Cheat On Math Test

[Vivien]

Im teaching a course at a community college called "Business Pre-Calculus", which is basically some varied rudimentary algebraic concepts integrated with some topics from basic economics and finance.

I give in-class exams for which calculators are provided and the use of a phone is prohibited. On the last exam, a student who had conceptual difficulty adding fractions, on the same test was able to solve a 3x3 linear system, a complicated rational equation, and an even more complicated rational inequality. His work in the space provided is mimnimal and makes absolutely no sense (I've already considered the "savant" possibility), and I cannot fathom how he could have come up with the correct solutions to each with any of these ridiculous "calculations". They resemble what you might see on a chalkboard in a cartoon: nonsense made to look like math to an ignorant observer. In all honesty, I feel like he gets the answers somehow, and then scribbles some "work" to avoid suspicion. But his answers are still correct, and seemingly out of nowhere.

Unfortunately, I don't think that there is any possible way to answer that question without being the student. Maybe they cheated. Maybe they got lucky. Maybe they did some work in their heads but were unable to communicate that work in writing. Maybe they saw that exact problem in a homework assignment or study guide somewhere and somehow managed to memorize a correct answer. Without being in the head of the student, it is entirely impossible to know how they got that answer.

In the classes that I teach, I strongly emphasize that most of mathematics is not about obtaining the correct answer, but about communicating to others how that answer was obtained. If you cannot communicate how you arrived at an answer, then you haven't done the basic work necessary for conducting mathematics.

I will also point out that I am very carefully avoiding the issue of cheating entirely. Yes, it is very possible that the student cheated. But if you don't have any evidence of that (other than some suspicious answers on an exam), accusing the student of cheating does absolutely nothing to resolve the situation. It is probably better to assume good faith and let the student prove in office hours that they have no idea what they are doing. Whether they are cheating or not, they aren't going to get credit for something that they don't understand.

Do you give full credit for answers without clear work?? If you don't then I suggest you give partial credit and meet with the student in the guise of helping him write his work more clearly so that he can get full credit next time and possibly even a little more credit. Put the responsibility on him to explain how he got his answer and help him write what he did clearly. If he can't explain what he did, then explain that this is why he can't have any additional credit. IF he is interested, go over the method with him. Find out if he has trouble writing down his thinking in general.

In my years as a teacher, I have seen students who can do all sorts of things in their heads and have no clue how to write it down. These students didn't cheat, just learned and worked differently. All their thinking was done in their heads and trying to write things down interfered with their thinking. If you required that they wrote something down it rarely matched up with what they did in their head.

All in all, I think he knew what he was doing. Of course there are some errors and the solution is almost unreadable, but still, I would not think that this student was cheating. I would think it is either that he thinks himself to clever to write such trivialities down, or he doesn't know how to properly document his work. Thus, I would suggest to talk to him, find out what is the case and then explain to him that he needs to properly write down things; both for you to understand it, and for him to avoid doing mistakes.

If possible you should teach him resp. your whole class that writing things down properly, even in seemingly easy cases, helps a lot with avoiding and tracking down calculation errors. And yes, such errors happen, to everyone.

Best example I can think of right now is the Gaussian algorithm to solve systems of linear equations. It might seem boring and students always want to be clever and do a really intelligent trick to solve the system faster, but in the end, just following the algorithm strongly reduces the number of errors due to slip of the pen.

Math can be hard. Sometimes you might feel overwhelmed and decide that you need to cheat on your next math test. Keep in mind, however, that there can be serious consequences to cheating if caught. Moreover, you're not actually learning anything by cheating. In fact, in the time it takes you to read about how to cheat, you could have probably studied for the same test! Nevertheless, there are several ways to cheat on a math test if you've decided that this is the way to go. Cheating has come a long way from simply looking over at another person's test!

I am a math professor. Several of our midterm questions were posted to Chegg. We found some students who clearly used them and gave them zeroes for the exam. We also had two students where I kept going back and forth. Most of their work was fine but, in each case, there was one answer which was surprisingly close to Chegg but not so close that I thought it couldn't be a coincidence. I kept sitting on the edge and finally decided to let it go.

I've been thinking, after all grades are in, of writing these students and saying "If you were cheating, you came very close to getting caught. You should be scared about how close you came and make sure you don't do this again; you clearly know enough to pass without it. If you weren't, than I am very sorry to have suspected you." Good idea or terrible idea?

If you want to announce to the entire class that there were a few other cases that were suspect, not naming names and not singling out any individual, that would be fine and the message would be delivered.

If you suspect cheating, one option is to ask the students directly to explain how they got answers that were so similar to the online source. In my experience, this often results in an immediate confession on the part of the students. If they come up with a story that's hard to believe, but you don't have enough evidence to get through the disciplinary process, then you can drop the matter.

If you ask Chegg, they would supply student data they hold. This includes not only those who asked the questions but also those who viewed the answers. If you have the right clauses in the honor code preventing students from seeking unauthorized help, then you can take students to the disciplinary tribunal with the evidence you obtained from Chegg.

Case 1: I cheated, and receive this email warning me I came close to being caught. This should be a good result. It would act as deterrence - after all, next time I might not be so lucky. Only thing to pay attention to here is to not reveal the evidence against me, since otherwise I might be tempted to cheat again except this time also to cover any tracks.

Case 2: I didn't cheat. In this case the warning is irrelevant to me. Like, the conditional is false, so whatever follows it is irrelevant. After all, the statement "if you cheated then pigs fly" is true! The allegation would only become a nuisance if I had to invest time and effort to fend it off (which I presumably don't in this case), or if it became public (which it doesn't have to, if you send private email).

If you are very worried about case 2 (which is reasonable), you could try looking around to see the effect of false allegations in online forums such as StackExchange. We do for example have rules against multiple accounts. One can never actually be sure that two accounts are actually the same person, which will invariably lead to false accusations and possibly investigations. I don't actually have the statistics on how people react, but perhaps a mod will be able to say. My experience elsewhere is that people get annoyed if they have to mount a defense, but if it's just being told they've been suspected, they might even react with laughter.

Edit: Based on the comments, different people come to different conclusions on this because they interpret things differently. I for example would consider the proposed email closer to being exonerated than being accused, but many others don't. Clearly the dividing line between the two very different reactions is extremely fine. If you do send the letter, you will have to word it very carefully. At that point, it might be better to just sidestep the potential quagmire entirely and not bother.

If exam questions are testing understanding and solving, it won't help your students when they are looking up the answers somewhere else. Therefore it doesn't matter if they look up answers. So I think you are fixing the wrong thing here.

Edit:For me it was not clear the questions were posted during the exam. That makes a bit of a difference. When remembering my math exams: besides the answer I had to give an explanation why the answer was correct. Without explanation you got only a fraction of the points. Depending on the teacher, even with a correct answer.When cheating was suspected you had to clarify your explanation. Which you are not able to if you cheated.

I'm teaching calculus 1 online this term and anticipate being plagued by the perennial problem of cheaters. I have seen suggestions for how to arrange the testing time to accommodate for traditional tests (such as this previous question and the questions it mentions) but I would rather improve my question-writing instead of impose onerous requirements on my students in terms of time. I would hope that by making these sorts of questions common in all assessment levels that this would also improve my students' learning, especially as they learn that I expect them to understand instead of merely regurgitate. I've also contemplated moving to projects, but have come to similar conclusions that it is difficult to evaluate students on procedural fluency with projects, and devising effective projects is probably going to take me more time than simply writing better questions.

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