When the tests are powerful and wrong
A great math teacher deals with dicey math, because it is on the test
“I’m providing Test Prep for students who have to confront this type of language regardless of its mathematical validity!”
One of the trickiest topics in K-12 mathematics is probability. It’s tricky for a number of reasons:
- It’s not a traditional topic. There are not decades of practices to use, improve, or rail against.
- Probability relies heavily on fractions, the gateway between arithmetic and algebra, the single aspect of grade school mathematics that we screw up (in this country) the most
- The subset of probability we teach, simple combinatorial probability, is not a standard part of college probability courses – we don’t have the usual crowd of post-secondary math people poking around and complaining about mistakes.
- Most people teaching probability learned their probability k-12, or from math ed classes that were based in k-12 curriculum. In other words, what we do poorly, we pass down not only to students, but to the next generation of teachers.
So this twitter exchange is with a great math teacher, retired. As department chair he took some of the most advanced classes (everyone does that) and some of the least advanced classes, full of kids who struggle (no one does that). Currently he is doing SAT prep. He prepares SAT-type questions, and I think he solicits the occasional comment.
Great Teacher: A pt is chosen randomly inside larger of 2 concentric circles. If the prob the pt is outside smaller circle is 84%, larger rad:smaller rad=?
JD: Is “random” smooshy here? If I randomly choose an 0 < angle < 360 and a radius 0 < radius < BIG Radius, is that not random?
3rd Party: Good point – ‘random’ doesn’t necessarily mean ‘uniformly random’
GT: Excellent pt re random. The language I used is common on stand’zed tests where “uniform” is implied. Pls reword it in <=140 char!
JD: Why use “random”? Why make it a probability q? 2 conc circ, Large and small. 84% of area of L is not in s. Radius(L) / Radius(s) ?
GT: Agreed but I’m providing Test Prep for students who have to confront this type of language regardless of its mathematical validity!