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Suppose I'm teaching out of a textbook and there's a question which has a fairly-clear intended answer, but is flawed in some other way. Do I point out the flaw to the students? If yes: how do I answer the question "what if this shows up in the exam" (the exam is not set or graded by me)?

As a notional example:

Q: If the ratio of the sides of a triangle is 1:3:5 and its perimeter is 63cm, find the length of the longest side.

It's pretty clear the desired answer is 35cm. However, the sum of any two sides of a triangle must be larger than the third side, which is not the case here, and the triangle is impossible.

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    @Daniel I think the point is that the concrete example would be understandable to less users here. (Say, if it were a textbook on algebraic quantum field theory.) Commented Sep 11 at 14:11
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    Just as an aside, the fact that 35cm is the desired or intended answer is strictly irrelevant in your example. That answer remains incorrect. Commented Sep 11 at 16:40
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    Assigning "Find the flaw with the following question" can be a useful alternative to pointing it out directly. Commented Sep 11 at 17:17
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    Such a triangle can exist on a sphere whose radius is not too large. Commented Sep 12 at 6:53
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    @user151413 maybe it's non-Euclidian triangle. Commented Sep 12 at 14:07

7 Answers 7

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Yes, you point it out.

(Unless you have a mean streak, and want your students to be able to work with impossible demands, which is quite prevalent in the workplace. But seriously, even for me as a proponent of realistic teaching, that would a bit much.)

how do I answer the question "what if this shows up in the exam"

Like this:

If you are set impossible questions and waste time on them, you will have very good grounds on which to appeal the result, and whoever set this question will have some explaining to do, both to you and to the university. Which is why we will do our very best not to set impossible questions.

But of course, stuff can happen. So if you do encounter a question that appears impossible to you, then please do X.

X here can be any of "point this out to a proctor", "note that the question is impossible on the answer sheet", "simply skip the question", and should be discussed beforehand with whoever sets the exam and whoever grades the exam.

Kudos to you for thinking about this now and not when this happens. Now go and talk to those people.

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    "Unless [you] want your students to be able to work with impossible demands" I experienced a similar scenario in middle school where one of the questions on the homework that had a seemingly obvious answer was based on an impossible premise. But when I pointed this out to the teacher, she gave me a very knowing look and said nothing. Sometimes teachers include trick questions just to see who is actually paying attention. Commented Sep 11 at 19:25
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    X might ought to be, "First, give what you think is the most reasonable answer, assuming you have time." It's more common for students to mistakenly believe a question is impossible than it is for a problem to actually be incorrect, in my experience, and if they skip the question they have no recourse if the question turns out to be well-formed after all. Commented Sep 11 at 20:11
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    The whole part about appealing and having some explaining to do seems wildly excessive to me, unless you are trying to turn the students into entitled brats. When filing my taxes in the US years ago, the instructions implied to divide 0 by 0, it was more useful to set the result to 0 than to try and get someone at the IRS fired. Sure, try to avoid asking nonsensical questions (and possibly adapt the scoring if you notice it too late), but students should be ready for them (point out the mistake if they see it, give the most sensible answer, don't waste too long on any question). Commented Sep 12 at 5:50
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Do you point it out? Yes. Absolutely. Although the authors of the textbook were almost surely just sloppy, this is actually a good lesson for students: THINK. Think outside the box. Think about the whole problem.

It's also a lesson that textbooks can contain errors. Many years ago I edited a high school algebra book; slightly more recently (but still quite a while ago) I edited a test guide for the Statistics AP exam. Both had numerous errors. I hope they had fewer when I was done, but I doubt I eliminated them all.

What if this shows up on the exam? Assuming you will be writing the exam you say "I will try hard not to put impossible questions on the exam, but if I do, and you point it out, you get extra credit.

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    Wrong assumption: "(the exam is not set or graded by me)" Commented Sep 13 at 6:14
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Don't use that problem! Don't waste students' time with a problem that is flawed.

Or, fix the problem and assign the fixed version of the problem.

If you're forced to use that problem by someone else who is setting curriculum, talk to whoever is forcing you. Or just ignore the command and teach it the way it should be. At the University level, instructors typically have considerable autonomy, so I would expect that you can skip that problem and do something reasonable.

We could have a conversation about the entire concept of teaching out of a textbook. Textbooks are intended to be aids to help you, not rulebooks that you must slavishly follow.

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  • In some systems textbooks ARE rulebooks that you must slavishly follow. Commented Sep 13 at 12:50
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How should one handle a flawed question in a textbook?

If at all possible, you should not assign questions that don't make sense. And if you are aware of textbook problems that don't make sense, then sure, warn your students about them (even if you don't assign the problem - students can still decide to work on the problem just because it's in the textbook and end up getting confused, wasting their time, and/or developing misconceptions about the material).

If you can fix the flawed problem by telling the students to change some of the problem parameters (for example changing the 1:3:5 ratios in your triangle example to something else that avoids the impossibility issue), that could certainly help your students as well. If you fix the problem, it's fine to assign the corrected version of course.

the exam is not set or graded by me

In that case, you should point out the issue to the person who does assign the problems. Surely they would see that it's a bad idea to assign such a problem without correcting it first.

If the person in charge refuses to correct the flawed problem or to not assign it, you will have joined the ranks of people around the world with unreasonable bosses who make bad decisions - a club that much of humanity belongs to. I suppose at that point you might decide to get subversive and explain the issue to your students directly. I hope that doesn't get you in any trouble (it wouldn't at my institution, but they also don't dictate to me what problems to assign, so I am a bit baffled by the situation you're describing).

how do I answer the question "what if this shows up in the exam"?

"I'll speak to [person in charge] to try to make sure it doesn't, but if it does, complain to [person in charge/committee in charge of correcting abusive grading practices/etc]."

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Regarding...

what if this shows up in the exam

... I think it is a good idea to say a few words about general handling of flawed questions in advance. If it were my exam and I'd also be responsible for marking, I'd say that in such a case (assuming I realise afterwards that it is flawed) I'd be very generous with marking this question, and particularly I'd give full marks to the intended solution as well as to students pointing out the flaw in the question. In case students go wrong I'd ask myself whether I believe this is due to the flaw in the question, in which case I'd also be generous. (It of course depends on the exact question to what extent the originally expected solution still makes some sense and can be found despite the flaw.)

I prefer students to have some information like this in advance to just stop them from panicking if this kind of thing happens. The general attitude should be that this shouldn't be to their disadvantage (even though the truth is that it may be hard to guarantee this 100% as I may not realise how some people lose time because of this).

One could also take a different stance and say that it's part of the examination to figure out whether a question may be flawed and then full marks are given if this is realised whereas people who hand in a solution that seems like they didn't understand what's wrong will not win full marks (although they still can win marks for otherwise good work there). This should come with a declaration that we try to make sure that no such thing happens but we're not perfect. I think that this is legitimate, but it's not my personal preference, because I think that exams are psychologically critical for many students, and I'd like them to only worry about the correctness of their own work, not mine.

Now you write:

the exam is not set or graded by me

I think it'd be worthwhile to ask the person(s) responsible for exam setting and marking to communicate something general about this, so I recommend to tell the students "I'll ask the boss" (or whoever;-).

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Assuming this is math or a few other fields, rather than point out the flawed question, I would tell the students that one of the exercises in chapter x is flawed and bonus points will be given to the first person to find it and explain why.

That assumes I know about it, of course. If a student were to point it out to me, I'd probably do a close look at the questions and if several are found, make a general announcement. And choose a different book in the future.

Students interested in the points or the challenge will take a look, but others will be wary of the questions. If there are too many questions, I'd narrow it a bit: one of the odd numbered exercises.

Like others answering here, I'd suggest students point out any errors in the logic of the questions, and giving points for doing so. I'd also probably make an announcement of the fact if anyone alerts me.

OTOH, my practice was often to put a very hard question on the exam and tell the students of its existence, but not which one. I'd also encourage them not to do the questions in order, but to look for the easy ones first so as not to lose easy points when stalled.

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  1. Don't assign the question.
  2. Tell students to avoid it. Only explain why if asked.
  3. Reconsider using that textbook next time.
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    If you would rule out using textbooks which contain some flawed problem, you would be in trouble. Commented Sep 14 at 8:51

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