Greetings from the Mathematical Sciences Institute (MSI) at the Austrlaian National Unviersity where Cameron Chamberlain from ANU School of Art, is presenting an Introduction to Animation. This is part of a project to teach educational film making to mathematicians, next week's workshop is on interviewing (27 May 2011).
Cameron pointed out that even the most sophisticated computer based animation still depends on the principles of live film making and animation. A an example, he used Disney's 12 principles, as documented in The ILLUSION OF LIFE: DISNEY ANIMATION (by Ollie Johnston and Frank Thomas, 1995).
He also recommended The Animator's Survival Kit, Expanded Edition: A Manual of Methods, Principles and Formulas for Classical, Computer, Games, Stop Motion and Internet Animators (by Richard Williams).
This may not seem relevant to teaching mathematics, but the conventions of animated film, film and live performance can be applied to make appealing educational animation.
People respond to animated objects with personality. This does not require realism, as Byron Reeves and Clifford Nass point out in "The Media Equation: How People Treat Computers, Television, and New Media Like Real People and Places" (Cambridge University Press, 1996), research shows that people were very accepting on simple computer animations.
The Wikipedia has a list of 2D and 3D open source animation software. Cameron commented that Blender was the most usable.
Cameron gave rhe example of a mathematics related, award winning file: The Dot and the Line: A Romance in Lower Mathematics. My favourite animation along these lines (pun intended) is Airport by Iain Anderson (2005), made using airport signs.
ps: Cameron at one point said "Turn it Up to Twelve", which I assume is a pop culture reference to This Is Spinal Tap.