I defined gaming as "aspects which influence the test results other than proficiency in the subject matter."
I did not define it as "education in the course material". Please don't make that assumption.
It's impossible to evaluate your example without defining the pedagogical goal. Your example test question cannot distinguish between proficiency in multiplying two three-digit numbers, and proficiency in selecting from one of four possible answers, where two are obviously incorrect.
That said, this question is biased in favor of students who have been taught estimation techniques, in this case, round, compute 20 * 10, and look for the closest answer. They will be able to answer more of these types of questions than students who can actually multiply the numbers, but haven't learned the approximation methods.
Had the answers been "1) 257.24, 2) 256.24, 3) 247.34, 4) 248.34" then the other class of students would fare better. Then again, those who learned casting-out-nines would be able to reject two of these quickly.
It's clear that sometimes ballpark answers are better than exact ones. In bookkeeping, it's clear that exact answers are better. It's possible to teach students both ... by taking time away from other skills which are also part of mathematical proficiency. A standardized testing system encourages monoculture teaching, so that all students are primarily taught the method most likely to be on the test, on the assumption that the test defines proficiency.
It appears that you have defined "proficiency in the subject matter" as "ability to pass a standardized test." If so, then by definition it's impossible to game the system, making this discussion pointless. Is that your definition of proficiency?
P.S. Here's another way to game the test system - expel your worst students before the state tests. In that way, your school gets the money (for the student) but doesn't have to be responsible for the poor grades, or even make an effort to educate them. See http://www.researchonreforms.org/html/documents/DumpingKidsO... for examples.
I did not define it as "education in the course material". Please don't make that assumption.
It's impossible to evaluate your example without defining the pedagogical goal. Your example test question cannot distinguish between proficiency in multiplying two three-digit numbers, and proficiency in selecting from one of four possible answers, where two are obviously incorrect.
That said, this question is biased in favor of students who have been taught estimation techniques, in this case, round, compute 20 * 10, and look for the closest answer. They will be able to answer more of these types of questions than students who can actually multiply the numbers, but haven't learned the approximation methods.
Had the answers been "1) 257.24, 2) 256.24, 3) 247.34, 4) 248.34" then the other class of students would fare better. Then again, those who learned casting-out-nines would be able to reject two of these quickly.
It's clear that sometimes ballpark answers are better than exact ones. In bookkeeping, it's clear that exact answers are better. It's possible to teach students both ... by taking time away from other skills which are also part of mathematical proficiency. A standardized testing system encourages monoculture teaching, so that all students are primarily taught the method most likely to be on the test, on the assumption that the test defines proficiency.
It appears that you have defined "proficiency in the subject matter" as "ability to pass a standardized test." If so, then by definition it's impossible to game the system, making this discussion pointless. Is that your definition of proficiency?