QUOTE(skeeterses @ Jun 3 2006, 03:04 AM)
But the reasoning on the SAT tests themselves is not complicated reasoning in itself. For example, some of the math problems include figuring out the sides of a Triangle. You can memorize every trigonometric formula in preperation for the SAT. But usually, the SAT expects you to know a more simple shortcut like remembering the ratios for triangles of 30 degree-60 degree vertices, or 45 degree-45 degree vertices. What the SAT usually tests is a person's ability to solve problems quickly. And you brought up the example of 2 artists using 2 methods to create the same picture. If an artist were to be tested on both methods, then the artist would be expected to learn both methods.
If indeed the key to the SATs is remembering a shortcut, then the test leans towards a knowledge based system anyway.
But lets say that the simple, shortcut trick was something that a test taker would have to come up with on the spot (Or reason their way through). The information given about the problem could aide one type of reasoning to the exclusion of another. Similarly, if the previous information were withheld and some other tidbits were revealed, another type of reasoning might be favored.
Using our artist example, if we gave them an eraser instead of a pencil, we could get totally different scores.
Lets rule out the generous test givers who might give the student both a pencil and an eraser. With those two, you almost have too many supplies to show your talent with one medium or another. Similarly, giving too much information ruins the problem. Test takers strive to give you just enough information to solve the problem.
The meat of your argument, however, is that the reasoning on these tests are so elementary that every type of reasoning should be mastered by the test taker.
This declaration, I believe, serves my argument because here we assume that there is one type of way to go through a problem, and that a student must have mastered every way to succeed. Granted, switching reasoning might only slow down an accomplished student, but it would serve as a type of favoritism for that particular problem nonetheless.
Not to mention, learning a different way to reason is just that, learning (knowledge), not reasoning. (Come to think of it, this is a philosophical discussion in itself and should not be belabored).
This leads to another question though, if one is phenomenal at one type of reasoning, and poor in another, is it really fair give them a mediocre score? If they can calculate the surface temperature of the moon on the basis of the average temperature of the sun, but for the life of them don't understand why hot is to cold like black is to white, is this person really mediocre? Interesting.
I think in general that there are so many ways to think about any problem it would be impossible to test everything. Your solution would be to test both the erasure and shading, but what if there are hundreds of ways to get the same picture, each way with a type of personality that best matched its reasoning? I can get the area of a triangle with some angles and sides, or all angles, or all sides, or if I cut out a triangle from a sheet of paper and measure the difference (The latter being similar to water displacement).
At the very least, grant me that these reasoning based tests can never be as accurate as a knowledge based exam (Do you know the circumference of the Earth? Either you do or you dont) due to the complexity of reasoning compaired to knowledge. There is only one type of knowledge as opposed to several types of reasoning (or hundreds) that must be accomodated for.