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I see a lot of students who repeat the whole question (i.e., before starting with anything which has some content, they write down all assumptions, claims, etc.) in their answers in homework or exams. At least in exams, I have the feeling that they are losing time with this.

  • Is there an explanation why students do so?
  • Are there any (psychological) advantages why this is done?
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  • $\begingroup$ It depends. Do you mean that they copy "1) $3\int x^2dx$"? Or a more lengthy question? $\endgroup$
    – user1729
    Mar 28, 2014 at 10:03
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    $\begingroup$ I once had a student copy out their entire linear algebra question paper onto their question book. It was presented beautifully and written in very neat and tidy handwriting. However, they didn't attempt to answer anything! They scored zero. $\endgroup$
    – user1729
    Mar 28, 2014 at 10:04
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    $\begingroup$ @user1729 I mean more lengthy questions. In an exam a few days ago I've seen some people who have written down more than one page (including hints, etc.), although the solution was only a few lines long. $\endgroup$
    – Markus Klein
    Mar 28, 2014 at 10:09
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    $\begingroup$ From my experience in highschool, there was a general culture of you can't be marked down for writing something not pertinent to the question, but there's a chance it could gain you marks. This often lead to students who didn't know how to tackle a problem just writing down the problem statement, writing down all formulae/theorems they know and generally just regurgitating everything they could remember from revision onto their exam paper in the hope that one of the shots hit the target. $\endgroup$
    – Dan Rust
    Mar 28, 2014 at 13:16
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    $\begingroup$ Daniel Rust -- you should flesh out your comment here as an answer! It would be a good answer. $\endgroup$
    – Chris Cunningham
    Mar 28, 2014 at 15:21

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In order to cultivate a greater appreciation for precision in one's mathematical statements, I ask my students not to copy the problem question, but rather to transform it from a question or problem statement into a theorem statement, which they then prove or solve.

For example, if the quiz question is

Is the ring $\mathbb{Z}_2\oplus \mathbb{Z}_3$ an integral domain?

Then the student is expected to write something like:

Theorem. The ring $\mathbb{Z}_2\oplus \mathbb{Z}_3$ is not an integral domain.

Proof. This ring is not an integral domain, because it has zero divisors, namely, ...

In a lower-level course, I ask my students to transform the question into a positive assertion of what they will do.

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    $\begingroup$ This is a very nice idea. $\endgroup$
    – Jon Bannon
    Mar 28, 2014 at 12:50
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Personally I encourage students to write answers that make sense as a self-contained piece of writing, because I think that that is a valuable skill. Certainly it is required when writing about mathematics in any context other than homework or exams. This generally means that they need to reproduce some or all of the content of the question, possibly phrased in a different way. Simply copying the question verbatim is not the best way, however.

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I recommend this to most people I have helped or tutored over the past years for a few reasons.

Problems are complicated when you don't understand them.

Basic problems are not as easily digestible to students, especially those who are less confident.

I have found people consistently make mistakes based on the problem definitions even if they are explicitly given and as a result I strongly recommend people to write them out. Even if it's repeating information.

This is true even for simple problems. As problems get more complicated this is even more important.

People don't read well.

I eventually tired of people making mistakes resulting from simply misreading or misinterpreting assumptions or even given information.

Forcing them to write this down at least somewhat helps, though, of course there's always opportunity for stupid mistakes.

It can be part of problem solving.

I can't count the number of times in the past I've had no clue how to approach a problem myself, but followed my normal approach of writing the problem down and as I was basically rewriting it, ended up with significant insight into how to solve the problem.

This is also the "if I write down lots of stuff it'll look like I tried" perspective, though, this is more "student led" than something I ever recommend..

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I can't really comment on the psychological reasons, but I can say from personal experience that some students have practical reasons for doing so: by copying the problem from the textbook or question sheet onto work paper, this allows directing focus entirely to the paper the problem is being solved on rather than having to switch between the two to verify parts of the question. However, in my case that usually also involved removing all the "extra" stuff in the question if present and reducing it to just the parts necessary to solve the problem, or at least summarizing the question in a more notational form, and I usually don't do that when the questions are already provided on the answer paper and no scratch paper is provided, so I suppose this might not be all that applicable to your question given that I'm probably not the sort of student you're more interested in for this.

Thinking back, I believe I developed that habit due to having had teachers in the past who required questions to be copied to homework/test papers (probably for the benefit of the grader[s], at least in part), wanting to keep the amount copied to a minimum, and later realizing that it did actually provide some benefit for me (and for graders) even in the minimal form; thus, I continued to do so even when it was not explicitly required.

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I'm going to hazard a guess - For 2 column geometry proofs, the repetition of every 'given' is required. When working with students on their Geo, it struck me that many times, the 'givens' are 2/3 of the solution, just a couple steps to finish the proof.

For algebra, the question is usually brief enough, it makes sense to re-write it on the answer sheet.

These two examples set the stage for a continuation of the process of re-write.

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