I think a few years ago I could have written a comment like this, but now I've been a teacher for a couple of years now.
It is hard to teach something. Being able to do it is isn't anywhere near the level of expertise needed to:
* Do it up on a board at a moderately quick but consistent cadence, with engagement and narrating the whole part through.
* Not be taken off track by inevitable distractions.
* Understand the stack of necessary knowledge in the ways needed to figure out what a student is missing.
* Completely reinvent your lesson plan when you find the students unexpectedly lost, providing whatever the missing bit of knowledge is to get your class back on track.
* Handle unexpected diversions and requests for deeper knowledge on the fly.
I didn't realise teachers went under some kind of assessment to teach particular parts of their subjects.
In the UK a mathematics teacher is just a mathematics teacher. They all have to teach calculus because that's part of the curriculum. If you couldn't teach calculus then you couldn't be a mathematics teacher.
(That's not a boast - we're poorer and less effective at maths than you are.)
What do you do if you're a mathematics teacher but can't do the calculus part? Handover to someone else for just that part of the year? Must be a bit professionally embarrassing?
> I didn't realise teachers went under some kind of assessment to teach particular parts of their subjects.
This is hugely variable within the US.
> In the UK a mathematics teacher is just a mathematics teacher. They all have to teach calculus because that's part of the curriculum. If you couldn't teach calculus then you couldn't be a mathematics teacher.
I think there's a lot of math teachers who would be a bit iffy teaching Calculus that have department chairs that schedule them to teach earlier math instead.
> (That's not a boast - we're poorer and less effective at maths than you are.)
I don't feel like our mathematics system is very good at all.
Sounds like the difference is in the UK a teacher teachers a cohort of students through all subjects, not a subject for all cohorts of students. We have one maths teacher who teaches you everything.
Maybe they're terrible at half of it? I don't know.
> Sounds like the difference is in the UK a teacher teachers a cohort of students through all subjects, not a subject for all cohorts of students. We have one maths teacher who teaches you everything.
Really? That's very interesting.
I had a different math teacher every year / level. I'm at a smaller independent school, where you may have the same math teacher a couple times but people definitely specialize-- we have the teacher who teaches mostly 6th grade math and pre-algebra, and a teacher who mostly teaches algebra I and geometry, and so on.
On the one hand, you lose continuity. But you also get a fresh start each year, with a new teacher who probably teaches the things you had trouble with in a different way...
This was not my experience in the UK - at a grammar school with a specialist mathematics designation (in the late 90s). There was a wide ability gap between the mathematics teachers, and very few could practically teach calculus.
Further, at that point in time, calculus was only part of the A’ level curriculum, and most people would never encounter it unless electing to do that course.
Just because you know it doesn't mean you have the pedagogical skills to help somebody else know it. By way of example, I am more than competent at introductory computer science yet I am wholly incompetent at teaching it--were a student to need help with something that basic in CS, I wouldn't know how to go about helping them understand, since I don't understand why they might not be understanding something.
This past trimester I taught a Computer Organization & Design class to middle school students for the first time, with curriculum that I developed.
Observations:
* Wow-- the brighter half of MS students can do nearly as well as bright undergraduates on this material if you go a little slower and make some allowances for attention span. The neuroplasticity, recent memory of learning arithmetic, and lack of fear of the material really helps.
* Holy crap-- I had no idea before trying to teach this how much number theory that I take for granted. Like, I forgot to cover how many possibilities there are for n-digit numbers in different bases and some early lessons on number systems took this for granted. Figuring out what you need to cover, and how, for something to make sense later is hard.
Most high school math teachers don’t know calculus, it’s as simple as that. Even at good public schools, there is often just one in the math department that can teach it, but maybe also some science teachers could, too. In my school, some of these were great, highly engaging teachers for more basic math classes when teaching average and below average students.
One of the high school math teachers explained to my brother “the square root of 2 is irrational because it says so on page XYZ” (true story). I’d say it’s fair to conclude that there exist math teachers who’ve taken Calc who can’t teach it.
