I've been thinking about speed lately, and particularly the speed with which we ask our students to do math. *ALL of the literature I've read lately says that expecting students to do math quickly has a toxic effect. I agree whole-heartedly with this notion, and I do my very best to incorporate techniques into my teaching that allow students personal space and time to think through things at their own pace, not rushed by me or by their peers. It's tough to manage, which is why I work really hard at it, and I am incredibly mindful of it in my classes.
Well, except, I don't actually agree with it, like whole-heartedly. It's more like, I agree that students should have lots and lots of space, and no time pressure, to be able to learn a concept to a degree to which they are comfortable with it, and fluent. But eventually, with enough practice, they should have enough fluency to be able to work much quicker. Which is to say, an algebra student who is learning about variables for the first time may need to have multiple conversations around how to add like terms, and why it works the way it does. But a calculus student should be able to add those like terms without pause.
I think about this in terms of practicing an instrument. When you first learn a new song, you play it slowly. Sometimes so slowly that you can't even recognize the tune. You pause to repeat certain phrases, to embed the physical movements and the sounds into your brain. You work to understand the music. Then, eventually, with enough practice, you can play through the piece at its intended tempo, which may be 3 or 5 or 20 times as fast as how you started out. The practice induces some fluency.
So, don't we want students to gain that fluency? I think we do, and there's a degree to which fluency can present itself as speed + accuracy. Which, I suspect, is the reasoning behind those dreaded xeroxed 100-problems-in-a-minute tests. To be clear, I would never advocate for those awful tests. I remember the anxiety they gave me in 4th grade, and how close I came to being dropped a level because of them (and I was, by many counts, in particular by my own impeccable memory, Good at Math in the 4th grade). However, I wonder if practicing for speed+accuracy has any place in math education. I think it does, and I am interested in figuring out how in a way that does not compromise the very important notion that the beginning of learning a new concept should not be rushed.
