On a sidenote, these kids were scoring in the mid to low teens, which seems awfully low to me. According to ACT, Inc, those scores are in the 9th to 26th percentile. According to this article, guessing randomly would get you around a 12. (They had sheets yesterday that showed how many questions you needed to get right to get a certain score since the ACT doesn't penalize for guessing, but I can't find one online right now.) I know when I took my SAT I scored well above the 50th percentile . . . are Springfield's gifted kids not really gifted?
And I didn't realize that perfect scores were so rare. 147 in 2000-2001. There's a great quote in the article from one of the kids who got a 36 which shows just how naive he is: "I think, with a 36, what more could they ask for?" Yeah, he'll get into most any public school, but if he wants to go to an "elite" school, a perfect score won't get him in, nor will it get him scholarships automatically. According to the same article, looks like about 1/900 score a 1600 on the SAT.
Anyway, back to the original point - while many decry standardized testing, it's a reality of our current educational system. (Those who know me know that rather than pushing for systemic change, I think it's better to beat the system. If you really want change, beat the system and then change it from the top, i.e. in this case, abuse the tests, get a job in school administration or as the head of a test company, and cause change, instead of just ranting about how unfair tests are.)
Wow, and I'm digressing again - quite the case of verbal diarhea tonight. Anyway, the original point of all this was that the teacher who was helping with math was teaching the right way to do everything, while I on the other hand thought that was a waste of time, and tried to show how to maximize the score, and beat the system. Thinks like using the side of your answer sheet as a ruler of sorts to measure figures if you don't know how to do the math (even though they say figures aren't drawn to scale, they're usually pretty close), or using common sense. I could tell this aggravated the teacher a bit, and we had a short discussion afterwards about how she feels that it's more important to teach the kids how to do the math, rather than beat the test. This may be true for many of the kids she works with (apparently she works with the "gifted" middle school age kids) who have 4-5 years before they take the test for real, for the seniors who are taking this test, they're not going to learn the math in the next two weeks. It's pointless for the seniors to put any significant effort into learning math they should have learned over the last 12 years of their lives, when using basic strategy will boost their score just as much as learning the math.
A good example would be the trig question where they showed a tree casting a shadow, and said that the length of the shadow was 12 ft. long. They also showed that the angle of elevation from the tip of the shadow to the top of the tree was 50 degrees in a figure. The question also listed the numerical values for the sine, cosine, and tangent of 50 degrees. The answer choices were the product of these values with 12: 7.71, 9.19, 12, and 14.30. There was a fifth answer choice, that was less than 12 as well, but I can't remember what it was. Now, the rule method would have shown that the tree was obviously taller than the shadow, leaving you with 14 as that was the only one greater than 12. Also, the angle being greater tha 45 should be a tip-off if you have a more intuitive grasp of geometry. If it was 45, you'd know the tree and the shadow were the same height. Since it's more than 45, the tree should be taller. With either approach, you can solve the question w/o knowing the math. In fact, in my mind, it's more important that you can solve it through either of those approaches, as those show that you can apply knowledge, rather than plug and chug some numbers. Yes, it's a test strategy, but both skills are more likely one that students will use, than trig, unless they plan on becoming engineers or something along those lines.