People who do something a lot often get better at doing it.
But once again we find ourselves with a proposition that turns out to be true in a far more limited sense, with more qualifications and caveats attached, than may have seemed to be the case.
But because such a large proportion of homework practice-oriented, we should evaluate this claim carefully.
There’s obviously some truth to the idea that practice is connected to proficiency.
As a result, they often can’t take these methods and transfer them to problems even slightly different from those they’re used to.
Or perhaps I should say this is what can’t do, in light of how many of us adults cheerfully describe ourselves as hating math or lacking any aptitude for it.Students may memorize the fact that 0.4 = 4/10, or successfully follow a recipe to solve for x, but the traditional approach leaves them clueless about the significance of what they’re doing.Without any feel for the bigger picture, they tend to plug in numbers mechanically while applying the technique they’ve been taught.Giving students homework that involves drill and practice is often said to “reinforce” the skills they’ve been taught in class.This verb is tossed around casually, as if it were sufficient to clinch the case. Unless it’s assumed that practice is reinforcing by definition, one would have to demonstrate that good results are indeed likely to follow from mere repetition.And it’s not at all clear that this is true, except under very limited circumstances.For example, it wouldn’t make sense to say “Keep practicing until you understand” because practicing doesn’t create understanding – just as giving kids a deadline doesn’t teach time-management skills.Learning isn’t just a matter of absorbing new information or acquiring automatic responses to stimuli.Rather, we human beings spend our entire lives constructing theories about how the world works, and then reconstructing them in light of new evidence.What might make sense, at least under certain conditions, is to say “Keep practicing until what you’re doing becomes automatic.” But what kinds of proficiencies lend themselves to this sort of improvement? Expertise in tennis requires lots of practice; it’s hard to improve your swing without spending a lot of time on the court.You learn to pull back and follow through with just the right movement so the ball lands where you want, and eventually you can do this without even thinking about it.