An update on where I am in my PhD program.
After completing all my required courses the previous year, I spent most of last year doing a huge amount of reading about various aspects of cognition, education, perception, design and other topics. I've actually been collecting papers and books on these topics since several years before I actually started my program and now have a thumb drive with over 3000 papers on it (many of which I've printed out), photocopies of relevant book chapters (from books from the SFU library and elsewhere), and a collection of purchased books that were too good not to own, despite my limited resources.
The point of all of this? I'm trying to get some sort of cognitive or other theoretical basis for developing a theory of onscreen mathematics design. There's very little out there even generally related to that topic, despite its relevance to education and mathematical publishing. There appears to be very little around on the nuts and bolts of actually designing interaction with onscreen content. (I don't mean screen navigation here – there's tons of stuff on that – but interaction with the actual mathematical content. For example, does dragging a circle or number tile around a screen affect the dragger's understanding of the math involved? and if so, how, exactly?) One result of all this reading is that I'm starting to see glimmers of how things all fit together, but that's a ways off yet, and still very nebulous.
Meanwhile, a deadline looms: I'm committed to completing my comprehensive exams next term. The first step in the process is to produce an annotated bibliography of about a hundred papers or equivalent relevant to what I propose to research. (Tricky, since I don't really have definite research topic yet, though that's also getting clearer.) Here's what I started with (12 file boxes of papers) and, in the shoe boxes out front, the results of the first cull.
Here's where I am now (about 20 file folders of papers and a dozen or more books).
Probably still too much, but I'm getting there! (Yet I keep discovering more books and papers that really should be included ... arrrghhh! ) I'm planning to write a short introductory essay explaining just how I think the materials I've chosen for the bibliography are relevant for what I intend to do. After the bibliography I have to answer both oral and written questions on the material. The bibliography itself may turn out more like a lit review than most annotated bibliographies – we'll see how that works out.
The upside to all of this, of course, is that, instead of swimming happily around in a large cloud of intriguing but uncertainly connected ideas, I'm being forced to think more carefully and explicitly about what I want to do for a research topic and to synthesize some of those disparate and confusing ideas into a coherent whole. I came across a nice quotation a bit back which seems to sum up the whole process and provide some motivation for it all: "Until you become confused about what you already know, what you know will never become wider, bigger, or deeper." (Milton Erikson). I hope he's right – I believe it, anyway.