Monday, December 23, 2013

Yes, And...

This winter session I'll be teaching College Algebra, which I rarely do (once a year or less). Students are definitely sharper than in remedial algebra classes, which is a delight, but they're also more honed into "playing the game" of grades for their own sake. That is to say: I get more incessant "will this be on the test?" cries than I do in other classes.

One thing I'm doing new this semester is to give open-response tests (not multiple-choice), so that I have the option on grading issues of correct writing format and the like. Or really anything else that comes up as an issue. (As a counter-balance, I'll be giving tests with fewer but more complex questions.)

But in conjunction with that, I'm mentally prepping to to try to answer those inquiries with a "Yes, but more importantly..." response. Like: Q: "Will our writing be graded on the test?" A: "Yes, but more importantly, that's how you communicate math to other people, and it's what you should be prepared to read in a math book on your own." Or Q: "Will graphs be on the test?" A: "Yes, but more importantly, it's the faster way to estimate or double-check any answer and avoid mistakes." So it gets the somewhat irritating question out of the way in the first word, and more importantly, it explains why that's really of secondary importance at best. Kind of like in improvisational comedy where you're supposed to respond to any creativity on your partner's part with "Yes, and..." ("and" being logically equivalent to "but", of course).

Do you have any clever ways of dealing with cries of "Will this be on the test?


Monday, December 2, 2013

Automatic Drills

I think we all know that certain skills need "automaticity", that is, such thorough learning and practice that they become automatic, unconscious, instantaneous. For example: Recognizing the letters of the alphabet, reading standard vocabulary words, times tables, negative numbers, etc. If you don't have those basic things working unconsciously, then you inevitably get distracted and make mistakes trying to attend to larger, more full-featured problems.

But I've been thinking lately that the expectation and need for these most fundamental skills is often not communicated to our students; in the era that frowns on structure and drills for automatic knowledge, many of our students have never seen such a requirement assessed directly anywhere. Of course, I'm thinking of the times-tables drills that people my age did in the 2nd or 3rd grade, and nowadays may possibly be done in the 8th grade or high school by the more exceptional and dedicated teachers (so I hear).

Might it be the case that in any class, there's at least one specific skill that is expected to become automatic, even if many of us overlook communicating and drilling on that? For example, it's occurred to me that we might expect the following regular speed drills to take place:
  1. In early grammar school -- Times tables.
  2. In late grammar school/college remedial arithmetic -- Negative number operations.
  3. In junior high school/college remedial algebra -- Matching a slope-intercept equation to the graph of its line.
  4. In statistics -- Estimating the area under part of a normal curve, or interpreting confidence intervals and P-values. (?)
I don't know, that last one perhaps I'm reaching too much for a uniform rule throughout all my classes. But I am starting to consider a timed test for those automatic prerequisites on the first day of my classes, and repeated timed tests on the "new" automatic skill in each class.

What do you think? Have you used timed drills to communicate the expectation of automatic skills? And for anything other than times tables?