Math Teachers: Do you give credit for correct answers using an invalid method?

Discussion in 'General Education' started by RadiantBerg, Sep 20, 2013.

  1. RadiantBerg

    RadiantBerg Cohort

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    Sep 20, 2013

    We had our first big math test today in my alg 2 class.

    One of my problems was:

    Solve (x+4)(x-2)=7. They needed to distribute, get it equal to 0, factor, and then use Zero Product Property to get the two correct solutions of x=3 and x=-5.

    One kid just did x+4=7 so x=3 and x-2=7 so x=9. Coincidentally one of his 2 solutions is correct, but he just got lucky there.

    I was planning on taking off the full 5 points as his method doesn't work, and he was just lucky to get one correct answer. Would you give any credit for that at all? Or in general, do you ever give credit if they use a completely wrong method, but just get lucky?
     
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  3. czacza

    czacza Multitudinous

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    I celebrate that there are many ways o et to the 'rigt' answer...I'd give credit for the answer, but pull him aside, tell him he's lucky and reteach.
     
  4. Aliceacc

    Aliceacc Multitudinous

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    .I would give one point for the answer.

    I'm VERY generous with partial credit. But that's because the work is worth something. I'm not checking for the answers... I KNOW the answers. I'm checking to ensure that you know how to tackle a particular type of problem. So the work you show is what I'm looking at, not really the answer. If a kid does a problem entirely right, but copies the original problem wrong (and hence doesn't get the answer on my key) I'll take off just one point. He's proving that he knows the process, and that's what's important.

    Lucking into the answer doesn't show me that.
     
  5. RadiantBerg

    RadiantBerg Cohort

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    Yes, I love when there are many ways to get the right answer as well, unfortunately his way generally won't work.
     
  6. RadiantBerg

    RadiantBerg Cohort

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    Yes, I agree with you on that copying the problem wrong part, as long as they don't somehow make the problem drastically easier or different than it was intended by miscopying. (i.e. copying 2x-2=2 as opposed to 2x^2-2=2 as that would be testing completely different concepts.)

    I think I'll give him 1 point...if nothing else, it will at least encourage him to keep showing work.
     
  7. Pashtun

    Pashtun Fanatic

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    If the method will typically fail and he honestly just got lucky. I would not give him any points.
     
  8. readingrules12

    readingrules12 Aficionado

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    Partial credit? yes. Full credit? no
     
  9. Catcherman22

    Catcherman22 Companion

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    I follow this as well. It's the same if said student mysteriously changes a - to a plus, or adds incorrectly. IN Alg 2 especially, it's about the process.. not the answer.
     
  10. Aliceacc

    Aliceacc Multitudinous

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    Right, that was a better example, since Radiant Berg was right-- I'll only give full credit if the accident doesn't change the level of difficulty.

    It's so easy to make a small error when you really do know what you're doing. I'm not going to take off major points for something like that.

    But I'm not going to award full credit to someone who hasn't demonstrated the knowledge of the process I've taught.
     
  11. mmswm

    mmswm Moderator

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    While that may be, in this specific instance the process used by the student shows a complete misunderstanding of what the "right" answer to a quadratic equation really is.

    The "solution" to a quadratic equation is simply the point(s) where the graph of said equation crosses the x-axis, thus the zero property rule. A failure to set the equation equal to zero and then solve demonstrates a complete lack of understanding of what's going on.

    That said, I agree with Alice. I'd give a point or a half a point for trying, if only to encourage the student to continue showing his work.
     
  12. Pashtun

    Pashtun Fanatic

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    When you give a point for trying, or any points for that matter, how specific is the feedback to the student? Do they know that the point they got was specifically for trying and putting something on paper? Do they know that it was for understanding the problem and just making a sign error? If they are asked do they know?
     
  13. Aliceacc

    Aliceacc Multitudinous

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    I give a point because finding the correct answer IS one of the steps in the problem.

    But, since it's only one step, I give only one point.

    As to just losing one point, yes, I circle the sign error and write "-1"
     
  14. Pashtun

    Pashtun Fanatic

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    I am referring to some of the people who said the student tried, do they know they got points for effort?

    How defined is your rubric to the students? Do they know they get 1 point for the right answer?
     
  15. mmswm

    mmswm Moderator

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    Actually, in my view of this particular example, the one point would be for remembering part of the procedure. The student knew that he was supposed to set each factor equal to something and solve both as individual linear equations. What he forgot was that "something" was "equal to zero". He lucked into getting one correct solution, which for me doesn't count for much (sorry, Alice...slight difference of opinion here :) ).

    To answer the other question, of course the student would know why he got partial credit. Between an in-class review and the open door policy for questions, my students had ample opportunity to review what when wrong, what went right, and how to fix things for the future.
     
  16. Aliceacc

    Aliceacc Multitudinous

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    Exactly. I don't use a rubric for each test, but I do go over each test and my kids know where any missing points went. Anyone who is unsure is more than welcome to stop by and ask.

    I have a good relationship with my kids. I always tell them to check my math, to ensure that I didn't accidentally deprive them of points they deserve. (If I somehow give them an extra point or two, it's no big deal... over the course of a trimester, those 3 points on one test will make no difference in their overall average anyway. But they DO make a difference to the kid.)
     
  17. msleep

    msleep Rookie

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    I can't wait till standards based grading will enter every school system. Then this type of problem with grading is gone.
     
  18. Special-t

    Special-t Enthusiast

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    Using the OPs example, I would give the student just a small point deduction in the "steps points" (I give points for steps and correct answer). I would write the correct method near the problem. I would take time to show the student the correct method.
     
  19. Aliceacc

    Aliceacc Multitudinous

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    Honestly, it isn't really a problem.

    To the best of my knowledge, the 4 of us here who teach secondary math pretty much agree. And the scale we all use aligns with the way NY State Regents exams have always been graded. (I've added in the red)

    "III. Appropriate Work
    Full-Credit Responses: The directions in the examination booklet for all the constructed-response questions state:
    “Clearly indicate the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.” The student has the responsibility of providing the correct answer and showing how that answer was obtained. The student must “construct” the response; the teacher should not have to search through a group of seemingly random calculations scribbled on the student paper to ascertain what method the student may have used.

    Responses With Errors: Rubrics that state “Appropriate work is shown, but…” are intended to be used with solutions that show an essentially complete response to the question but contain certain types of errors, whether computational, rounding, graphing, or conceptual. If the response is incomplete; i.e., an equation is written but not solved or an equation is solved but not all of the parts of the question are answered, appropriate work has not been shown. Other rubrics address incomplete responses.

    IV. Multiple Errors
    Computational Errors, Graphing Errors, and Rounding Errors: Each of these types of errors results in a 1-credit deduction. Any combination of two of these types of errors results in a 2-credit deduction. No more than 2 credits should be deducted for such mechanical errors in any response. The teacher must carefully review the student’s work to determine what errors were made and what type of errors they were.

    Conceptual Errors:
    A conceptual error involves a more serious lack of knowledge or procedure. Examples of conceptual errors include using the incorrect formula for the area of a figure, choosing the incorrect trigonometric function, or multiplying the exponents instead of adding them when multiplying terms with exponents. A response with one conceptual error can receive no more than half credit.

    If a response shows repeated occurrences of the same conceptual error, the student should not be penalized twice. If the same conceptual error is repeated in responses to other questions, credit should be deducted in each response.

    If a response shows two (or more) different major conceptual errors, it should be considered completely incorrect and
    receive no credit.

    If a response shows one conceptual error and one computational, graphing, or rounding error, the teacher must award credit that takes into account both errors; i.e., awarding half credit for the conceptual error and deducting 1 credit for each mechanical error (maximum of two deductions for mechanical errors)."

    From http://www.nysedregents.org/geometry/813/geom82013-rg.pdf
     
  20. 2ndTimeAround

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    Sep 22, 2013

    Not math, but when I taught chemistry, sometimes I did take off if they used the wrong method. If I was teaching dimensional analysis, I expected them to get the answers exactly as I taught them to. The method, not the answer, was what was important (and part of our standards).

    Students, parents and even admin, fought me on it. They all figured that if a student could do it in his head, all the better. But that isn't the point - the point is to use the method so later down the road when problems are more complicated, you'll be able to solve those.
     
  21. Aliceacc

    Aliceacc Multitudinous

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    Right. It's not about the answer. The answer shows that you've somehow managed to solve this one, solitary problem, a problem that I've made up.

    It's about the process. My job as a math teacher is to give you the tools to solve a variety of problems, as well as the tools to extrapolate that knowledge so you can solve other problems down the road.

    So if my Algebra I kids learn to use charts to organize info for a coin problem and a distance problem and a percent mixture problem, then hopefully they'll think to set up a similar chart when they're trying to determine which cell phone plan makes the most sense. Or at which point the Disney Dining Plan stops making sense for their family. (You KNEW I would work that in somewhere.) Or whether buying or leasing a car makes more sense for them, given the pecularities of their own lifestyle.

    It's not about the answer to one pretend problem. It's about developing the skills to solve real life problems down the road.
     
  22. DrBill

    DrBill Rookie

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    Hi,

    Assessment is a very complicated topic. You have to ask yourself what the question was measuring. If the student showed no evidence of learning what you wanted to measure, then you shouldn't give any credit for it as doing so would indicate some level of learning.

    Have you thought about grading more qualitatively? If you were to have a Learning Target that said, ""I can solve quadratic equations by using the zero product property."" and you were to grade on a rubric from i to 4, you wouldn't have this challenge.

    Dr. Bill
    PD Corner
     
  23. Aliceacc

    Aliceacc Multitudinous

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    Sep 26, 2013

    Sometimes the intanglibles enter into it as well.

    Over the course of this trimester, I will have given 5 full period tests and probably 15 quizzes, and will have checked at least 40 homeworks.

    Giving a kid one point on a test for getting the correct answer, even by the wrong method, will make no statistical difference in his average.

    Giving him a couple of points per test, assuming he's done absolutely nothing right but is a good guesser (and, no, I don't do multiple choice, so this is pretty unlikely) won't pull a 0 average to anywhere near passsing.

    But getting a 0% on a test will have a huge effect. The kid will be demoralized and will very likely shut down completely. Remember, as tall as they are, these are still kids. Zero sends a message like few other numbers do-- it says you are a complete and utter failure, incapable of doing anything right.

    Mathematically accurate or not, that's not a message I'm willing to send to any kid. So, yes, I'm generous with partial credit, because I believe that the process is the point. But I'm also unwilling to tie myself down to a rubric if it means that some 15 year old leaves my class feeling worthless.

    So, unless a kid leaves a test COMPLETELY blank, or is caught cheating, he's not receiving a zero on a test in my class. I will find SOMETHING he's done right and he will earn at least a few points. And if needed, I will use those few points as leverage to convince him that he is capable of doing much, much more.

    Yes, I teach math. But I also teach kids. And it's an important thing to remember. If they leave my class having only learned a tiny fraction of what I've taught, but knowing that they ARE capable of learning and of doing math, then I'll sleep just fine at night.
     

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