Standardized tests (again)
When does learning become rote?
Over the summer our tutoring consultant has been focusing largely on standardized tests, since there is less formal schoolwork to help with (though some students take summer courses). That means dealing with a large set of mathematical problems on which the student may spend no more than one or two minutes each. Some are straightforward tests of whether the student remembers this or that bit of mathematics. Others are word problems, the infamous short stories which must be translated into math and then solved. While the variety is in principle endless, in practice they fall into a fairly limited number of types, for which there are specific strategies.
Drawbacks of the system are obvious. Given the short times allowed, for most students he must “teach to the test,” that is, concentrate on strategies that are of no general use but apply only to the task at hand. He consoles himself that some students (at least) learn more general lessons about how to organize and interpret information quickly. But for the most part, his opinion of standardized tests has not been improved by his experience tutoring for them.
A few steps above (but only a few) he finds the great body of problems given to students in beginning Physics classes. While Newton’s Laws apply with great accuracy to enormous swathes of the universe, the variety of problems that actually have closed-form solutions is very small, and those that can be handled by first-year students fewer still. Hence the Inclined Plane (with or without friction) figures in very many, with Ferris wheels and vertical loops accounting for most of the rest. It’s quite possible to work out a few templates, and then successfully push out the required numbers without actually understanding anything that’s going on. Years ago this “pattern-matching” approach was identified as a problem in teaching Physics, with much effort expended to combat it. There seems to have been some success.
One can argue about what “understanding” beginning Newtonian Physics actually means; we won’t go into that here. Instead, we point out one major drawback of a standard word problem or a patternable Physics problem: someone has to package a bit of the universe into a tidy, solvable piece. The process must be quick and relatively straightforward, and the numbers must work out. Solving a general cubic equation by hand can’t be involved, and you must be sure that none of your circles turns out to have imaginary radii.
Perhaps more important, all the necessary information must be provided. Under standardized test conditions you really can’t require some reasonable assumptions or approximations to be made and stated. And even beginning Physics students are uneasy with assumptions and approximations, in part because they lack the experience necessary to make them.
And in other part because they are so used to having their problems tied up in neat, solvable packages. This is, we feel, the worst part about these simplified problems: they provide a misleading picture of the world, which is actually a rather messy and uncertain place.
