.com/wordpress/