Here's my tuppence worth on algorithms: GED students sometimes specifically ask to learn long division. I teach it if they want it, even though I tell them that the reality is that nobody uses it in this electronic world and it isn't necessary in order to pass the GED. But if students want to learn long division, I teach it because it gives them confidence and therefore helps with math anxiety and also it provides an excellent workout for multiplication, estimation and multiplicative thinking.
Gail, for the Teacher2Teacher part of this Math Forum, has passed on to me the following modification of the long division algorithm, with explanation. The message from Gail uses the non-breaking space everywhere and includes paragraph breaks inserted either by the T2T word processor or by the Math Forum system or by WGU email protocol -- so it's hard to say what it will look like on the new Math Forum discussion page. [NOTE: it looks good, Gail's non-breaking space method is effective.] Anyway, here it is: