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Unicorns roaming the æther – NY State Mathematics in context

April 16, 2009 pm30 10:34 pm

While I am focussing on set theory, that does not mean that bad questions get a free pass. So far, in just three Integrated Algebra Regents exams, the NY State Education Department has offered two free response questions relating to set theory. And both of them, don’t act surprised, stink.

Let’s look first at poor Maureen:

  • 06/08 #33 (free response, 2 points) Maureen tracks the range of outdoor temperatures over three days. She records the following information: [the exam has three number lines, for Day 1, Day 2, and Day 3 respectively. The ranges indicated are -20 ≤ t ≤ 40, 0 ≤ t ≤ 50, -23 ≤ t ≤ 45]. Express the intersection of the three sets as an inequality in terms of temperature, t.

Dear readers, can you help me identify the poor community that is plagued by 50, 60 or even 70 degree swings in temperature over consecutive days?

In Washington DC this year, there was a 42 degree swing in a day. The Washington Post saw fit to write an article:

March Temperature Swings Gone Wild

Between Tuesday and Saturday last week, the high temperature at Reagan National Airport (DCA) soared from 29 to 71. I went back into the record books (since they’ve been kept at the airport in 1942) to see if there had been other instances when the high temperature had risen that much in 5 days or less. The answer: no. That 42 degree rise was the biggest such 5-day rise in March in at least 65 years.

Five days or less? Forty degree swing? Record? The Post writers should travel to Albany. Perhaps they should fly up on unicorns, and stop at Oz along the way.

Now lets look at some poorly coached players:

  • 08/08 #33 (free response, 2 points) Twelve players make up a high school basketball team. The team jerseys are numbered 1 through 12. The players wearing the jerseys numbered 3, 6, 7, 8, and 11 are the only players who start a game. Using set notation, list the complement of this subset.

T them up! The digits 6, 7, 8 and 9 are never allowed in NCAA or high school basketball. That will be a technical foul. Or will it be one for each illegal jersey? Unless King Arthur and Spider Man and Harry Potter intercede, and suspend the normal rules.

The New York State Education Department brings in teachers and then blames them for okaying this crap, but it is SED’s process that produces nonesensical question after nonesensical question. It is time to clean up the question writing/vetting/approving process. This is not ok.

10 Comments leave one →
  1. April 17, 2009 am30 1:47 am 1:47 am

    Really? 6, 7, 8, and 9 aren’t allowed in HS/NCAA basketball? [looks it up… ah!]

    I had no idea. And yet, I can’t quite follow you in classing this a “nonsensical question” on that basis. They’re asking a reasonable question about a reasonable (if technically not real-world) situation.

    Perhaps if someone proof-reading this test had known this bit of minutia, they’d have changed the question to being about an NBA team.

    • April 17, 2009 am30 5:25 am 5:25 am

      Yeah, not minutia for kids who play.

      How many years between the Declaration of Independence, in 1621, and the Emancipation Proclamation, in 1973?

      If they’re not on your radar, no problem. But if you have some knowledge, there is upset here, there is frustration.

      It’s the same thing.

      Plus, they just should not be making this many mistakes. It’s every lousy exam. And no one stands up and says “sorry” and no one even stands up and says “I am responsible for the quality of the questions”

  2. April 17, 2009 am30 2:59 am 2:59 am

    I fear I don’t get the weather reference. Isn’t the DC bit talking about the change in daily high temperatures over several days? In the SED problem, the high temps appear to be 40, 50, 45, hardly a notable shift.

    Can the high and low on any one day be so disparate as the SED data? A quick check reveals that the high and low in Flagstaff, AZ on Feb 20, 2009 were 56F and 5F. I suspect bigger swings could be found if one looked — high altitude arrid climates are likely places to check.

    A 42 degree swing is probably quite unusual in a coastal city like Washington DC (or NYC), where the ocean has a stabilizing influence on temperature swings. Shifts of that size or larger in daily highs are fairly common during winter and springtime in northern inland cities….

    I suspect I’m missing something here….

    • April 17, 2009 am30 5:21 am 5:21 am

      60 degree shift each day, three in a row? Really not a surprise?

      But I stand with the complaint, either way.

      If it is a surprise, then they’ve created ridiculous context (again!)

      And if it is not a surprise, they’ve created some, is it called “cognitive dissonance” for the kids in the City and on the Island that registers as nothing in Buffalo and Rochester.

  3. April 17, 2009 am30 10:39 am 10:39 am

    Then again, at the bar tonight, my position did not get much sympathy.

    Except when I pointed out that they could have stripped out the context and run exactly the same problems, and what would we have lost?

  4. April 17, 2009 pm30 2:07 pm 2:07 pm

    I went to the National Weather Service website, and poked at a couple locations that seemed likely to have extreme daily temperature ranges. (I did not look for record setting events, and I did not look systematically.)

    After three tries, I found:

    Lake Yellowstone, Wyoming:

    April 4, 2009: high 30, low 3
    April 5, 2009: high 34, low -12
    April 6, 2009: high 46, low -10
    April 7, 2009: high 49, low -4
    April 8, 2009: high 41, low 13

    not *quite* as extreme as we’re hoping for, but in the ballpark certainly. I suspect a more extensive search (in space and time) would turn up examples of consecutive days at one location with daily temperature ranges of 60F or more.

  5. April 17, 2009 pm30 2:43 pm 2:43 pm

    I get your message on cognitive dissonance, and yet…. If SED writes exam questions that *are* based on the familiar experiences of kids in the 5 boroughs, what will schoolkids in Clyde make of them?

    I suppose the safest ground would be to eliminate any (pseudo) real-world references, and only ask questions completely devoid of context. But that’s a rather sorry state of affairs, and sends a horrid message about the relevance of this beautiful content.

    Thank goodness I’m not in the high stakes exam writing business. I thought teaching real analysis was hard… but it pales in comparison to this.

  6. April 17, 2009 pm30 3:06 pm 3:06 pm

    [Ah, now I know why TwoPi was looking up temperatures in Flagstaff last night!]

    I agree that 0 to 50 in one day is pretty extreme, especially since it jumped back down to -23, so it wasn’t a sudden warming trend. And that’s enough to be distracting on a state test in Clyde or NYC [says the person who has been known to stop reading books at times because she gets so distracted by incorrect “facts”]

    But as a minor side note, I don’t think the Washington Post article is about the same topic. It doesn’t seem to be talking about a 42 degree difference in one day, but about a 42 degree difference in the HIGH temperatures. The State test examples only had a difference of 10 degrees in the high temperatures, despite the wild swings.

  7. April 17, 2009 pm30 4:03 pm 4:03 pm

    “we get to make up whatever lies we want;
    your role is to struggle mightily to guess
    what we want you to do and accept it
    whenever we blame you for guessing wrong.
    there’s sure no hope of us telling you clearly;
    we don’t even know ourselves. make us look good.
    or else.”

    just like most paperwork jobs.
    the system appears to be working as designed.
    welcome to the machine.

  8. Clueless permalink
    April 17, 2009 pm30 4:58 pm 4:58 pm

    The SED question did not say three consecutive days, giving themselves enough wriggle room :-)

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