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Serendipitous teaching moment

April 9, 2007, 12:10 pm

Before spring break, I gave a test in my linear algebra class. My linear algebra tests are always a combination of hand calculations and more “construct-an-argument” kinds of questions where students can use Maple and their knowledge of the theorems to draw conclusions about certain questions. (For example, given a matrix with determinant = 10, is it always the case that its echelon form has determinant 10?) So it’s possible, if all one knows how to do is perform row reduction and isn’t solid on the conceptual/theoretical results, that these tests could take a long time to complete. And that’s by design. The “A” and “B” tests will be given to those who have gotten the concepts down, not just the calculations.

However, this particular class — which is as sharp and focused of a math class as I have ever had — all had problems getting done on time. Most of the time, if a whole class has time issues, I can look at the tests and see big conceptual knowledge gaps. This time, for once, I didn’t see that. I saw good work that just took longer than expected to do.

So what I decided to do was: (1) give the student the entire next class meeting to complete the test, and (2) not tell them about it until class started. So it was a “pop revision”. Because they didn’t know they were going to do a revision, they couldn’t go out and prepare themselves. They could only use the same materials as before — Maple and a handout with the Invertible Matrix Theorem on it — and what content knowledge they still possessed two days after the test.

The nice product of doing this is that I got to see just who learned the material for real, and who merely memorized things for the test. The revision assessed how much of the material the students still retained after the primary assessment was over. And this is a pretty important thing to assess, because we want students to learn for the long term and not just to barf things out on a test, never to be remembered again (except for the final).

Fortunately, most of the class really learned the stuff and were able to complete the test with good results. Unfortunately, I’m not sure how often I can pull this off in a single class!

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