Identifying problems and identifying solutions

I'm a little stuck on a paper I want to write, and blogging about it often helps. So here's the story:

- in my research methods course, three students became intrigued by the analemma (which they discovered b/c Boise has an analemmatic sundial, so when we were discussing the motion of the sun and they went to see a sundial, that's what they saw). I want to say that this is the right kind of thing to be intrigued by: it should give most undergrad science majors an intellectual itch that needs scratching. The weird things about it: it says our days are not uniform, despite the fact that the earth's rotation is constant (there is slight variaton - but milliseconds - not minutes). It has two "periods" in a year: in one year, noon is earlier than average, later than average, earlier than average, later than average. But there's just a circle and a tilt - what's the two-ness of this?

so story 1, I think, which is consistent with Anna Phillips's work: the students landed on a real problem that begs explanation.


more interesting for me (for this paper) is the next bit: identifying solutions. (I keep thinking about the Agnes Callard piece on aspirational faith! - it's not the same but there is something there...) how do we think we might make progress, particularly when we don't know what the answer will look like? what kind of explanation will "count" as explanation? what steps did students take, and what did they find satisfying? I want to say that the "math" solution that is (mostly) google-able is not satisfying (nor, really, "understandable" to most of us - including me); the modeling-it solution - both physically and computationally - was only moderately more so; the solution I find most useful (there are two "kinds" of days happening in 24 hours - a rotational day and a revolutional day - and these "days" have different "shapes") feels so SATISFYING.


things I wonder: in some ways, this is a cultivated, aesthetic "sense" - it's like developing someone's taste in classical music or in hip hop or cheese :) - but there's also a sense-of-mechanism-ness to it. there's stuff to say about the affordances of representations, too...