The lecturer in our Numerical cognition course told us of a result that went along the following lines. A schoolteacher was trying to teach his students to do basic arithmetic, and seeing them get the calculations wrong time after time. Then one day he decided to follow them out into town, where he saw that some of his students handled arithmetic just fine when they were doing grocery shopping, or working part-time selling things. Inspired, he returned to class and reworded his assignments to be about shopping, and guess what happened? The students failed just as miserably as they had before. The cognitive context was just too dissimiliar to the environment where they'd picked up the practice.
I got the impression that this wasn't just an isolated anecdote, but had also been replicated in more controlled studies. The reference he gave is to Jean Lave's Cognition in Practice - I have a copy of the book from the university library, but haven't had the time to read further yet. I'll see if I can skim it through this evening to find the part he was talking about.
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This post is an example of the dangers both of fictional evidence and generational forgetting. Less than 100 years ago teachers did beat their pupils. Corporal punishment was an accepted part of educational practise. My parents are in their 80's and can remember this.
The script writers for The Wire are too young to have experienced this themselves, so they put a plausible line in their script: "They beat you if you get the count wrong." If they had been beaten themselves in their schools days they would know that it doesn't actually work. Worse they seem not to have realised that beating children to make them learn is only just dropping out of living memory. They could have asked around and realised just how ignorant the line is.
Being beaten into learning your sums is a perfectly plausible idea. Toddlers become competent at running about through a painful process of bumps and bruises administered by their environment. Perhaps an artificial environment with tawse administered by the dominie would work as well for sums?
Ofcourse it is no longer plausible once it has been tried and proved surprisingly useless. I'm disturbed to witness a dead educational idea coming back to life through a combination of fiction and forgetting.
(The point about toddlers may also be false. There is a rare genetic condition that results in pain receptors not working. The popular accounts I've read give the impression that sufferers run and play like normal children, with the exception that freed from the constraints of pain, they are more daring than normal children and do things such as breaking their legs by jumping off walls that are too high. So painful bumps and bruises may not be part of motor learning skills even when their presence is inevitable.)
I'm not positing that the beating helped the kid learn. See Kaj_Sotala's comment above for an example of how students perform math better when say, doing their job but they can't at school. I found the Wire anecdote plausible, but I didn't mean to suggest I accept the kid's understanding at face value: I generalized to the kid being motivated, which may've well been the case even if the kid hadn't been beaten but having been beaten, that's the explanation the kid looked to. Also, I think your historical evidence doesn't necessarily prove your point. My impression is that corporal punishment was often rather arbitrary and to enforce social norms more than teach math lessons (though that too), and I would guess that if kids are beaten for reasons they often can't understand (which is my impression from reading accounts), then being hurt for reasons they can understand (not memorizing their multiplication tables) has a diminished effect. I'm having trouble recalling any specifics, but I'm pretty sure I've read accounts from kids that suggest they saw the punishment as a motivating force for learning, whether it actually was or not. Just to be clear, even if corporal punishment were shown to be effective in certain ways if used in certain ways, I wouldn't be in favor of using it and would guess it would decrease self-motivated learning long term and there are hopefully more humane ideas to make learning motivating.