We're back. It's been a while.
While the REU seemed to eat up less of my time this summer, revisions on the book (to appear early in 2012 under the title Student writing in the quantitative disciplines: a guide for college faculty) and work on the Curriculum Review Task Force seemed to take up every last bit of whatever was left.
We're now four days into the Fall 2012 semester, and I already feel as though I've found a groove in Precalculus. I've not taught this course for three years, and I must say that I've been looking forward to teaching it again. I've thought a bit about how I would approach the course, I've come up with some new activities (like this one), and I'm coming at it with renewed energy. So far the class has been great. (It doesn't hurt that the department's choice of text is not catastrophically awful, like the text we'd adopted the last time I taught that course.)
We spent today motivating relations and functions, and I ended class with a low-stakes writing exercise (who, me?) asking the students to work in small groups to come up with several examples of relations or functions which have real-world relevance, expressed as "pairings" between sets of numbers. They came up with some fantastic ones, some of which could the basis for interesting statistical surveys. A sampling (all verbatim):
- The decrease of the temperature paired with the increase of the elevation
- The number of texts you send paired with the time spent on your phone
- Pair the childhood obesity with each child's level of poverty
- The profit of the lemonade stand paired with the amount of sugar used
- The speed limit of an area paired with the number of car crashes in the area
- The amount of wildlife disturbances compared to the average of the new developments
- Pair the number of baseball ticket sales with the baseball team's winning record
- Pair the profit made by jacket companies based on temperature
Abstract Algebra has yet to get into the same groove, but as yet we've only met twice, and yesterday's class meeting was dedicated to an intentionally chaotic consideration of a boatload of multiplication tables I'd asked them to construct. In asking them to analyze and explain the patterns these tables exhibit, I'm leading them to begin thinking about what salient features the most "well-structured" algebraic objects (sets equipped with a binary operation) might possess. We'll make that more explicit tomorrow when we define monoids, groups, and semigroups.
More to come soon, I promise! On CRTF (oy), on the QEP (oy oy), on many more things...