This is a math-related post. I’ve tried to keep it as broad-minded as possible because, as much as I believe I’ve found the best way to assess mathematics, I haven’t the foggiest how to translate it to other disciplines. And I need help.
(Prerequisite: It’s essential to assess math by concepts and skills rather than by chapters, for reasons I outlined here, but specifically in this case because assessing by concepts means I can remediate like a pro. A student comes in with a low overall grade in hand and I know exactly which of our (currently) 21 concepts are bringing her down. We tutor, we reassess, grades go up, comprehension goes up, everyone’s happy.)
Ranking a close second in importance to concept-based assessment is the selection of good concepts. Here’s where I almost went wrong this last week.
We’ve been assessing Cones (#19) for a couple weeks now. It’s a straightforward concept. All you need to find the surface area of a cone is the slant height (19 inches in the picture) and the radius of the circular base (7 inches).
So here’s the temptation. We’ve now covered Pythagorean Theorem, which means I could conceivably give them the height of the cone (which is just a distractor, typically) and through our new theorem, find the slant height, which is essential. We’d be tying new knowledge to old, adapting new skills to serve old ones, and making a richer, more complex assessment.
This is a problem.
Because we’d be tying new knowledge to old, adapting new skills to serve old ones, and making a richer, more complex assessment.
If a student fails an assessment that’s been stitched together Frankenstein-style from several disparate concepts, what do I know about her failing grade? Did she fail because she doesn’t understand the Pythagorean Theorem or because she doesn’t understand Cones?
The triumph isn’t obvious here, particularly, I imagine, to a lot of math teachers, the kind who are thrilled by these rich, multilayered problems. I’m no different and I will be tossing the new format onto openers and classwork. My triumph was to resist assessing it, to instead give the Pythagorean Theorem its own concept (#20).
Under the alternative I would’ve given up one of my best weapons to combat ignorance simply to showcase something clever and challenging. It would’ve felt satisfying to some extent, but I’m too deep into this system to ignore how far it would’ve set me back as an educator.
[Update: check out the comprehensive resource.]