I like this, but I don’t think mimesis is always a bad thing, at all. It’s often a useful stage on the route to deeper understanding. You see this in teaching sometimes: you’re trying to teach the cross product, but they’re learning that they need to underline their vectors, and that they should put some punctuation and explanatory words between their equations so another person can follow the argument. Eventually they will definitely need to learn both sets of things, but if you just get back vector salad with explanatory words interpolated between it they’ve still learned something that will be useful in their mathematical career.
I’ve never been a teaching assistant for a proofs course, but I imagine you have to mark a lot of epsilon salad, because I’m pretty sure I produced a lot of epsilon salad as a student in the course of internalising the language.
These days as a relatively noob programmer it’s normally me doing the babbling, and I’ve used this strategy consciously: offer up some network protocol salad or version control salad and gauge from my boss’s face how much it sounds like the real thing. I find that when I’ve filled in an outline like that and know roughly how to talk a language, it’s much easier to fill in the detailed steps.
If I were against mimesis and perceptual learning, I’d have to be against babies, but babies are good.
It makes sense that people who haven’t learned the syntax at all might have to learn that before learning substance. But it sounds like the sort of pedagogy you’re describing is trying to pretend to teach things much faster than most of the students are ready for.
Hm, I think people vary a lot on this. I like to have a blurred outline of a thing before I fill in detailed steps; I find it painful and frustrating to be dragged through detailed logical steps without that context. I find mimesis is good for producing the blurred outline.
Agreed that classes also often go way too fast. University intro maths courses (in the UK at least) are often pretty terrible for this. But I have no problem in principle with people learning a mix of syntax and substance at the same time.
I like this, but I don’t think mimesis is always a bad thing, at all. It’s often a useful stage on the route to deeper understanding. You see this in teaching sometimes: you’re trying to teach the cross product, but they’re learning that they need to underline their vectors, and that they should put some punctuation and explanatory words between their equations so another person can follow the argument. Eventually they will definitely need to learn both sets of things, but if you just get back vector salad with explanatory words interpolated between it they’ve still learned something that will be useful in their mathematical career.
I’ve never been a teaching assistant for a proofs course, but I imagine you have to mark a lot of epsilon salad, because I’m pretty sure I produced a lot of epsilon salad as a student in the course of internalising the language.
These days as a relatively noob programmer it’s normally me doing the babbling, and I’ve used this strategy consciously: offer up some network protocol salad or version control salad and gauge from my boss’s face how much it sounds like the real thing. I find that when I’ve filled in an outline like that and know roughly how to talk a language, it’s much easier to fill in the detailed steps.
If I were against mimesis and perceptual learning, I’d have to be against babies, but babies are good.
It makes sense that people who haven’t learned the syntax at all might have to learn that before learning substance. But it sounds like the sort of pedagogy you’re describing is trying to pretend to teach things much faster than most of the students are ready for.
Hm, I think people vary a lot on this. I like to have a blurred outline of a thing before I fill in detailed steps; I find it painful and frustrating to be dragged through detailed logical steps without that context. I find mimesis is good for producing the blurred outline.
Agreed that classes also often go way too fast. University intro maths courses (in the UK at least) are often pretty terrible for this. But I have no problem in principle with people learning a mix of syntax and substance at the same time.