As I said recently, quadrics hold a special place in my heart and I get excited every time the topic comes around in Maths 1B. Quadrics have so many cool things you can say about them, and are such a great opportunity to talk about the deep connection between algebra and geometry. I personally could teach an entire 12 week course on nothing else. But paradoxically, this is also why I feel a sense of frustration every time the topic comes around in Maths 1B.
You see, quadrics have such a short appearance in Maths 1B — just long enough to be an application of orthogonal diagonalisation, but not long enough to get anything close to understanding them. To have even a slight feeling that you understand quadrics, you actually need to spend a bit of time near them investigating how they behave, but there’s barely long enough to learn half their names (indeed, I’m told that this semester they’re not going to be expected to know their names for the exam at all).
Some people might say this isn’t a problem because the students can just learn the bits they’re told and leave it at that. But the students have been told so many times that it’s better to understand things than just do them, and have failed in the past when they took a surface approach to maths, so they try to understand things if they can. Plus, many of them can see that quadrics might actually be quite interesting and they want to understand.
Normally I would rejoice that students had a desire to understand something I love, but in this case, when quadrics are such a tiny bit of their course, it stops them putting energy into other, more mark-worthy bits of the course. Like the Dufflepuds in the Voyage of the Dawn Treader movie, I would prefer that either we did them the justice they deserve or left them out entirely.