Hi All:
Thanks a bunch for the comments: I'm just going to reply to everyone in one email for now, to keep things simple and, hopefully, brief! My latest question for you is here, and answers to your earlier questions are below.
NEW QUESTION: METHODOLOGY ADVICE?
What methodologies can I use to research this question?
"What are the ingredients of mathematical knowing?"
ASSETS
As I see it now, the main assets I have are:
(1) PlanetMath's historical data over the last 10 years (minus whatever was lost due to one or two hardware malfunctions);
(2) The opportunity to add new things into PlanetMath's system, including new metrics for gathering data, and I also have inside track with some of the new technologies that have been developing in the online mathematics field;
(3) The opportunity to organize courses at P2PU;
(4) Access to Wikimedia data for comparison (especially assuming some of you can show me the ropes with that!);
(5) Most likely I could get access to the Math Overflow data (they use the same Creative Commons license as PlanetMath and Wikipedia).
There are probably a few other things I'm forgetting now, but even just (1)-(3) seem enough to create an interesting story.
BACKGROUND
I have a B.A. in Mathematics, did some work in artificial intelligence related to mathematics, and I'm also interested in computer-mediated communication of mathematics more generally (I'm on the board of directors of PlanetMath.org), and in various "commons" issues.
My current position is as a research student in the Knowledge Media Institute at The Open University, UK. KMi (as it's called) is part of the Centre for Research in Computing, and so I'm currently a "computing student", just by another name.
SKETCH OF A PLAN
As of today I think that adding facilities to PlanetMath for *submitting*, *solving*, *hyperlinking*, *marking*, and *keeping track of* problems would be enough to make me pretty happy.
Of course, that's not a research question or methodology -- but it does seem to get at some of "the ingredients of mathematical knowing".
E.g. it would possible to use such a system to *share* problems of interest, *link* them to relevant material in PlanetMath's encyclopedia and other related problems, and start working one's way through, *ask* for help from other people on the site, *give advice* about techniques or other approaches, and *keep track of* things one had *learned*.
The "who" here would be a mathematics learner -- and most likely at the university level (since that's where most of PlanetMath's current content and user base comes from). Other people would surely be involved (e.g. teachers or course designers) but wouldn't be the focus of the research project as I currently envision it.
Joe
PS. Regarding The Math Forum: I know one of their developers, but I've tended to stay away from systems that don't use a free license.