They say people who are bad at math are great teachers, because they know how errors happen and don’t just expect things to come easily to everyone. (“Those who can’t, teach” right?) I think that’s crap, and would much rather just teach some math genius to slow down than put a bad mathematician in front of a classroom. If you don’t know math well, you can’t break it down and build it back up smoothly, you can’t analyze and address the myriad different ways to solve a problem, you mess things up in front of kids and confuse them, you shy away from material you aren’t comfortable with and pass your anxiety on to your students. Instead of showing kids that math is beautiful and dynamic and accessible, you show them a narrow version of the material and your limitations make them assume that struggling is inevitable. We don’t want that for kids.
I took the Mathematics Praxis Test this morning. I had taken the Arizona test (AEPA) to start teaching, and Colorado needs me to take Praxis since I’ve taught for fewer than three years. (Because, you know, all your mathematics knowledge suddenly comes in your third year of teaching. But whatever.) If you’ll allow me a moment of cockiness, it’s important for you to know that I’m pretty good at math. The Arizona test gives scores back as a series of little bar graphs, and all of mine were entirely full. Because I teach a high-school credit advanced class, I teach material through 10th grade geometry and don’t have questions about any of it. Despite that, I don’t know if I passed this test.
The majority of the test was on higher-level versions of the content I teach (very few questions were 8th grade level or below, but they were at least related). I felt fine about all those questions, and hopefully there were enough of them for me to pass. But then there were questions about things that I haven’t seen in years and had blatantly no idea how to do. There was crazy stuff that I hope I learned in high school but couldn’t even remember having seen before, and I did a really disappointing amount of guessing C.
If I don’t pass this test, it will be because I don’t remember calculus, and yet it will stop me from being able to teach eighth graders. Does that make sense?
On the one hand, it’s entirely reasonable. Like I said, we want math teachers to be really good at math, and we should put them through challenging tests to make sure that’s true. Since teachers often need to cover a variety of levels even at one school (See: me, teaching 8th, 9th, and 10th grade math at an elementary school) it makes sense to certify them broadly across grade levels. And if I pass without knowing the twelfth grade material, a high school could hire me to teach their AP math class and be none the wiser. Sure, I could probably function in front of a calculus class, but I’d be one day ahead of the kids in the textbook. It would be years before I could build conceptual understanding, spiral in prerequisite skills, and include real-world applications in the way that a teacher should. If you look at it that way, suddenly I shouldn’t pass this test at all.
On the other hand, I really, really, really don’t need to know the twelfth grade material on this test for the job I do, and it would be silly for me to fail. I’ve taught a broad range of material for two years and the reason I don’t recognize those questions is because those topics are completely irrelevant to my curriculum. Why am I even tested on something that I don’t need to know how to do?
I should also add that there are plenty of people who pass these tests and will admit to guessing straight through them. And we can’t really change that, because we can’t afford to shrink our already small supply of math teachers.
Doesn’t it seem like there should be a better way to give teachers the “Highly Qualified” label? Certification by subject, maybe? (Middle School, Algebra, Geometry, Pre-Calc/Calc, etc.) Conceptual understanding tests, rather than question-answering-ability tests? (I took a really cool one of those once, which did things like present crazy ways to solve a problem and have you decide if they would always/sometimes/never work.) I don’t know. We should think about this.