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.