The Law of Cosines is a beastly formula, which, yesterday, for the first time in five years, I didn’t ask my students to memorize.

I gave them my reasoning: basically, that ten years down the road, ten months, maybe ten days, they’d forget this formula. It’s inevitable. I’d rather them pour their guts into creatively operating the formula than memorizing it, since, in the Google era, that’s an appropriation of resources I could no longer defend.

At the end of my monologue, I wrote the formula on the board and started passing out tests. One student in the front held up her hand, smiling, the Law of Cosines written brazenly across it.

Blowing It

Me, on our last concept quiz, balling both Law of Sines and Law of Cosines into the same heading:

I watched kids tear Law of Sines apart and then get torn apart by Law of Cosines. I was about to toss 2 points out of a possible 4 into the gradebook for, like, seventy students.

But then they come in for help a week, maybe two weeks down the line and what? How does that 2/4 direct my remediation? Which don’t they understand? Law of Sines or Cosines?

And here I try so hard to imagine: how in the world did I ever lump a dozen skills under the same “Chapter [x] Test” heading, the preferred grading strategy of the world’s math teachers?

Disaggregation is the name of the game. It empowers students and teachers. So, on the next test, I did:

Nailing It

Frank N., from the comments, co-opting this assessment strategy for physics.

Now, has all this craziness made a difference? I can tell you this: the kids don’t feel defeated by physics as they did in years past. They can get a 2/10, realize that they didn’t know what they thought they knew, and come back to get a 9/10 and feel great. Plus, when it comes down to grades, there isn’t anything stopping them from getting a 100 each quarter. The ball in in THEIR court. How can a parent argue with a system like that?

In addition, I can immediately tell which topics need re-teaching by me and which the kids get right away.

Exactly.