Anthony, What a great post. You use interesting words to describe teaching and learning math in the online environment. I had not thought about imagination in math, but that is really critical thinking. I have a friend that teaching statistics online and f2f and she has used applets to help demonstrate mathematical equations. In using the applets students see the possibilities of an equation by adjusting slope. There are are so many applets. I know you are teaching math but I thought I would share it with you. Here it is: http://sapphire.indstate.edu/~stat-attic/index.php Dr. Kelly Wilkinson