Shelly Blake-Pock just posted a question on his blog about teaching math in a paperless environment (in fact, since I started gearing up to respond, he’s posted some follow-ups as well).
Last year, wearing my math teacher hat (nominally given to me as a member of the Math & Computer Science department — normally only worn on the most formal occasions), I got involved in a project with my department trying to work with our students to develop a mathematical Wikipedia. The idea was that kids would write up their mathematical knowledge for the younger students and their classmates, creating a review site focused on what the students thought was important to know about the material we were covering in class.
The big idea was that this would push the students to both reflect on what they knew (as they worked to articulate it for less experienced students) and take part in some independent learning (as they researched their topics to figure out how to write them up). It wasn’t really a rousing success, for a number of reasons, not the least of which was that the kids were assigned topics (rather than selecting their own) and ended up mostly parroting their textbook into the wiki. There wasn’t any real collaboration or peer-review going on, at least not in a really critical sense (“Why did you explain it the way the text book does? I didn’t get it then and I don’t get it now… do you get it?”)
MathML requires a plug-in for Internet Explorer 7 (no idea about 8, but I’ll bet it still needs the plug-in), but Firefox can read and parse MathML natively. Peter Jipsen has links to some helpful fonts to download to make it all look a little nicer, but they’re truly optional. Once it’s set up on your server, you just include a magic incantation at the beginning of the page to invoke the translator, type in your calculator equations, and whamm-o: pretty equations!
Now, this only handles equations on the web. We didn’t get to graphs or diagrams in our experiments last year. But I can tell you where I would look for graphs — Google has an embeddable chart generator that might work. I hope there are other similar tools.
Again, all this is with the stated goal of readable, editable, shareable mathematics online. This doesn’t address doing the exploratory work: this is the write-up and reflection after the exploration. Without a tablet, I’m not convinced that one can do general mathematical work on a computer. And with a tablet, I’d add FluidMath (still in beta, I think) to the list of must-have applications.