Recently I commented over at En Tequila Es Verdad, saying in part that I thought too much mathematics homework was a bad thing, education wise.
The response to headlines about US falling behind in education (say, like this one) is usually to increase homework.
Well, a paper in Econometrics Journal apparently concludes that for average students (about half of them, speaking roughly), lots of mathematics homework is not productive.
[Of course, this is looking at relatively short term effects. What will be the effects of too much homework five years down the line? My guess is that long term it will probably be unproductive for an even larger percentage.]
The linked news article says: According to Henderson, the learning process needs to remain a rich, broad experience.
Which is one of the main points I was getting at in my lengthy comment over at Dana's blog. Nice to see I'm not talking complete bullshit.
Think of it this way:
Imagine art class consisted of having to practice drawing a duck, over and over, until you could produce a good outline of a few very particular kinds of duck, drawn just so. You would do half an hour of ducks every night for homework. Then back to school the next day for more ducks. Then you'd move on to chickens. The generalization to all birds would be sort of handwaved, because the curriculum is kind of packed. It's time to move on to drawing fish! If you didn't learn to draw ducks, you would get even more work on drawing ducks. Some aspects of what you learned in drawing ducks could be used in drawing fish, but the relationships aren't very intuitive, and anyway, there's just so many bits to remember and it's all so confusing and WTF, now I have to go home and do fish for an HOUR?
And then suddenly you're drawing battleships, and while drawing kind of made sense before, suddenly it makes no sense. You never quite got the hang of ducks and now you're trying to catch up that, fish and now battleships? How on earth are you ever going to remember all the parts of a battleship? And god forbid you should draw the parts in the wrong order!
If art was like that, most people would hate it.
Imagine Rembrandt at a party, who desperately wants to convey something of the beauty and importance of chiaroscuro. What would he hear, over and over, as he brought up the topic of art?
"Art? I was never any good at that. I always hated art! My worst subject. All those ducks! You must be very strange."
Most people - if you forced them - would be able to draw a fairly reasonable-looking duck, but there'd be precious little art in their lives. They'd certainly have no sense that it could be moving and beautiful - or indeed that it was about anything other than ducks and fish, and maybe something painful about battleships.