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I'm looking for a clear, definitive answer to the following question: Is taking someone else's writing, and changing some of the words, inherently plagiarism?

I find resources that describe plagiarism are usually a bit vague around this issue. For example, one commonly-quoted book says this (Pechenik, 2001, p. 10):

Don’t plagiarize. Express your own thoughts in your own words... Note, too, that simply changing a few words here and there, or changing the order of a few words in a sentence or paragraph, is still plagiarism. Plagiarism is one of the most serious crimes in academia.

Now, the fact that this passage refers to changing or moving "a few words" leaves open the question of whether changing or moving more words, or many words, would possibly be not-plagiarism. Is there any threshold at which changing words becomes not-plagiarism? Possibly all of them?

The practical concern I have is that recently I've gotten a high frequency of students I've caught for plagiarizing in my courses (around half) saying something like, "Ah yes, when I took that file I didn't change enough of the words because I was rushed for time. I'm sorry, next time I'll change more of the words."

Ultimately I'm wondering if the best response to that is, "That would still be plagiarism [even if you changed all of the words]!", or if the response needs to be something different and more complex. (I find that for such students with possible language problems, more complicated responses are likely to be disregarded, so I'm looking for a minimalist communication in these situations.)

The best answer will not go into discussions of practical issues of detecting plagiarism. A reference to some authoritative source on this issue would be a value-add.

It may be helpful to note that "plagiarism" is emphasized here because it's central to my institutions' (and others') academic integrity definitions and enforcement mechanisms. In our case, "Copying another person’s actual words or images..." is the primary (but not the only) example of what counts as plagiarism.

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    Unfortunately, I think that many students are often actually taught that copying and plagiarism are the same thing. Also, don't expect students to grok plagiarism (or anything else) as if it were a genetic trait of humans.
    – Buffy
    Jan 10 at 14:26
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    For the specific context of responding to that student, I'd respond with: "It's not about changing words, it's about the contribution you put into this project/paper/course. I don't want your biggest contribution to be simply changing words. This course is about ____, so you can contribute synthesis or novel idea about this course, but not about knowing how to paraphrase."
    – justhalf
    Jan 11 at 6:33
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    Do not use the term "plagiarism" in a teaching context at all. As many answers below point out, plagiarism is using ideas without attribution, which is completely irrelevant in a teaching situation: it is customary to use ideas taught in the course or written in a textbook without attribution. (Imagine having to attribute all "ideas" in a solution to a standard math homework/exam problem.) What's more, few lecturers/textbooks care about proper attribution in the first place.
    – Kostya_I
    Jan 11 at 8:31
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    What you are forbidding/discouraging is not "plagiarism", but specific ways of working on assignments: copying from elsewhere verbatim, paraphrasing from elsewhere, etc. E.g. I advise students that they are allowed to read any sources, but that they should close them as soon as they start writing the assignment.
    – Kostya_I
    Jan 11 at 8:39
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    @Kostya_I: Unfortunately, that is pretty much the opposite of our institution's (and others') definition of plagiarism, and central use of that term in its academic-integrity policy and enforcement mechanisms. I've added that detail to the question at this time. Jan 11 at 14:52

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Is taking someone else's writing, and changing some of the words, inherently plagiarism?

The most concise, clear answer I can think of is the following: Plagiarism is about protecting ideas, not words; however, the way something is written is often a (protected) idea. The writing's structure and organization, the details that are included or excluded, the transitions, the figures, the references -- all of this may be protected intellectual property, and none of this is addressed by simply substituting some words for others.

Hence, students are wrong when they believe that all they have to do is "change a few of the words" -- even if one does not steal the words, they are still stealing the writing, which is much more than just word choice. (On the other hand, detecting plagiarism is much harder when these substitutions are made...and many students honestly believe that plagiarism is defined by what TurnItIn can detect).

So I'd love to say the answer to your question is an unambiguous "yes" -- but consider this sentence:

Elementary particles comprise quarks, leptons, and bosons.

Many students mistakenly believe that they need to make some trivial modification to this sentence to avoid plagiarism. But this sentence contains no "novel ideas" -- certainly not in the content, but not really in the writing either; there are only so many reasonable ways in which one can state this fact. Indeed, it is likely others have published this exact sentence before. Hence, taking this sentence without attribution (with or without having changed some of the words) would probably not be inherently plagiarism.

Some other notes:

  • What about citations? Adding a citation allows you to use someone else's "content" -- but it does not entitle you to steal their writing (and remember, writing is more than just words...so citation + changing words is not enough either).
  • It's true that plagiarism is not always completely clear. Even at the best of times, "our own ideas" are heavily influenced by the other things we've read.
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    'many students honestly believe that plagiarism is defined by what TurnItIn can detect' AIUI, they don't just spontaneously believe that: they're encouraged to believe it by well-funded social media marketing campaigns: not from Turnitin LLC itself, but from essay mills seeking to legitimize their products. Jan 10 at 10:05
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    Your boldfaced passage leaves me very confused ("Plagiarism is about protecting ideas, not words"). My institution's (CUNY) formal policy defines plagiarism primarily as this: "Copying another person’s actual words...". A secondary bullet point refers to the taking-ideas issue. (Link) In your estimation, is the primary CUNY definition simply wrong? Jan 10 at 14:46
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    The policy you quote states: "Plagiarism is the act of presenting another person’s ideas, research or writing as your own." This is consistent with my bold passage -- plagiarism protects ideas, and both "research" and "writing" count as ideas. "Words" by themselves may or may not count as ideas -- some words (like poetry) certainly are, while others (like the quark sentence) probably are not. The key point is that plagiarism is much broader than just taking the "actual words" (though I agree that stealing the actual words is the most egregious, and most detectable, form of plagiarism).
    – cag51
    Jan 10 at 15:32
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    "Plagiarism is about protecting ideas, not words": Do you mean antiplagiarism is about protecting ideas?
    – Massimo Ortolano
    Jan 10 at 15:56
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    Ha, thanks, never considered that reading. Strictly speaking, yes, I suppose "antiplagiarism" would be more technically correct, or something like "The reason plagiarism is disallowed is to protect ideas, not words." But both of those sound a little strange to me; will try to think of a less awkward way to improve the wording.
    – cag51
    Jan 10 at 16:15
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Students sometimes believe or claim to believe that plagiarism is some highly technical, perplexing concept. While it is important to clarify what plagiarism is and is not to the student, in an actual discussion with a student who believes that they should have "changed more words", I find it helpful to start from an ethical principle that the student will find it much more difficult to misunderstand or claim to misunderstand, namely to give credit where credit is due.

Here is a concrete suggestion. One can get the conversation going by asking whether the student found it helpful to have the relevant passage as a starting point. Make the distinction between using general ideas found in some text and using an actual passage in some book or article as a starting point for one's own writing. This way of putting it makes the number of words they changed irrelevant. Even if they change every single word, the point is whether or not the specific writing in the source passage was substantially used in the writing process, whatever the end result of this process.

If they answer negatively, you can express skepticism about their answer, since they did in fact actively choose to use it as a starting point for their own writing. If they did find the work that the author of the original passage helpful in composing their own writing, you can ask them whether they believe that the original author is due some credit for that. Whatever they answer, explain that owe some credit to the original author. Then you can get into a discussion of what plagiarism is or is not, but I believe that grounding it in a familiar ethical principle will help. (Confession: I myself find it useful to think in terms of fair vs. unfair use instead of plagiarism vs. not plagiarism, and to use the term "plagiarism" primarily when ill intent is clear.)

Another approach if they say that they will "change more words" next time is to paraphrase this back to them as: I will change more words so that I can avoid citing source X. Then ask them why they wish to avoid citing source X.

If you want to wax philosophical, you can then explain that science only works as a cumulative enterprise which encourages people to stand on the shoulders of giants and ordinary mortals alike. This cannot work unless it is a win–win situation for the people involved. Other people's work allows you to see further and write better, and conversely, they benefit from having their share in your work acknowledged.

(The point raised by Massimo Ortolano is also important to get across to the student.)

Edit: the other answers focus on using other people's ideas, which is justified but potentially a bit nebulous. You can also choose to focus on using other people's work instead, which I find a bit more concrete in this case: they are building on the work that some other person has already put into composing the passage in question.

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    These kinds of "give credit" and "use citations properly" suggestions seem very tangential to the kinds of cases I'm dealing with. The kinds of assignments I'm dealing with are fairly short (one-page) scientific problem-solving, and looking up and copying answers to them is entirely outside the scope of the assignment. I find students don't think plagiarism is a perplexing concept; they are confident it involves changing more words in a submitted answer. Unlikely this will be the selected answer. Jan 11 at 15:02
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    @DanielR.Collins You might want to clarify that in your question. I think the question with that clarification is less about plagiarism and more about bad assignments and/or plain old cheating. Even a third grader can be expected to show work for "2*12=24" without copying someone else's, even though the visible outcome is probably exactly the same as if they had copied. Jan 11 at 15:50
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    Fair enough, this is not the kind of assignment that I had in mind when writing the answer. Jan 11 at 17:14
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    @DanielR.Collins Adam is correct about what plagiarism is, but that doesn't mean that plagiarism is the only problem an assignment could have. If a student copied an entire book for an assignment, and cited it properly, they have not plagiarized. They arguably also have not done the assignment, since they weren't the ones who wrote the answer, so you'd probably be justified in giving them a zero grade. But there wouldn't be grounds to bring them in front of an academic misconduct board, since there was no dishonesty.
    – Ray
    Jan 11 at 22:07
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The clear, definitive answer to your question

Is taking someone else's writing, and changing some of the words, inherently plagiarism?

Is YES, and you need to go no further than a dictionary.

the practice of taking someone else's work or ideas and passing them off as one's own.

The moment your students (or anyone, for that matter) tries to solve a writing task by looking for what someone else has written and then trying to include it in their work as their own, it becomes plagiarism no matter how many words they can change; it's the action of putting/trying to put someone else's work into theirs what constitutes it.

The thing is, the rest of the body of your question shifts it to both "how can I tell my students/make them understand that what they do is plagiarism?" and "am I wrong by assuming that what my students are doing is plagiarism?".

The latter is easier to answer: no, you're not wrong. The former, though, is a bit trickier.

Your students already believe that plagiarism is about what can be detected as such, and not what they're intending to do. This probably isn't on purpose - they might not be "evil" students, merely misled. You need to make them understand that their offense is not "not changing enough words", it is "thinking of taking the writing of someone else without proper acknowledgment".

Maybe you can make it clear by establishing it with a simple "do/don't" rule:

DO: write your own thoughts and conclusions, and use citations from other authors or written material to support them.

DON'T: take the writing of other authors/material and put it in your work as yours, neither by copying it as is nor by changing or paraphrasing it.

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Looking at this definition of Oxford University, plagiarism is using other people's ideas without acknowledging them. Under this definition, even if you were to change all the words, or rewriting the whole thing in your own words, you would still commit plagiarism, as long as you don't give credit to the original source where you took the idea from.

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    Formally correct, but note that a student accused of plagiarizing the underlying ideas can deploy the "common knowledge" defence, whereas a student accused of plagiarizing the particular wording can't. Jan 10 at 10:14
  • Admittedly, the linked page says "work or ideas" -- not just ideas alone. The first two bullet-point cases under Forms of Plagiarism are (1) "Verbatim (word for word) quotation...", and (2) "Cutting and pasting from the Internet..." This is the same priority seen in my institution's policy, too. Jan 10 at 14:49
  • @DanielHatton that's precisely why this concise answer is so important. What the students seem to be worried about is not so much what plagiarism is but what gets them caught.
    – henning
    Jan 11 at 9:16
  • Relativity was not my idea, but when I talk or write about it, I do not want to keep having to cite the many men that made it possible.
    – Tvde1
    Jan 11 at 9:53
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    You changed a very important word when quoting that definition: "Plagiarism is presenting someone else’s work or ideas as your own." Not using but presenting as your own. This is paramount. There are many ways to use other people's ideas, work and research and most of them are not only OK but very desirable. Presenting as if it was your own is the problem.
    – Gábor
    Jan 11 at 10:54
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Changing a few words is the worst form of plagiarism. It's basically proof the student knew it was wrong and is trying to hide it (I saw it most often with students copying from a friend's assignment, but same idea). "I'm sorry I didn't change more words" is really shorthand for "I know this class doesn't matter and you don't care. Let me go and I'll cheat better next time so you can pretend everything is fine".

There are two reasons we care about plagiarism. One is so our graduates don't do it. A few years ago an influencer (Rachel Hollis) posted "still...I RISE" without saying it was from Maya Angelou's "And still I rise". She got ripped a new one and never recovered. And she changed almost half of it! If you have to write an original article and start by rewriting someone else's, people go nuts. Here's one about a fired student reporter from my Alma Mater "Tibbs ran an editorial that was about to be published through a plagiarism checker: 71 percent." Strangely, the article doesn't mention whether 29% changes were enough -- apparently copying with any number of changes is fireable plagiarism. Huh.

The other reason we care about plagiarism is that the assignments are meant to show what you know. Being able to turn it into your own words is the proof you understood something. If you just use an internet search and a thesaurus (also on the internet), that proves nothing, so is worth 0 points, and is also lying. "I wrote this" means you thought of all the words.

For dealing with it, one fun thing is to talk to other students. I've found that most fully understand doing your own work vs. copying. And they get seriously angry if they think someone is getting away with messing up the curve and the school's reputation by cheating. Getting a faceful of "tell me you're not going to fall for their bullsh*t and let them pass" may be helpful. For a real earful, also tell the student "but they changed a lot of the words".

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    "It's basically proof the student knew it was wrong and is trying to hide it" Or they honestly didn't understand what "plagiarism" means. Jan 11 at 5:52
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I don't think there can be a clear definition. The point is whether "changing a few words here and there" meets the learning objectives of the assignment. If not, then it is trying to pass off the the content of the passage that does meet the learning objectives as being their own work and ought to be viewed as plagiarism.

Using a thesaurus or grammar checker to paraphrase the passage probably does not demonstrate any understanding of the topic in addition to the choice of passage. So being able to choose a suitable passage is all that the student deserves marks for (which probably isn't very much). What value have they added by paraphrasing? What understanding have they demonstrated?

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  • Separate from the academic grade-credit issues, we also need to think about how this interfaces with the school's mechanisms for academic-integrity enforcement actions around plagiarism. So I think the emphasis here is at best half of the issue. Jan 11 at 15:07
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    I think this is a useful answer in explaining it to a student though in a way they can understand. Why is plagiarism bad in a university assignment? Well firstly, it is bad because in the "real world" passing off someone else's ideas as your own is one of the worst kinds of misconduct, but also 2) because if you copy someone elses work, you don't demonstrate understanding (an academic, rather than disciplinary issue), but it you change the words, you are trying to hide you lack of understanding (a disciplinary issue). Jan 12 at 10:48
  • @IanSudbery exactly, I suspect some plagiarism cases are because the student has come from an educational culture where paraphrasing wikipedia etc. achieves good marks, and they don't realise that they are not meeting the learning aims, or that there is anything wrong with it. Jan 12 at 11:51
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First, at the end of the day, in a course setting, plagiarism—or the acceptable level thereof—is what the professor decides it to be.

But I think that instead of concentrating on the amount of words changed, the key point that needs to be addressed with the students is another: if you have to read and change the words to write your essay, it means that you didn't understand the concepts enough to make use of them and, consequently, to pass the exam.

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    "First, at the end of the day, in a course setting, plagiarism—or the acceptable level thereof—is what the professor decides it to be." No, it's not Plagiarism isn't just an academic issue, it's a disciplinary one. Jan 11 at 5:42
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    @Acccumulation Yes, but it's the professor who decides whether to trigger a disciplinary action or not, according to their judgment. So, it's what the professor decides it to be.
    – Massimo Ortolano
    Jan 11 at 6:35
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    If they aren't using a standard definition, their charge will not be upheld, and making charges based on idiosyncratic definitions is misconduct. Jan 11 at 6:36
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    @Acccumulation I'm not speaking of idiosyncratic definitions.
    – Massimo Ortolano
    Jan 11 at 6:39
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Yes, this is a form of plagiarism called close copying.

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The easiest thing to tell your students is this:

If you use someone else's work, cite them. If you don't, you're committing plagiarism.

When this issue comes up in undergraduate work, it almost inevitably comes down to intellectual laziness. The student in not focused on school; s'he wants to slide through to a passing grade with minimal thought and effort, because s'he has other concerns: social life and dating, activism, emotional issues or anxiety, etc. These other concerns are natural and important — we all go through a lot of crap in that age-range — but part of the job is encouraging students to learn focus and balance. You're not doing them any favors by being overly lenient.

If I were in your shoes, I'd look them in the eye and tell them that I understand (because I really do), but that the behavior isn't acceptable. They need to step up. I'd give them a choice between a zero on the assignment, or a chance to rewrite the paper in a way that convinces me they understand the material. And I'd let them know I'd be reading the revised paper extra carefully. If you can find a way to break the myopic fixation on grades and get them to focus on acquiring knowledge, this problem should solve itself.

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Types of Plagiarism

It often helps to break down plagiarism into different types. That's what Harvard does, for example, breaking it down into six kinds. A lot of other universities use the same or similar categories. The beginning of the course is the best time to (re-)explain what plagiarism is (ideally quoting your school's own policies) to hopefully prevent it before it happens.

If a student points out they didn't use the exact same words as the original author, you can point out that they are referring to only a single type of plagiarism (usually called verbatim plagiarism). The type of plagiarism you're seeing where they "didn't change enough words" is called either inadequate paraphrase (the wording is too similar) or uncited paraphrase (paraphrased without citation), or both.

The key is that it's not plagiarism if they paraphrased completely (changing enough of the words and wording) and cited their source. And if they did both but they weren't allowed to consult with sources, that's a violation of academic integrity (but not plagiarism).

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  • The last para about citing sources seems odd. The problem was that an original assignment was copied, right? That makes it sound like they could include: "This assignment was copied from [link] and you can see I made 15% cosmetic changes", and get an A (or maybe a B with a note about better places to copy from?) Jan 11 at 16:44
  • @OwenReynolds "15% cosmetic changes" still sounds like inadequate paraphrase. The last sentence of my answer was intended to address points like solo assignments that use other students' work (similar was mentioned in another answer) or anything where the student used sources that weren't allowed (e.g. quoting the internet when only the textbook was allowed during a test).
    – Laurel
    Jan 11 at 22:25
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From my experience, this is taught by high school teachers because they, themselves, do not understand plagiarism; at least, in the US. I wouldn't blame the students as they were never taught what any of this means: they were taught they have to produce the work required, and if they don't produce the work required, they cannot continue and will fail the class and are not given any sort of out or alternative path.

This is a version of Goodhart's Law ("When a measure becomes a target, it ceases to be a good measure") in effect; so many words are required in that assignment, where they come from doesn't really matter. On top of this, they are taught that referencing anybody's work (while simultaneously teaching them how to cite work and what citing means) is wrong: if you cite too many works, teachers will happily shave points off your grade as if you had done something wrong.

Sometimes an argument is complex and requires citing a lot of previous work, and all your core contribution is providing the glue for a bunch of cites. In science, this could be the form of a meta-study and all you did was pull your conclusions out of a wider body of work that no single cited paper represents, and it's entirely possible your paper just concludes that multiple papers agree and reinforce each other and finding that out was your contribution to science because no one else ever wrote this.

Citing other people's work is not plagiarism, citing other people's work and paraphrasing it (without changing the meaning) is not plagiarism. Copying it verbatim without cite is plagiarism, paraphrasing without citing and without adding anything meaningful to the new version is plagiarism. This is commonly not taught to students, so don't blame them, just try to teach them.

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Regardless of whether it is plagiarism, think about the context: if a student does this in an assessment then all they are demonstrating is the ability to use a thesaurus. Assuming the goal is not to assess the student's ability to use a thesaurus, any coursework demonstrating only that ability deserves a very low mark.

This follows regardless of whether you call it "plagiarism". That matters if you are deciding whether to put the student through the institution's procedure for academic misconduct. I would do this if the student failed to cite the source they had mangled, and not if they had cited it properly. But either way, "work" done this way gets a very low mark because it deserves one.

What I tell students is this:

The ideas are supposed to go from the textbook (or whatever other source) into your head, and from your head into your coursework. If the ideas are going straight from the textbook into your coursework, without going via your head, then you are missing the point.

The problem is not that the work they submitted is "too similar" to the source material, it's that the process by which they are working does not and cannot lead to useful, meaningful learning. That is true whether or not the process is called "plagiarism", so I'll leave that question to the philosophers.

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Yes.

As a student, many institutions provide access to plagiarism checkers, which highlight text that may be dubious.

I used a small paperback version called APA: the Easy Way, my father had once shown me a similar compact Chicago Style Manual.

Here is a link to Worldcat's list of libraries around Washington DC that have a copy of the first one:

https://www.worldcat.org/title/apa-the-easy-way/oclc/1183823482&referer=brief_results

These work, but you need to read and refer to them.

As a teacher, see if your institution offers a plagiarism checker (turnitin, for example https://www.youtube.com/channel/UCG9mtsMkQaDDq3PSxa5zMEA). These allow you to show students exactly how to check themselves and are worth some class time to teach them what's expected, what's accepted, and what isn't.

They also lighten the load for submissions, grading and (in the case of the one I mentioned above) designing assessments.

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The key concept of plagiarism is presenting someone else's work as your own. Deception is central to it. If you copy a passage verbatim, that's not plagiarism if you openly declare it to be a quote. It might be copyright violation, and handing in a paper that consists of nothing but direct quotes is unlikely to receive much credit, but it's not plagiarism.

Where it gets confusing is that if you're a student, obviously you're not doing your own primary research. If you write that most of Napoleon's troops in the Russian invasion died, then (unless you're in a really advance program, maybe) nobody's going to come away thinking that you pored through historical record calculating how many the initial and final troop numbers were. Obviously, you looked up someone else's work. So using general facts from other people isn't deceptive (but that doesn't mean you shouldn't cite them!).

Using other people's wording, on the other hand, is deceptive. And "using" doesn't mean just copying verbatim, it also means taking that wording as a basis. Changing someone's words around is different from writing something de novo, and presenting the former as the latter is deceptive. Taking the dailies from a movie and editing them into a new cut doesn't make you a director. That's not a perfect analogy, though, because there's a clear line between actually shooting scenes versus using someone else's scenes (and, actually, re-editing a movie is a creative act, it just doesn't constitute "making a movie"), but there isn't such a bright line between "moving someone's words around" and "writing something new".

As to the language issue, while you should make accommodations for language difficulties, ultimately this is your student's responsibility. It's your student's responsibility to learn what plagiarism is, failing that it's their responsibility to learn enough English to understand an explanation of what plagiarism is, and failing that it's their responsibility to find someone who can translate the explanation. It's not acceptable that "more complicated responses are likely to be disregarded", and if they have such a cavalier attitude towards core academic concepts such as plagiarism, they have to live with the consequences. They don't get to dodge disciplinary repercussions just because "this is hard to read".

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To answer the titular question: absolutely yes.

Now when it is dealt with, the bigger issue at hand is that students don't understand your expectations and the reasoning behind them.

Make sure they understand what materials they are supposed to use for their assignments, how and why. Similar to how students doubted the need to not use the calculator for arithmetic in school, they now might be doubting the need to calculate something else by hand when Wolfram or Maple exist. To the similar tune, if they looked it up online and there is the exact solution to their problem, why not just use it? Are they to pretend they never saw it?

To me, the perfect approach is when they either already know from your material or find in someone else's work the approximation to an answer and have to fill in the gaps, and if the problem is purely technical, doing calculations by hand is helpful but only if they are your focus as a teacher, and some people struggle more than others with those; you might need to consider accommodating them as well. If taking prior work is fine by you long as the proper attribution is given (after all, someone has to teach students to work with literature!), state that explicitly. Unfortunately, school focuses on "no cheating/copying" in a way that leads students to the "just don't get caught" mentality you seek to get rid of.

So meet the students where they are, consider what skills you deem important for them to develop, and sit down with them so that they explain their solutions to you.

As an exercise, you might even ask them to explain some relatively trivial fact so that they know the difference between common knowledge, where the attribution is not needed, and deriving works.

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It is not a question of proportion, or how many words: plagiarism is a qualitative assessment. It is largely a question is claiming as own the idea of someone else.

Clearly direct copying without attribution is plagiarism, but consider the following examples.

During a final exam, two students Charlie and Bob make the same sequence of conceptual errors on a question where they are asked to evaluate the ground state energy of a molecule (for instance). One or both of Charlie and Bob could be guilty of plagiarism even if the texts explaining the calculations are largely different.

As another example, suppose Bob somehow accesses the work in progress of Charlie, and decides to redo this work on his own without acknowledging the source of the work as Charlie’s. Even if Bob’s paper is significantly different in language and structure from Charlie’s, Bob can still be accused of plagiarism.

In the examples above, one can argue that the ideas were improperly claimed to be that of one person (say Bob) whereas in fact they are Charlie’s idea.

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    I'm confused by the first example - if Charlie and Bob answer the question independently, it's not plagiarism if they use the same line of reasoning, or even if they write the exact same words by chance alone. If Charlie and Bob never see each other's paper (and I don't see why they would in an exam setting), it's impossible for them to plagiarize. Of course, proving that would be difficult given identical incorrect answers. Jan 10 at 15:33
  • @NuclearHoagie yes. I would better have said that in this instance once can rightly suspect plagiarism, and differences in wording would likely not make up for the low probability of independently making the same sequence of errors. Jan 11 at 16:07

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