Hi Don Simmons, and welcome to Tikiwiki community!
You might be interested in having a look to Mod AulaWiki and their workspaces feature, for tiki 2.x. Aulawiki comes with the workspaces_my module, which acts as a dynamic menus generator for each workspace you are at. I.e.: when you are at class (Workspace) Algebra, the links in the menu get updated to show only the ones for that class (workspace).
See the documentation (in pdf and in several langs) here: Mod AulaWiki
However, I haven't tried for anonymous... that should work, anyway, as far as I know.
Alternatively, you can try adding some custom code to the modules containing your menus, so that each module is shown when the categoryId variable (whichever it is) is equial to X, in that case. I mean in a similar way to what is explain for multilingual modules:
Finally, join us at http://edu.tikiwiki.org !
Hope this helps.