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Sometimes when assigning homework, it is possible that the homework can be found in some books or lecture notes, sometimes even referenced by yourself.

As long as the proofs and arguments there are good and/or students bring up their own thoughts about the question, there is nothing bad in grading it.

The problem comes up if there is a bigger part missing in reference book or if there is even something wrong there and students copy that without adding the missing parts (One time, a whole course with more than 80 students did exactly copy a solution which was solved in some lecture note with a contradiction proof, but the contradiction did only cover a small part of the statement. Only very few students got that.).

The question is now: How should one grade such solutions? If you do not give full credit, how can you explain that the students without making them angry (Since you gave that particular book as reference)?

The question is related to How to assign homework when answers are freely available or attainable online?.

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I've been given 0 points for "not doing it the way I was taught", and so have most students. When a prof gives you a book, and tells you to solve the problem the same way, you solve it the same way. It doesn't matter if it's adding apples and donkeys. –  Davor Apr 8 at 7:22
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"When a prof gives you a book, and tells you to solve the problem the same way, you solve it the same way." - That approach is so wrong and corrupting that I had to make an account on ME, and express myself. You should do it in a way you understand it, and make your though-process clear so its possible to retract your thoughts. (ofc that is my opinion). I also think you cannot take credits if someone follows the guides recommended by you, unless they were wrong. What is a poor solution in math? Why would you recommend poor materials? –  luk32 Apr 8 at 8:49
    
@luk32 Welcome to the site! I hope, this will not be your only comment! To answer your question: I am only the assistant for this lecture and my advisor gave reference to a few books and lecture notes in order to cover the topics. I made one question of which is was not aware that an answer of this question was written in one of these books, but very poorly solved (In my example, there was a big part missing). Normally, you do not look at every proof in given references, but at least if the book covers your topics and is well-written in general. –  Markus Klein Apr 8 at 8:55
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Not really an answer, but cure them of "proof by authority" by paying the price of a coffee to the first person reporting to you any error in the book reference or course materials, including proofs presented in lectures. Publish errata to all students with acknowledgement to the finder(s), so that everyone sees that errors are being found by their peers. You might even get the prof to refund you the ones that are his errors ;-) –  Steve Jessop May 6 at 18:23

3 Answers 3

up vote 16 down vote accepted

Students are used to other people being the source of truth.

Even in an algebra class, they will do something like this:

$(x + 3)^2 = x^2 + 9$

and then ask me if it is correct, or if it actually goes a different way. The implication is that I know the truth and they cannot know it without me. My goal then becomes the following: show the students that they can independently identify objective truths.

So, I think the answer here is the same as it is there: Regardless of what is printed in some book or another, the correctness of a proof is essentially an objective fact -- one that they must learn to measure themselves. This is a difficult point! The students may rebel and use the book as evidence that the truth is in fact subjective, determined by a semi-arbitrary grader. This is the underlying misunderstanding to dispel.

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Just in case any badly informed students come along this forum and think this sum is actually correct: it's not. The real answer is x² + 6x + 9. (a + b)² = a² + 2ab + b². –  Nate Kerkhofs Apr 8 at 11:03
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@NateKerkhofs The real answer is that it depends on the context. It is true in some and false in others :) –  Gamma Function Jun 22 at 0:49
    
@GammaFunction ....in what context is Nate's statement not true? –  Tutor Jun 22 at 2:50
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@Tutor In abstract algebra, there is a context where one might consider something in characteristic 2 or characteristic 3; essentially a setting in which arithmetic works and $2=0$ or $3=0$, in which the above equation is indeed correct. Of course, if a student asks you if this is really correct, you don't blather on about rings of positive characteristic... –  Mike Miller Jun 22 at 2:59
    
Good point Chris. I'll sometimes intentionally write down an incorrect step like that and ask them if it's correct. This seems to give them more confidence and, at the same time, makes it easier to start a conversation about their own misconceptions. –  Carlos Jun 25 at 1:47

Make clear that the "make sure the proof is correct" is part of the work to be done in the homework. If it is my proof, or yours, or from <famous textbook> that is wrong, the answer is wrong.

(Yes, need to emphasize that even the above cited authorities get it wrong sometimes).

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I'd like to comment on this question because I fully agree and I would to like add my $0.02. I think it is just a misunderstanding. IMO, it doesn't matter if solution is copied or not, it should be clear to student, that they have to understand the proof, and that you can check it. There is a big difference in wrong, and "poor" proof from what I understand. Student can always be asked to fill in the gaps if its a homework if its poor (especially if he followed a book), I don't see a problem. If its logically wrong, then he did not understand what he copied, and that would be bad. –  luk32 Apr 8 at 9:20

By recommending some book you implicitly acknowledge all of its contents (unless specified otherwise). In fact it would be similar if the student used a solution you presented, which happens to be wrong, but you only discovered the flaw when grading the exam. What would you do?

First, I would not penalize the student for copying the solution from the book, actually I would deal with it as if the student happen to write exactly the same solution by himself/herself. The reason is that the modern math is built upon previous results and reinventing the wheel is not a good strategy.

Then, there are three solutions I would consider:

  • Give full credit. The solution might be wrong, but you don't expect the students to recognize the difficulty (perhaps even the teacher missed it at first). One can give bonus points to those who did.
  • Give partial credit. The fact that some respectable author got it wrong is some indication that it might be a "reasonable mistake", that is, the approach could be mostly correct but for some subtlety that is non-intuitive and hard to spot. Partial credit is always tricky, though.
  • Grade it like everything else (perhaps no credit). Wrong solution is not a valid solution independent of where it comes from. If the students think the solution is good enough to copy it, they are wrong and should be graded accordingly.

My preferred one is the third: in math the meaning of authority is slightly different than in other areas and students should understand that nobody is exempt from following only valid inferences. On the other hand, it would be weird to enforce this rule unless you told the students about it.

Partial credit is the most common solution from my experience. Many professors grade not only what was written down, but also what kind of understanding the work implies. The solution might be incorrect, but the intuition behind it might be still valid. However, it is inherently hard to grade understanding and what is obvious from one perspective might be difficult from another point of view. The fact that the book's author got it wrong suggests that there is some other intuition that works just as good as yours (e.g. the rest of the book is great), but handles this particular case badly. Therefore, it could still seem like an obvious mistake to me, but I might opt to give some more points nevertheless.

Rarely, but it happens, you may want to give full credit. I don't like it, but I see why someone might want to use this solution. One case is when you don't want to bother students with subtleties, for example

  • in some engineer classes, where theory is secondary at best, you could accept solutions that miss the fact that some matrix could be singular in a problem where a random distortion of input data fixes the problem;
  • in a discrete math course, some series-related theorems work only with proper convergence arguments, however, appropriate techniques/formalizations might be too hard or not that important (e.g. the topic wasn't covered in depth); a correct, formal solution would be to guess the result using the incorrect derivation, and then proceed by induction (or whatever), but some deem such a level of scrutiny unnecessary.

Another case is when the problem set wasn't tested enough. There was an exam once in my student times where the lecturers did a mistake about what works and what does not. In result, one task came out much, much harder than it was meant to be. Most students missed the subtlety (i.e. used the same solution that the lecturers thought it worked), others did notice and presented a counterexample. There was an announcement and both types were accepted with a perfect score.

I hope this helps $\ddot\smile$

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Thank you for your good answer! I think, your last point mentioned is completely okay since it was in an exam which should only asked what you learned; but for homework, you should learn something new and if you copy a wrong solution, then this should be made clear in the hope that you will do it better next time. –  Markus Klein Apr 8 at 6:28

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