Re: [math-fun] NY State math exam flapment
But you're actually making an important point. These tests _do_ measure cultural issues. So what? If the issue is to get along in _this_ society -- i.e., go to college, get a job, etc. -- then cultural issues _do_ matter. Rather than trying to eliminate them from the test, let's put them back into the curriculum. Let's take everyone to a baseball game, so that they know what "America's pastime" is all about. This business of trying to protect immigrants from American culture is B.S. I recall several Vietnamese immigrant kids who managed to learn enough English in 2-3 years to _win_ the spelling bee! The best time to learn culture is when you're a kid -- it comes effortlessly.
From what I can tell, these tests are already doing what they are intended to do: determine who can function in our society.
So what if I went to France or Germany and couldn't perform on their math tests. If I were planning to live there, then I would expect to have to learn something about their language & culture. My brother-in-law studied physics in Germany, and they didn't provide any "special education" for him -- he had to learn German, and fast. A doctor friend went to medical school in Switzerland. Ditto. He had to learn French, and quickly. I don't see Saudia Arabia making any special provisions for non-Moslems. We're not doing people any favors through "race-norming" or "culture-norming", because the society at large isn't "race-normed" or "culture-normed". We're just putting off the inevitable day when they discover that they have to learn the same stuff as everyone else. At 02:39 PM 7/3/03 -0400, William Thurston wrote:
The main issue with "common sense" needed for word problems is: common to who? It's quite hard to filter out the extraneous cultural issues in word problems. I was on the ETS math GRE panel for a while. ETS tries very hard to do it, and their tests are relatively high quality, but still there are many cultural biases hard to eliminate. ETS does a lot of "validity testing" which I don't think the regents exam is subject to---i.e. no matter how hard you try to think from the student point of view, you can't really tell how students might interpret or stumble or misinterpret a question until you try it out on them. One of the complaints about the regents exam is that it is only NY, so the test writing companies aren't financially motivated to put much effort into the test. It's not necessarily as predictable from year to year as other standardized tests.
In the juice container / straw instance: do the students in question actually encounter juice containers like the ones described? Do they interpret the question to mean you actually try to squeeze the straw through the hole into the container?
In other common sorts of questions, do the students actually play or at least watch baseball? What is their common sense notion about the typical size of a house? What variant of English do they use everyday? I once had some students who were struggling with word problems in calculus ... it turned out the issue was things like "needle and thread". Even though they spoke fluent English they were from Indonesia and terms like this which are everyday words for some people were unfamiliar. The math itself was easy for them, and with a little personal interaction they did well in the end.
* Henry Baker <hbaker1@pipeline.com> [Jul 03. 2003 21:47]:
But you're actually making an important point. These tests _do_ measure cultural issues. So what? If the issue is to get along in _this_ society -- i.e., go to college, get a job, etc. -- then cultural issues _do_ matter. Rather than trying to eliminate them from the test, let's put them back into the curriculum. Let's take everyone to a baseball game, so that they know what "America's pastime" is all about.
Agreed. However, in math books I find the (not so rare) baseball examples pretty annoying. It should in in almost all cases be possible to find an analogue that doesn't use baseball. (I am german & have absolute no clue about baseball). -- p=2^q-1 prime <== q>2, cosh(2^(q-2)*log(2+sqrt(3)))%p=0 Life is hard and then you die.
I thought I'd add a little more raw material from the exam. I'd attach the PDF version if it were allowed, but instead I'll just type in a couple more questions: 14. If the expression 3 - 4^2 + 6/2 is evaluated, what would be done last? (1) subtracting, (2) squaring, (3) adding, (4) dividing I guess it's easy for us to guess what they want --- but it seems silly, and also it assumes you disregard the commutative rule for addition. It's significant for compilers to analyze computations and do them in efficient, rather than most obvious orders. 20. How many different five-member teams can be made from a group of eight students, if each student has an equal chance of being chosen? (1) 40 (2) 56 (3) 336 (4) 6720 I think the correct answer is not among these choices: 1 It's very poorly phrased, being neither colloquial English or typical mathematical/combinatorial English. 21. The student scores on Mrs. Frederick's mathematics test are shown on the stem and leaf plot below: 4 | 3 6 | 0 5 5 7 9 7 | 2 5 6 8 9 9 9 9 | 0 1 2 5 9 Find the median of these scores. --this is a new one for me. I'm clueless, even seeing the key, which I'm not printing.
--- William Thurston <wpthurston@mac.com> wrote:
I thought I'd add a little more raw material from the exam. I'd attach the PDF version if it were allowed, but instead I'll just type in a couple more questions:
14. If the expression 3 - 4^2 + 6/2 is evaluated, what would be done last? (1) subtracting, (2) squaring, (3) adding, (4) dividing
I guess it's easy for us to guess what they want --- but it seems silly, and also it assumes you disregard the commutative rule for addition. It's significant for compilers to analyze computations and do them in efficient, rather than most obvious orders.
This could be fixed up if the test question design process were to bring in feedback from outside the exam committee.
20. How many different five-member teams can be made from a group of
eight students, if each student has an equal chance of being chosen? (1) 40 (2) 56 (3) 336 (4) 6720
I think the correct answer is not among these choices: 1 It's very poorly phrased, being neither colloquial English or typical mathematical/combinatorial English.
What interpretation yields the answer 1? This looks like a perfectly clear question to me, and the extra irrelevant probability information doesn't affect the result.
21. The student scores on Mrs. Frederick's mathematics test are shown
on the stem and leaf plot below: 4 | 3 6 | 0 5 5 7 9 7 | 2 5 6 8 9 9 9 9 | 0 1 2 5 9
Find the median of these scores.
--this is a new one for me. I'm clueless, even seeing the key, which I'm not printing.
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participants (4)
-
Eugene Salamin -
Henry Baker -
Joerg Arndt -
William Thurston