Travelers' tales

It's been a much better day today.

A highlight: another meeting of the minds in my office, involving three 280 students who'd stopped by after class for a debriefing on their recently-returned homework assignments. I'd mentioned in class just an hour before how beneficial others had found such debriefings, and these three had come hoping to reap the same benefits.

The meeting was wonderful. Sibyl, Nigel, and Quark joined me in a rough circle in front of my desk, and we went through the homework together, one problem at a time. Sometimes it took no more than a minute to iron out the wrinkles they'd worked themselves into, and other times we spent ten or twelve minutes puzzling through a problem's subtleties. They fed my wisdom and of their own, which was often richer. It's good for the students to see that others often have the same struggles they do (more than once they made the same kind of mistakes on the same problems), and it's good for them to hear their peers' explanations (often more lucid than my own). We ended the meeting with my giving them a few impromptu inductive exercises for practice with the technique. (Prove: n nonparallel lines in the plane determine n(n+1)/2 + 1 regions, bounded or unbounded.)

I left our meeting invigorated. I love this aspect of my job.

A second highlight: I realized this afternoon, while rereading Stanislas Dehaene in preparation for MATH 179 tomorrow, why it is I've had such a hard time getting into the mathematical aspects of my Ethnomathematics course this semester: the book, by Marcia Ascher's Mathematics elsewhere: An exploration of ideas across cultures, is awful, at least for my course. It's a bad fit. It's boring, condescending, pedantic, preachy, and is aimed at entirely the wrong level. (It's too dry to intrigue most math majors but too mathematically sophisticated to appeal to non-mathematicians.)

By comparison, Dehaene's book, though not strictly speaking about ethnomathematics (it deals more with the psychology and neuroscience of math and math learning), is intriguing, engaging, and written in a manner that's neither condescending nor confusing. I think the students will find it much more interesting than Ascher's text. We'll start drawing from it tomorrow and next week.

It's been a good day; I'm looking forward to another one tomorrow.

A closing note: my thanks to all of you who offered me support after my day of frustration yesterday. I'm sure regular readers will recognize that blogging is a cathartic exercise for me (need evidence? Check out the "anxiety" and "bitching" tags on the right!), and I often feel tremendously better after writing.