Is there a name for the way Maxima does algebra?

Hello,

I think a fair characterization is that Maxima implements a
"little boxes" approach to algebra:
variable = box with a label on it, value = content of box,
axiom or theorem = license to replace some boxes.
That seems pretty naive (which is OK by me; I imagine
that's how I do algebra too). Is there a name for this approach?
What are the names of some other general methods?
If that's not how Maxima does algebra, what's a better
characterization?

Thanks for any light you can shed on this question.

Robert Dodier