How would you have graded this simple test?

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  • Daryl
    replied
    The first thought that came to my mind was dyslexia, but they might not of had that back then. The second thought was, "My long lost brother in arms at math", I stunk.

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  • Alex Franke
    replied
    Originally posted by mpc
    That quiz shows a "common mode failure" in the less-than/greater-than/equal-to section. [snip] A single miss-understanding of the ">" and "<" symbols though totally destroyed the intent of that section: does the student understand the numbers.
    This is really interesting. It seems like you could grade the test a completely different way that related directly back to the goals (whatever those might have been).

    - Did he understand how to add larger numbers? Yes (top part)
    - Did he understand the concept of equality/inequality? Yes (= versus <>)
    - Can he tell when one value is bigger than another? Yes (mechanics)
    - Does he understand the comparison symbols? No (symbolism)

    ...so score would be 75% graded like this, but it certainly more subjective. For example, if the wrong answers weren't so consistent, the teacher might not know how to answer one of them.

    So instead of "beating the dead horse," it might have been better to design the test with 2-3 questions that relate back to each specific goal, right?

    Originally posted by phrog
    Edit: Can you believe there are so many opinions on a decades-old arithmetic test?
    No kidding! I thought it was interesting, but I didn't know people would be so passionate about it! I think it's great.

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  • LarryG
    replied
    I concur on the dead horse stuff, but having thought about this overnight, two brief, final thoughts:

    1. That the test included more comparison problems than was really necessary is an excellent point. There were, what, fifteen of them? A half-dozen would have been enough.

    However ...

    2. The inclusion of the two "=" problems (12 __ 12 and 4 __ 4) reinforces my contention that this test was as much about understanding the proper use of the three symbols as it was about understanding the underlying mathematical concepts. It is obvious that the numbers on each side are the same, therefore the only thing being tested by these two questions is, "What is the correct symbol to describe this relationship?"

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  • phrog
    replied
    Originally posted by mpc
    It's the testing equivalent to beating a dead horse. This test was graded fairly... but I think it was a poorly designed test thanks to a common mode failure.

    Understanding the "why" is often more important than "what" in events:

    mpc
    "Beating a dead horse" - That's what I was trying to say. Wish I had said it like that.
    Richard

    Edit: Can you believe there are so many opinions on a decades-old arithmetic test?
    Last edited by phrog; 01-28-2010, 10:41 AM. Reason: Addition - no pun intended.

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  • LCHIEN
    replied
    this thread has probably gone on enough. But as a final thought, there's three things on the test... some addition, some mutli-digit addition and some <=> relationship stuff.

    Tests not only test what an individual knws but also how the class in general has picked up the knowlege. And identifies who needs help.

    In this case by careful examination she may have determined the "student" knew the relationships but was confused between the two similar symbols. OTOH she may have missed that and was just grading the results (maybe her sister the english teacher was helping grade that evening.)

    IN any event there would have been at least a dozen other "narrow scope" tests and such an anomaly would have worked it way out by the law of averages if the student was really any good.

    And for all we know maybe the teacher did see the student to explain that he swapped sybols, or maybe he was smart enough to figure it out on his own or his parents in reviewing the tests told him (you guys do look at your kids work, don't you?)

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  • dkerfoot
    replied
    Originally posted by cgallery
    They're both (concept and correct answer) important, right?

    Otherwise, why ask kids to show their work?

    Otherwise, why give partial credit where there is a slight computational error, but the work shows the pupil was on the right track?

    Otherwise why not hand every kid a calculator and tell them "all we care about is the answer, and this is the fastest way to get there?"
    Sorry CGallery - I forgot to add the sarcasm/irony emoticon...

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  • Alex Franke
    replied
    I just heard back from a friend on this, and her response was a bit different so I though I'd share it. She's a middle school math teacher, and I posed the question out of context this time. (I'm guessing that "S" means "satisfactory.")

    She said: I would probably do an oral exam to be sure he understands the concept of the inequality symbols ... to find out if he truly has no clue, or just got the symbols mixed up because he doesn't know the words for the pictures. For me the symbols would not be the point of the lesson ... probably record an S, but with a note, and spend a little extra time driving it home.

    Originally posted by dkerfoot
    Since the U and the VG are just symbols like the < and >, you really shouldn't care which one is used, so long as you get the concept that it is better to get answers correct. Right?
    Maybe he shouldn't, but a kid probably would care if he does understand what U and VG mean. It seems to me that you could clear up the confusion and "make it stick" -- especially with a kid who's not used to bad grades -- without whacking him over the head with it. I think this is the power of the "see me" solution...

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  • cgallery
    replied
    Originally posted by dkerfoot
    Since the U and the VG are just symbols like the < and >, you really shouldn't care which one is used, so long as you get the concept that it is better to get answers correct. Right?
    They're both (concept and correct answer) important, right?

    Otherwise, why ask kids to show their work?

    Otherwise, why give partial credit where there is a slight computational error, but the work shows the pupil was on the right track?

    Otherwise why not hand every kid a calculator and tell them "all we care about is the answer, and this is the fastest way to get there?"

    Leave a comment:


  • dkerfoot
    replied
    Since the U and the VG are just symbols like the < and >, you really shouldn't care which one is used, so long as you get the concept that it is better to get answers correct. Right?

    Leave a comment:


  • mpc
    replied
    My reply pretty much agrees with what Richard posted earlier:
    That quiz shows a "common mode failure" in the less-than/greater-than/equal-to section. It appears (to me at least) the quiz was intended to test the student's comprehension of what various numbers mean. Just what is "3" compared to "7" for example. There were a handful of basic addition problems to demonstrate "math" ability with the numbers, then a whole slew of the less-than/greater-than/equal-to problems. A single miss-understanding of the ">" and "<" symbols though totally destroyed the intent of that section: does the student understand the numbers. The test answers indicated "no, the student doesn't comprehend numbers at all" which is not the case - most folks reading this thread have commented it is clearly a problem with the symbol comprehension - thus the "come see me" suggestions.

    Instead of so many similar less-than/greater-than/equal-to problems - which leads to the "common mode failure" - a test with only 3 or 4 of a particular type of problems and instead a lot more varied types problems would have probably have resulted in a far more representative testing of this student's math/numbers comprehension. Testing ONE method over and over won't help determine what a student did or did not learn - if you test the thing he "didn't get" then it appears he didn't learn anything. It's the testing equivalent to beating a dead horse. This test was graded fairly... but I think it was a poorly designed test thanks to a common mode failure.

    Understanding the "why" is often more important than "what" in events: why did the bridge fall down, why did the student miss every single question in the less-than/greater-than/equal-to portion of the quiz? With multiple types of questions, a teacher/student/involved parent can isolate what is the weak spot in a student's understanding. With big class sizes today, limited time, and parents that expect the schools to do everything, unfortunately students rarely receive the analysis of where their weak understanding spots are and what they need to focus on. A friend of mine, with a struggling junior high school aged son, was an example of this. The son struggled in just a few areas in school... during a semester his mother spent the money to send him to the Sylvan program. They took the time to figure out just where his understanding was lacking and worked on that. One semester of weekend classes made all the difference in the world.

    mpc
    Last edited by mpc; 01-27-2010, 09:39 PM.

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  • cgallery
    replied
    Originally posted by LarryG
    Good questions. Fair questions. I expect you already know what my answers are.

    Of course I would ask for a warning. And no, the lesson would not be lost on me if I did get off with only a warning. But I'd definitely remember the "lesson" a lot more vividly if I had to open up my checkbook.
    Good.

    So in which scenario would you learn more:

    (1) Cop pulls you over, writes ticket for 1-MPH over the speed limit.

    (2) Cop pulls you over, writes you a warning for 1-MPH over. Explains that there is a child that lives on the street with severe developmental problems, and when the child sees her grandparents (that live across the street) outside, she is inclined to dash across the street without regard for traffic.

    In scenario #1, you've learned to avoid exceeding the speed limit, to avoid the wrath of the cop.

    In scenario #2, you may find yourself going 15-MPH on that street, being careful to look for kids outside. You may avoid that street altogether in the future. You may tell other people about the troubled little girl so they know to be careful on that street.

    I submit that scenario #2 > scenario #1. But scenario #1 would certainly be more upsetting or traumatic for you.

    You don't need trauma to learn a lesson.
    Last edited by cgallery; 01-27-2010, 07:30 PM.

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  • cgallery
    replied
    TWO YEARS AGO, my now 13-YO's school had a drill to prepare teachers/students in the event that someone entered the school w/ a gun.

    They prepared the students on a Monday by telling them about the drill.

    My daughter was absent that day.

    The next day, my daughter was in the restroom when the drill came. All that she was able to hear was a loudspeaker announcement that contained the words "gun" and "lockdown."

    She was in a stall and ran to the classroom as fast as she could. The door was locked, the teacher would not let her in, and told her to "go hide somewhere" through the glass.

    She ran to another classroom, same routine.

    She ran back to the bathroom to hide. There was no lock on the door.

    Remember, she is 13-YO now, 11 when this happened. She was under the impression that there was an armed gunman roaming the halls.

    She was found ten minutes later, curled up in a ball. Completely traumatized, and couldn't stop crying.

    Daughter asked for her parents. Staff (probably scared now) refused.

    Traumatizing kids should not be a component of education.

    And for a kid that never failed a test before, that made an obvious mistake w/ symbols, handing them a "U" without any further information could be (not saying it is, but it certainly could be) very traumatic.

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  • Uncle Cracker
    replied
    I'm thinking you should've played the dyslexia card... The confusion of symbology is a bona fide medical concern, and should not have resulted in a failing grade...
    Last edited by Uncle Cracker; 01-27-2010, 06:53 PM.

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  • Black wallnut
    replied
    Originally posted by phi1l
    Well in that case I guess I would have agree with the U grade. Mathematics is a highly symbolic subject where precision is most important. By the time you get to studying inequalities, you are getting past the basic arithmetic & into the more symbolic concepts. So the meaning of the < & > signs, in this case is the point of the lesson.
    Now for a bit of nit picking....... Alex wrote greater than and less than and yet you posted "< &>" while you should have posted ">&<" to not only prove that you know what he is saying but also to keep the cadence of the conversation.

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  • phi1l
    replied
    Originally posted by Alex Franke
    I was probably thinking "greater than" as I was writing the "less than" symbol.
    Well in that case I guess I would have agree with the U grade. Mathematics is a highly symbolic subject where precision is most important. By the time you get to studying inequalities, you are getting past the basic arithmetic & into the more symbolic concepts. So the meaning of the < & > signs, in this case is the point of the lesson.

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