The Inspiration program seems to have so many useful tools that make is much easier to manipulate your way around ideas, outlines, and graphs. This program is especially interesting in the way that what ever you do to one aspect of your web/outline it is also carried through out your project so you won't have to change every part every time you come up with something new.
In the classroom I would believe that the best use of technology would be this outline/web/graphing layout. Easy manipulate, view, and understand. If your teaching time is limited, you could simply have your lesson plan written out in an outline, so that the students already have the issues in front of them and are able to meet with each other to diagnose what problems they have with understanding things and figure it out together. Although, I'm not too sure that using technology would be playing a big role in this. You may also have a slide show or something of the sort to show the students, with the beginnings of an idea and ask the student to correlate with each other to figure what else could be related or connect with the given idea. The best way to go about teaching others is of course to know your stuff. This would incline that you would do some extra research on the subject just so that you could be prepared for any questions thrown your way. The extra research may actually surprise you with more knowledge then you knew to begin with, hence you have the chance to learn more about your subject and are more clear with all the processes or issues.