Partial credit on college math tests?

Discussion in 'Off-Topic' started by strantor, Jun 22, 2012.

  1. strantor

    Thread Starter AAC Fanatic!

    Oct 3, 2010
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    I just got my most recent exam back (MATH0312, Intermediate Algebra, Community college) and I got a very good grade - a 96%. I was a little surprised though, when I looked through the exam, the -4 points was for 4 separate instances of (-1 pt) missing exponents or incorrect +/- signs. These questions were worth 4 - 10 pts each.

    The way I see it, math is not creative writing. Signs and exponents are not punctuation marks. An answer with an incorrect sign is completely wrong. There should not be any partial credit. It's either right or it's wrong.

    When I re-grade my my exam according to my criteria, I got a 69, not a 96.

    Is this partial credit just because I'm in a remedial class, or can I expect this to continue through the next 4 years?
     
  2. Sparky49

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    Jul 16, 2011
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    Often, it's not about getting the answer right, but about how you got to the answer.

    Eg, if you had a question on binomial theorem, worth 5 marks, an examiner would give you the 5 marks straight away if you came up with the right answer. Why? Becuase you know how to apply and use binomial theorem - how else did you get the right answer? :)

    And this is what they are testing for 99% of the time. Often only one or two marks in a question will be given for getting the right answer. The bulk of it will be given for following the correct method, and knowing how to implement that method.

    So what if you mixed up a sign? That's not what they're testing for.

    It's for this reason that maths is a great qualification to have for any subject or job. Although beging able to integrate doesn't serve much direct use for a degree in history, it shows that you are able to think, plan and follow a method to achieve a goal.

    That's where the marks come from. :)
     
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  3. justtrying

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    Mar 9, 2011
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    If I was graded by your criteria, I would fail all my math courses. I am sure you will meet a teacher who only cares about the right answer, but in reality, 80% of the mark is given for understanding how to get to the answer not whether it is actually correct.

    p.s. signs have a habit of changing mid-way through the problem anyway...
     
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  4. WBahn

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    Keep in mind that the primary goal in an academic environment is for someone that doesn't know something to learn it and that learning is not an all or nothing process.

    Imagine you were teaching someone how to be a cabinet maker and you showed them how to make a certain type of cabinet and then had them do it. They almost certainly are not going to do it perfectly and are very unlikely to do it well enough that you would even consider selling it to an actual customer. So should they be given the equivalent of an 'F'? No, because that doesn't accomplish the goal which is to let them demonstrate a skill and then provide feedback on what was good and, particularly, what wasn't. You wouldn't grade the whole cabinet as pass/fail, you would examine each part of it and tell them where they made mistakes and need to work on getting better as well as letting them know where they are doing fine and can consider a skill sufficiently mastered (for now, anyway).

    That's what partial credit is really all about -- to let the instructor say, "Your approach on this problem was mostly correct, but you got this piece wrong and you made a mistake here at this point. I'm going to penalize the specific pieces and places where you had problems because I want you to focus on correcting those things. The places where I am not penalizing you are places where it appears you have an adequate grasp of the material and how to work with it."
     
    Last edited: Jun 22, 2012
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  5. strantor

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    me too ;).
    Good thing neither of our exams are graded by me.

    All you guys more or less are saying the same thing, and you're all making a good point. I guess I've been too long removed from the educational setting to remember what it's all about. Every time I've had to do math in the past 9 years, it was only the final result that mattered, and it really mattered. In real life, for example you're calculating a component value for a circuit, and you misplace a (-) sign, well, you just screwed the pooch and you're circuit won't work as expected (at a minimum) or could hurt you.

    Well, I guess I won't feel guilty about accepting the grade then.
     
  6. atferrari

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    In fact any calculation must be checked before accepting the outcome as acceptable.

    In my professional activity, prior-PC time, calculations, including position at sea (using the fixes taken to stars) or the trim calculation solving moments required lot of math. I developed the habit to check every similar operation all together to be sure I could move on to the next steps.

    Not trying to derail the thread, but let me tell that the risk of teaching any calculation as a mechanical procedure, that is, without knowing what you are actually doing, when it comes to check a result the sole possibility is repeating the whole thing trying to iron out an eventual mistake. A rather poor way. If you know what parameters are involved you then can judge it, maybe even not needing to re do the whole math.

    BTW, congratulations. Wish I could be actually studying what I wanted my whole life.

    Be well.
     
    Last edited: Jun 23, 2012
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  7. steveb

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    Jul 3, 2008
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    Even professionals make these simple mistakes. No matter what level of math you are doing, often getting the sign wrong, or being off by a factor of 2 is where the mistakes are made. Einstein published papers with factor of 2 errors in them.

    Not that mistakes should be taken lightly, but they do happen and they are part of being human. In the real world you have more opportunity to double check your answers. Personally, I have never had to solve a real world engineering problem in 15 minutes under high pressure.

    I'll echo the comment of "Congratulations !". If your teacher thinks it's a 96, then you did well.

    Keep in mind that there are many teachers that have your opinion about mistakes. They give zero credit if the answer and the method are not 100% correct. That's just the way it is. You will encounter these teachers. And, you may not like them by the end of the course because most of them have that policy to make their grading task much easier, not to teach you the good lesson of minimizing mistakes. If they cause a creative person that does not do well on tests to flunk out or quit school from getting discouraged, they do not care.

    However, I like the fact that you want to hold yourself to a higher standard. Keep this attitude and do all you can to minimize mistakes. It can only help you if you have the inner strength and discipline.
     
  8. #12

    Expert

    Nov 30, 2010
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    EEK! I hope it wasn't the one about E=MC2!

    Back 2 the subject. Perfect example of when a partial score seems fair: A chemistry problem required 11 factors in the equation but I only had 10. Reason: "Proof" in an alcohol beverage is not the percentage of alcohol. (I didn't think about that because I don't drink.) The instructor gave me 9 out of 10 points because I did 10 out of 11 factors correctly.

    That seems very close 2 "fair" from my point of view.

    PS, I have always held myself 2 a higher standard than most people require of me. You have my permission 2 continue with that value system :p
     
  9. JoeJester

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    You you think these engineers got "partial credit"?

    Actually they got full credit for the consequences. You can bet they were all on the same page on the subsequent mission.
     
  10. WBahn

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    Yep. There have been airliners that have run out of fuel because someone didn't convert between pounds of fuel and gallons of fuel. Lot's of other mistakes, many of which have cost people their lives, have occured because someone couldn't be bothered to carry their units throughout their calculations and then clearly document what those units are in the final product. It is perhaps the single most powerful error detecting tool available to an engineer. Personally, I think that making a mistake that causes significant harm but would have been caught if units had been properly tracked rises to the level of criminal negligence for a practicing engineer.
     
  11. atferrari

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    I work quite frequently with cargoes going up to 300 MT weight.

    Those coming from USA, not frequently thanks God, fail sometimes to show the units. While we know where to look at to solve the doubts, such a thing is a point of concern.

    For the cargo list, one of the lines produces two separate cargo lists in metric and imperial units. That solved also the confusion problem that plagued the operations in the past.

    For when the weight is indicated in pounds, I taught stevedores to simply divide by two for an approximation in Kg. Simple for them but just in case, they ask me again and again.

    Another problem, much more frequent than you would like to believe is the wrong indication of centers-of-gravity and lifting points.

    Loading bulk cargoes in several terminals in USA, as a Chief Officer I was asked to prepare our stow plan and sequence of loading in short tons. Never met those units again not even in cargo documents.

    But the strangest thing was when loading chromite in South Africa: the foreman requested me to calculate the quantities required to trim the vessel in "scoops". After much talking I found out that he was referring to the weight that a payloader they had in the storage area was loading every time in the rail cars coming alongside. He believed that was a standard for everyone. Go figure.
     
  12. panic mode

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    easy peasy, when such ship arrives just refuse to unload and move on to the next one.

    time is money and i can see someone getting frantic call about f***ng units.
    probably not something to forget ever again....
     
  13. atferrari

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    It is much more practical to browse documents than stopping the lady alongside. Owners, one of the two most frequent customers in the last 6++ years would not appreciate that. :)

    Anyway if I am not satisfied we will stop until the information comes or simply discharge something else.

    After all, a good Chief Officer, and they are so, is a valuable help in these cases.
     
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  14. Brownout

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    Jan 10, 2012
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    In real life, one usually doesn't get just one chance to get it right. He has peer reviews, simulations, validations, testing and more testing. Accurate work is of course very important, but a math test is a poor representation of what you'll see in practice.
     
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  15. JoeJester

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    And yet we still had that experience of a miscalculation. Of course I am assuming that NASA does work in real life.
     
  16. Sparky49

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    No, they faked the moon landings.
     
  17. JoeJester

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    Damm, and I wasted my time watching that on TV ... live.
     
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  18. strantor

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    All around us are examples of peer reviewed, simulated, validated, and extensively tested failures. There's enough material for not nearly all-inclusive TV show about it.
    Buildings falling down, bridges failing, planes falling out of the sky, etc. all because of bad (uber redundantly checked) math.
     
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  19. WBahn

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    That's probably going a bit too far. If you look at all the failures and grouped them by cause, I would bet that undiscovered math errors is a pretty small fraction of the total and probably a pretty small absolute number, as well. I would still, however, love to see a program that catalogued a few hours worth of them.

    I'm gonna check out the DVD series you linked, but I can already tell from a quick look that they are going to claim engineering failures for events that were completely human failures by using 20-20 hindsight to proclaim that the engineers should have foreseen such and such.

    I wonder if they spend any time at all on disasters averted, such as the CitiCorp Center building. Now THAT's an interesting tale of a curious student asking a question about something he didn't understand and an engineer asking if the answer made sense, and taking decisive action when the answer was, "No!"

    Among other sources for catastrophic failures that should be segregated and highlighted are instances where management overrode strong recommendations from the engineers (as well as any instances that go the other way -- I'm sure there are at least a few). Also, they should have a category that deals with miscommunication which, when all was said and done, is really what happened in the NASA Mars probe fiasco.

    Many disasters have happened, such as the Kansas City skywalk collapse in 1981, when changes to a design were made, usually for completely reasonable and sound decisions, but the original design was predicated on unusual aspects that were not obvious and not well documented. So the people that changed the design had no idea they should be looking at some unusual aspect and the people that did know either weren't informed of the changes or weren't around anymore, or didn't pay enough attention because they had moved on to other projects and no longer had the needed mental immersion to spot the deficiency.

    Having said that, my recollection is that in the case of they skywalk collapse, the people that made the changes should have be able to spot the resulting issues with any kind of a reasonable engineering review of them.
     
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  20. strantor

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    It would probably depend on the agenda/bias of the person presenting the information. If one really had it out to make engineers look like a bumbling bunch of math incompetents, they could probably dig down into each case as far as necessary to until they hit math, and just start pointing fingers. It would be hard to defend. And they could always make this claim:
    On the flip side, someone with an oppositely polarized agenda could dig into each case totally avoiding math and find equally compelling directions to point fingers at management, communications, etc.

    I don't think it's something you're ever going to see set out by the numbers in columns, these attributed to math errors, and those attributed to bad leadership. Unless the cause is officially established in court proceedings, it's subjective. Even then the verdict is subject to the court of popular opinion (did OJ do it?).
     
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