The past couple of weeks, I've been helping a friend's daughters with a college math course they're taking over the summer. I'm geeky enough that this is fun, and getting paid is a nice bonus.
While doing so, certain things have struck me more than they might while working with my own students. So I figure, why not share?
Even math teachers don't remember all the math, all the time. Conic sections ... I've never actually taught them as a whole topic. I'm fine with circles and parabolas, because those come up regularly on their own. Ellipses and hyperbolas, however, not so much. I remember some general things about them, but not how to find the coordinates of the foci, or how to rewrite an equation to the proper form. Fortunately, all it takes is twenty seconds glancing at the right material in the book.
Math teachers don't always agree. When tutoring, I almost always come up against something where the way the teacher showed them is bonkers (in my opinion). I try to determine if there's any good reason to do it that way. If there is, I go along with it. If there isn't, I try to determine whether the teacher will know or care if the students do it a different way. If not, I'll show the kids my way, explain how it relates to the teacher's way, and tell them they can choose whichever they like better.
Math teachers don't always act rationally. Often these college courses don't allow the use of calculators. I understand the idea—with some calculators these days, you could solve every problem on the test without engaging more than a couple of your own neurons. But it's kind of ridiculous when the long division to reduce a fraction takes longer than applying the math concept that's actually being tested.
And the thing is, I'm sure I'm guilty of all of the above in my own math classes. Somewhere out there a math tutor is saying, "Miss Lewis said that? Is she nuts?"