Can I ask you (and keldaris) what precisely you mean by geometric algebra, and how you would propose to teach it?

I'm a math professor. To me "geometric algebra" refers to any use of geometry in mathematics to illuminate algebraic principles. There are very very many of these -- this article illustrates one good example. I try to incorporate intuition from geometry into my teaching whenever possible.

It seems that the two of you are referring to some particular unifying framework, and/or set of definitions and notation. Could I ask you to elaborate on what you mean?

Thanks.