Back to school

UNCA serves a large number of nontraditional-age students who are returning to school after taking time off for other things, and many of these folks are older than I am. Therefore I'm used to not being the oldest one in the room when I'm teaching a class; I've only been the eldest in maybe five or six of the 50-60 class sections I've led at this school.

But I'm not used to being one of the youngest in the room.

My MLA (Masters of Liberal Arts) course, Number sense: The philosophy and psychology of mathematics, met last night for the first time. I've got eight students in the class, four or five of whom are my senior in age and in life experience. It's a great bunch, and I can tell I'm going to learn more from them than they're going to learn from me.

We started off with some freewriting, through which I asked the students to probe into their own mathematical pasts. I hoped to find out what it is that makes these folks tick mathematically and to determine what they perceive to be the most basic and fundamental of mathematical operations. If we can get at the these operations, we'll be in a position to start our study of mathematical cognition where our brains begin, with approximations of enumeration.

I'm delighted to report that there's considerable diversity in the class when it comes to mathematical background. I found it interesting that the two gentlemen in the class reported more facility and familiarity with mathematics than their feminine counterparts (with one exception). Both of them described delight at working with statistics and geometry, and obsession with game-lake mathematical puzzles. The one woman with more mathematical experience is a former UNCA math major with whom I had the pleasure to work when I last taught Abstract Algebra I (in Fall 2008). This is her first semester of study in the MLA program.

The other five folks have considerably less mathematical background, but will provide perspectives from other points of view, reporting interest and expertise in psychology, history, and philosophy. I'm excited to learn from Samantha, who is taking time off from her work as a teacher for special-needs children. She mentioned how frustrated she is with mathematics education, and hopes that our class will give her the skills to help improve the way students are taught math at a young age. More power to her! Her high expectations for the course will definitely keep me on my toes.

After we probed our mathematical pasts for a bit, I presented a few exercises and experiments I hoped would whet their appetites for the material we're about to study (from Dehaene's Number sense). With no promise that this link will be evergreen, you can find Mathematica files for these exercises on the course website under the entry for January 12th.

In the first exercise I challenged students to hold in their memory progressively longer randomly generated strings of digits, demonstrating the means by which we tend to use our linguistic faculties to store such strings in short-term memory. (This use underlies linguistic differences in the ability to memorize and compute with numbers: the brevity of number words in many Asian languages allows native speakers of those tongues to outperform speakers of other languages in basic memorization and numerical manipulation.) The second exercise demonstrates how the arrangement of objects affects our sense of their number: more densely packed objects tend to appear more numerate than those that are sparsely spaced, and more orderly-arranged objects appear more numerate than those that are randomly placed. For the third activity, I asked the students to report any sort of synesthesia they've ever experienced: do they sense that numbers have specific appearance, texture, color, smell, relative spatial position, or gender? I think the students found it odd when I reported I've always had a very well-defined sense of the gender of every digit.

We wrapped up with a short discussion of formal expectations for the course, a topic I'm trying to de-emphasize as much as possible. I'm looking forward to next week's discussion. I'm curious to see if the students will find Dahaene's book as intriguing as I have.