[math-fun] NY State math exam flap
Does anyone know any more about the problems referred to below with the NY State Math "Regents exam"? In the NYTimes there was an example of one of the problems on the test, which simply asked what the diagonal distance of a rectangular (3D) box is in terms of its sides -- not an especially difficult question for a junior or a senior in high school who has even a smattering of math and/or physics. I guess this brings up the age-old question of "how much math _should_ the average person who graduates high school should know?" A lot of students think that math is really out of touch with reality. E.g., in today's world of ubiquitous calculators, why waste time on teaching long division? A more relevant question (which my gardener/landscaper just failed) is "what sprinkler pattern covers the grass best?" (Answer is _not_ a cartesian grid.) So clearly high schools aren't teaching even highly relevant math. The diagonal distance of a rectangular box may not be the most relevant question, but I just met a decorator who flunked the 2D version. Shelves in kitchens are priced by the "linear foot"; how many feet of shelves do you have if the shelves are at an angle? (Dunno.) We now have a nation full of math idiots! I have a solution: we give a test to everyone who wants to immigrate to the U.S. If you pass the test, you get in; if you don't, you don't. Since the U.S. birth rate is falling (as it is in every "first world" country), at least we can get an educated population through immigration. ----- http://www.nytimes.com/2003/07/02/nyregion/02REGE.html?pagewanted=print&posi... ------ July 2, 2003 Math Failures Are Raising Concerns About Curriculum By KAREN W. ARENSON Everyone knows now that the June 17 Math A Regents exam was problematic, with almost two out of three test-takers failing. The question is why. Richard P. Mills, the state education commissioner, nullified the test results last week for juniors and seniors, and he and the Regents will soon appoint a panel of experts to figure out what went wrong. In the meantime, parents, teachers and others have their own theories. Some of their explanations have to do with the mechanics of the test: poorly worded questions, lengthy questions that required students to be good readers, multiple-choice questions that had more than one valid answer. Some educators say they were the sort of problems that could have been caught by closer scrutiny of the test before it went out. "If someone had paid me $100 to proof this test, I could have picked out the problems that would create problems," said Daniel Jaye, chairman of the math department at Stuyvesant High School in Manhattan. But some explanations touch on deeper issues, including whether the Math A curriculum is too broad, how much harder it is for students to solve problems than to manipulate equations, and whether unqualified teachers are even less likely to succeed in preparing students than they were with the old math curriculum. When the Math A exam was introduced in 1999, the State Education Department proudly declared that it was harder than Math 1, the old first-level test. There would be more word problems, and students would need a deeper understanding of math and math concepts to do well. Instead of covering a year's worth of material, as most Regents exams do, Math A was meant to be learned over three semesters. Although some students complete the work in a year, some schools have added extra instruction periods and tutoring sessions, and have stretched the course out over four semesters. For a while, the state offered both the old Math 1 exam and the new Math A test. Some schools moved their students quickly to Math A, while others dragged out the transition. The Math 1 test was given for the last time in January 2002. Alan Ray, a spokesman for the Education Department, said that the scores on Math A had gradually improved. In June 2002, 86,000 students took the test, and the passing rate was 61 percent. The department does not yet know how many students took the test last month, but a preliminary survey suggests that only 37 percent of the students passed. The shift from rote learning to a greater emphasis on mastery of concepts is welcomed by some college professors in math and science, who have been trying to accomplish the same shift. They say that although mastery of some facts is critical, students who focus on memorization may do well in a course but remember little of it six months later. "Many of the students are coming from an environment where the tests are pretty much about facts, not about how to puzzle something out, or whether the data you have been given makes sense," said Robert B. Suter, a biologist at Vassar College. "It takes students coming in a while to learn that they are in a somewhat different ballgame." But high school math teachers in New York say that the shift in the state math curriculum has not been smooth, and that schools, teachers and students could not keep up with the changes. "There has to be a balance between skills and concepts," said Mr. Jaye at Stuyvesant. "But the weight shifted a little too quickly for us to keep equilibrium here, and collectively we capsized. "I'm not a champion of the old Regents, which was cookie cutter all skills. If you studied the three previous exams, there would be no surprises. But in the effort not to make Math A cookie cutter, the kids got flamed." Part of the problem, he and others said, is that the curriculum expanded and expanded, and nothing was taken away. Many teachers felt that they were racing through material without giving students the time they needed to master it. "One of the big problems is that the curriculum is so broad that you cannot go very deep," said Bob Hazen, president of the Association of Mathematics Teachers of New York State. "It used to be with the old Math 1, 2 and 3 tests that you could just bone up on old tests and pass them and not have a firm grasp of the concepts," Mr. Hazen said. "But now you are looking at a standards-based assessment, and it is very difficult to look at the past tests and know what will be on the next test." Some educators say teaching students to be problem solvers takes more skill on the part of teachers, a challenge when there is a shortage of qualified math teachers. "Teachers are not really prepared to prepare kids for this test properly," said Alfred S. Posamentier, dean of the School of Education, City College of New York, and the author of books on problem solving. "There is very little training for teachers in problem solving; it's assumed they will get it along the way." Commissioner Mills said he stood by the Math A curriculum. "There are a great many people who say we should just teach students how to balance a checkbook," he said. "But that is a level of math that is learned by the fourth grade. Are we ready to say that the most minimal level is all students need?" "The Regents made the fundamental policy choice here, and I support it," he added. "The standards represent a level of knowledge and skill that's essential for every child." Copyright 2003 The New York Times Company | Home | Privacy Policy | Search | Corrections | Help | Back to Top
On 2 Jul 2003 at 21:35, Henry Baker wrote:
In the NYTimes there was an example of one of the problems on the test, which simply asked what the diagonal distance of a rectangular (3D) box is in terms of its sides -- not an especially difficult question for a junior or a senior in high school who has even a smattering of math and/or physics.
I guess this brings up the age-old question of "how much math _should_ the average person who graduates high school should know?" A lot of students think that math is really out of touch with reality. E.g., in today's world of ubiquitous calculators, why waste time on teaching long division?
But this has been happening for a long time --- I'm told that the generation before me learned to extract square roots by hand, but certainly that wasn't taught to us [although we did learn long division..:o)]. And odd skills like interpolating log tables and such seem quaint to have learned [I'm not sure I could FIND my old book of log tables any more]. There are a lot of 'math skills' that different generations learned that are, in retrospect [IMO!], more compensating for the available (or rather _un_available) aids/technology than they are 'real math'. And, indeed, I'd probably say that long-division might well be one of them [OTOH, being able to estimate a division result in your head is *NOT* one of them -- that's an important skill that many folk, even those who CAN do long division, don't do very well]
A more relevant question (which my gardener/landscaper just failed) is "what sprinkler pattern covers the grass best?" (Answer is _not_ a cartesian grid.) So clearly high schools aren't teaching even highly relevant math.
I guess that I'm a bit stumped, too --- there must be something I'm missing about the available patterns and what 'best' means in this context.
The diagonal distance of a rectangular box may not be the most relevant question, but I just met a decorator who flunked the 2D version. Shelves in kitchens are priced by the "linear foot"; how many feet of shelves do you have if the shelves are at an angle? (Dunno.)
We now have a nation full of math idiots!
Just so --- and interestingly I think this has little or nothing to do with knowing the sort of math skills involved in learning long division or knowing the quadratic equation or the like. How would/should we go about teaching folk the *essential* parts of math? What math knowledge should your gardener or decorator have had to help them with their problem? Certainly not how to take a cube root by hand... Much of what I see of the critical/practical parts of mathematics has to do with how one perceives and analyzes the things around them, rather than having to do with specific computational skills. Most of us acquired those analytic skills as a sort of happy-coincidence byproduct of learning a lot of [in fairness!] otherwise irrelevant math. If there were some way to teach the wisdom without the largely-not-useful stuff that generally goes with it, that'd probably be what we need, but I don't know how to do that [wasn't "the new math" an attempt to do that?]
I have a solution: we give a test to everyone who wants to immigrate to the U.S. If you pass the test, you get in; if you don't, you don't. Since the U.S. birth rate is falling (as it is in every "first world" country), at least we can get an educated population through immigration.
But what would you put in the test? /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--
On Thursday, July 3, 2003, at 12:35 AM, Henry Baker wrote:
Does anyone know any more about the problems referred to below with the NY State Math "Regents exam"?
In the NYTimes there was an example of one of the problems on the test, which simply asked what the diagonal distance of a rectangular (3D) box is in terms of its sides -- not an especially difficult question for a junior or a senior in high school who has even a smattering of math and/or physics.
I looked at the exam on the web. There were many questions that to me seemed poorly designed. This particular question as you paraphrased it may be something that you think most people *should* be able to do, but in reality I think few high school graduates actually master it, since, in particular, solid geometry is generally not taught. The actual question was about a juice container something like 2" x 4" x 5", and it asked how long a straw would fit diagonally, to the nearest tenth of an inch. A straw is not the same as a line, and the thickness of the straw (not specified, of course, and *intended* to be disregarded) would actually be likely to change the answer. People who've been taught a particular mechanical formula for this particular question can do it, but otherwise, it's likely to be a time-consuming and futile exercise, compounded by trying to calculate square roots presumably without a calculator. Another question that annoyed me: there was a multiple choice question, what's the inverse of the statement "If Jane works hard, she earn lots of money". This term "inverse" I haven't seen or heard used for a long time ... what's the point in teaching it, especially in this context where logic is a frivolous exercise. The immediate problem is that it's a poorly-designed test, with no care taken to remove cultural snags (the built-in assumption that people are from well-off suburbs) and without calibration to the actual subjects. The fact that 2/3 of the population failed it doesn't mean anything, as an isolated statistic, except that the test was not suitable. The bigger problem is that the entire testing mentality has been working to undermine teaching kids to actually understand math---especially kids in underperforming schools, where intense pressure is brought to teach to the test. Bill Thurston
What is the length of the longest 1/4 inch outside diameter straw that can fit in a 2 inch by 4 inch by 5 inch box? exact length or to the nearest 1/10^33 inch.
It depends on how well the straw scrunches. On a multiple choice, I'd guess the answer would be "none of the above". Greg Fee wrote:
What is the length of the longest 1/4 inch outside diameter straw that can fit in a 2 inch by 4 inch by 5 inch box? exact length or to the nearest 1/10^33 inch.
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participants (5)
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William Thurston