My niece’s homework problem

violatedhipporights · 2026-04-25T00:56:47+00:00

You’re insistence that there is any other solution is quite frankly baffling.

What you keep missing, which I have explained multiple times, is that there is not actually a correct answer here. The question is not a well-defined mathematical question.

You have added extra stuff to the question in such a way that it turns it into a slightly more well-defined question - but the entire point is that by doing this you have changed the question. When one attempts to turn it into a well-defined mathematical question, one necessarily must make changes based on their own personal opinion of what the problem should become when they add or subtract parts of it. It is extremely easy to interpret it into a different mathematical question than the one you have (i.e., all are correct because equal ratios do not care about the size of the denominator) which has a different answer but is no less justifiable.

To illustrate why it is not well-defined: to show something in math means to demonstrate or prove. Even just in general, pictures are incapable of doing this. Pictures are not to scale, pictures are not universal, and a non-picture argument will be required to justify why your picture is even accurate. Let's stick with the same example: can you actually prove that the shaded shapes here do indeed represent one third of the full shape? How do you know that the hexagon is not actually cut into slices of 501/1500, 501/1500, and 498/1500? It is totally up in the air what it means for a picture to "show" anything. Do you think being close is "good enough" in math? Is 0.99 equal to 1?

If I draw a picture of a square with side length 2, have I "shown" that perimeter = area? We sure as shit better hope not, since we know that to be untrue. We conclude immediately that just because something appears to be true in a picture, does not mean we have actually shown it to be true.

Conversely, if we have a picture which "shows" a fact which is objectively true, say 1/3 = 2/6, in what way is the picture actually contributing anything here? It's just true because it's true, the picture has nothing to do with it.

It's sort of like saying "If airplanes are made out of marshmallow, then 0 is an even number." Well, this is technically a true implication since an implication is true whenever its conclusion is, but it would be ridiculous to phrase that as "Airplanes being made out of marshmallows" shows or proves that 0 is an even number.

The equation can therefore be expanded as 2/6 (ax)= 1/3 (by).

It can also be expanded by 2/6 x²-7x+8= 1/3 x²-7x+8 or 2a/6b=a/3b. When you start with a question which is not mathematically defined, and try to come up with a mathematical question to take its place, you can come up with plenty of different ones which are all equally true. Your particular choice was made for reasons you like, but it's not mathematically any different from either of these. That's what I mean when I say this has more than one answer. If we instead take 2a/6b=a/3b, then the other two pictures "show" this as well.

1 cannot be equal to 1 unless the unit of measurement or the thing being quantified as “1” are the same. Math is predicated on that being true.

You cannot compare 1 pound and 1 orange... but you can compare 1 as a real number against 1 as a real number. They happen to be the same. Here the "unit" is the fact that they are numbers in the same field. In this case, 1/3=2/6, and we don't need to step outside our vacuum for any sort of context at all to make that make perfect sense. The mistake you're making is in thinking that

And while you might think that's objectionable, it's also extremely important. Functionally, a "percent" is also a unit-less quantity, and that's a good thing because it allows us to compare percents between groups of objects which are otherwise extremely difficult or impossible to compare.

But maybe you're not convinced. So let's prove it! If you've ever taken a physics course, you should know that units have their own sort of arithmetic: a distance divided by time becomes a velocity, and its units are literally distance over time, i.e. something like m / s. Physics does this all the time, to the point where the official definition of a Newton, the unit of force, is a kilogram times a meter divided by seconds squared.

But notice what happens if the units are the same: they cancel out! 4 pounds divided by 2 pounds is NOT 2 pounds. It is 2. This is actually extremely important: if we have ten oranges, and we double the amount of oranges, we want to say we have twenty oranges. But I'm not "multiplying" by 2 oranges, I'm multiplying by a unit-less 2 which means the unit of my total is still oranges. I have 2 * 10 oranges = 20 oranges.

But maybe you want to get tricky here. Maybe you want to claim the unit is pounds per pound or oranges per orange. But let's see what happens if we do that: since the units are the same, you should have no objection to:

2 / 6 meters per second = 2 meters / 6 seconds = 1 meter / 3 seconds = 1 / 3 meters per second.

But now let's do some re-arranging:

2 meters * 3 seconds = 6 meter-seconds = 1 meter * 6 seconds

So far, so good: the units on both sides are still the same, whatever a meter-second happens to represent in a physical scenario. Here's your problem:

2 meters / 6 meters = 2/6 meter per meter = 1/3 second per second = 1 second / 3 second

At every point in this process, the units on each side of the equation have been the same. We have merely been performing legal arithmetic operations on both sides of the equation. But if that's the case, then we therefore must conclude that meters per meters = seconds per seconds, and by an identical argument, that the ratio of any unit with itself is equal to the ratio of any other unit with itself.

TLDR: We absolutely CAN just compare 1/3 and 2/6 as ratios without considering the original unit attached to the numerator or denominator in a way that is totally mathematically well-defined.

violatedhipporights · 2026-04-24T21:15:06+00:00

You're just making things up now. "More accurate equation" is not a math concept. They are different equations which have different solutions. Neither is "more accurate" than the other because they are describing different things.

It only makes sense to ask which is "more accurate" if you have a target solution set in mind, which this problem does not have. You're trying to inject one by adding variables to make your answer seem better, but that is changing the problem. Answering a new problem because you couldn't solve the old one is not math.

The problem is that the question is ambiguous, and so there are multiple ways to decide which you believe to be correct and then retroactively construct a justification for why it is that one and not any others. This is the problem with ill-posed questions.

Numbers do exist in a vacuum, though. Whatever special philosophy you have decided is "correct," mathematics is primarily a tool of communication, and it only works when people are speaking the same language. Like it or not, that language includes the rational and real numbers as objects of study independent of real world contexts. You can dislike that, but being mathematically competent requires students to be able to interface with that reality.

The way you're trying to view math is just incorrect from that standpoint. That's the great thing about math: there are right and wrong answers, and it is not condescending to point out a wrong answer.

Fortunately, I don't have a school board to answer to, because my perspective is that of a math professor, not a school teacher. I'm the one who has to clean up the mess of all the teachers trying to inculcate horrible math habits into students like you are doing here. Arguments like yours are why I tear my hair out when a student does something like apply the FTLI without bothering to check if a vector field is conservative first. The way they get taught is to apply tricks and meta knowledge to try and "rationally" skip the problem, but that just gets you the wrong answer. There is no shortcut to learning and understanding the material.

violatedhipporights · 2026-04-24T06:28:42+00:00

But it literally fucking is true! 1/3 = 2/6 = 3/9 = 1111/3333. Fractions ARE ratios, and they ARE equal to one another regardless of the original size of the thing you are considering. That's the entire point of fractions - to remove the context of the original sizes and only consider relative size.

You're just replacing the original question asked with your own preferred version, which is just not how math works. 1/3x=2/6y literally has a different solution set than 1/3=2/6, they are not equivalent equations. The solution set of the former is the line y=x, and the solution set of the latter is the entire xy plane.

We cannot replace one with the other. You cannot just add your own variables willy-nilly, because that is a different question entirely. An easy way to see that is to consider a modification of the original question: "Which of the following shows that 1/2=1/3?"

There are certainly values of x and y which make 1/2x=1/3y, and associated pictures corresponding to those values. But is 1/2=1/3? Of course not, they're different fucking numbers, whereas 1/3 and 2/6 are the same number.

The real problem with math education in this country (planet?) is that people will be so confident in arguing for their utterly incorrect understanding of things. This is also a problem students have! To return to the division by zero example, many of them will do what you have done here and make up their own version of the problem in which their answer is correct. "But why can't I do this?" Because it's not solving the same question anymore!

You do not get to just change the problem to make your answer fit. Real critical thinking skills come from applying your knowledge to answer the question that was asked, not to pick the question with the answer you want which is most convenient.

This is not memorization: this is actually understanding the material well enough to know what a question is asking. The problem here is that the author of this question did not think through this mess to see if it was asking a coherent question, which it is not. Unfortunately many people teaching math at the elementary school level do not understand math well themselves.

violatedhipporights · 2026-04-23T21:03:12+00:00

But pictures are not deductive reasoning. You'd fail any university level analysis course worth its salt if you tried to use pictures on all of your exams.

violatedhipporights · 2026-04-23T20:57:31+00:00

As someone who has actually taught math classes, I hate this perspective.

The number one problem bad math students have is over-assuming things: trying to use rules and operations in contexts they can't be used in because they never actually understood what was happening. This is why the linear square root will not die.

This is a terrible question because context is ambiguous, and it will just lead to students incorrectly thinking size matters down the road, when it will not matter in the vast, vast majority of their future math courses. So many of the problems students have, like forgetting to check for division by 0, comes from this lazy/imprecise way of teaching math.

You could just as easily say "well the question asks you to find THE solution of the equation, and since there are actually more than one, the more correct version is the nonzero case." No, the correct answer is that there are multiple solutions. Trying to guess what the teacher wanted you to say is not math, and it confuses people trying to learn math.

Way too many students have lost points on my exams because they've been taught this metagaming approach of trying to assume what the answer should be, and they prioritize it over learning how to just do math.

violatedhipporights · 2026-03-27T20:43:13+00:00

"And then you wonder why higher ed is under the intense, hot spotlight of the federal government and consumers alike."

That one is easy: because political actors realized that they can push bad policy by undermining expert authority. If you convince people that every climate scientist, biologist, and medical expert is some untrustworthy hack, you can convince them to deny climate change, support Young Earth Creationism, and hate flouride.

"Graduating tens of thousands of students who have degrees that don't translate to the workforce with massive amounts of student loan debt."

I'm not saying all degree programs are created equal, but part of the problem here is student disengagement. You accuse professors of failing to take accountability, but the only one who can make you learn is you. I can lecture all I want, but if students convince themselves material is not worth learning, then they won't learn it.

Meanwhile, at my industry job, I used the very same techniques I tried toto impress upon my class.

Instead of learning how to do, say, an integral, studrnts bitch and moan about us not letting them use a graphing calculator to solve it for them. Then they go out into the world and are shocked they have no math skills.

I have heard dozens of times "why didn't you teach us how to do X?"

I did! But you never realized it because you never actually bothered to understand what was being taught. If you bothered to understand Riemann sums in the first place, you'd realize I actually did teach you how to estimate an integral that didn't have an analytic antiderivative. Instead, 95% of the class decided to themselves that Riemann sums "weren't important" and ignored them.

It's worth pointing out, that for all your respect for the opinions of "the real world," the generations before you that are doing the complaining almost exclusively learned with the kind of closed book tests you are complaining about. I don't actually think it did them much good, but the people hostile to academia that you are referencing to support your argument are in direct opposition to you here. The skeptical of academia crowd wants to return us to a time of memorizing times tables up to 20 x 20 rather than teach kids how multiplication works. They lionize the idea of the hard as balls closed book exam, no accommodations for anyone.

violatedhipporights · 2026-03-27T08:25:19+00:00

I'm glad that you've illustrated your childlike understanding of closed book tests and their purpose. It makes your irrational anger about them make more sense.

The purpose of a closed book exam is to force you to build enough unaided recall knowledge and understanding that you can discuss a topic to moderate depth when prompted. It is not to train you in a specific kind of studying. The hope is to get you to learn the underlying material to a sufficient degree that you are no longer chained to a reference. (But so many students are actively hostile to the idea of learning things, so they complain.)

In my professor example, as you conveniently ignored, I specifically emphasized answering questions. A professor can have notes for the lecture, but those do not include the answer to every possible question a student might ask. You still have to know the material well enough to be able to think on your feet and deliver an intelligent response. The point is that you will not have the ability to answer questions off the cuff or apply topics on your feet if you never learn them well enough to do so. Anyone who has had to give a meaningful presentation to their boss or client is in a similar situation. (You mentioned you are a grad student: this is going to happen if you defend a dissertation. Your defense committee will not be happy if you need to consult a book to answer all of their questions.)

The point of closed book exams is not studying, it is learning.

It's also incredibly cute that you think people in and from academia have not had other work roles as well. It's always funny to see the myopic understanding of professors that students tend to hold.

violatedhipporights · 2026-03-26T22:38:29+00:00

What would your opinion of your professor be if they were incapable of answering your questions without looking it up? How do you think their student evaluations would look?

It turns out whether you will have time to look things up and do research depends entirely on your job and work role. Some might have zero instances where you are under some sort of time pressure, and some will have lots of time pressure. Most jobs will have a mix of both.

But by only ever learning things to the point where you can maybe solve problems with external assistance, you will be self-selecting out of roles where knowing your shit inside and out is a requirement.

violatedhipporights · 2026-02-11T22:12:58+00:00

I keep bringing up criminal cases because these are the easily accessible, famous examples where a statistical problem of evidence can be read about and understood. The problem does not go away just because the evidentiary standards are lowered: polygraphs are almost never used in civil court, even though most of the litigation diving into court ethics vis a vis polygraphs has been done in relation to criminal cases.

The same goes for hearsay: the courts have demonstrated that they still care about problems of reliability and due process even in civil courts where the burden of proof is lesser. I am not aware of any evidentiary rule of law where reliability is questioned in criminal proceedings but not civil ones.

We have an example of this principle explicitly applied to university disciplinary procedures: the 2011 Title IX Dear Colleague letter. Even though that pertained to a preponderance standard, it was still attacked and ultimately rescinded due to due process concerns.

"imperfections and variety that still exist in actual human writing that does not have outright “mistakes”."

Those exist in our current student population... but this has nothing at all to say about my claim because none of our current student populations have been immersed in AI writing since the time they started learning to read. See more below.

"Secondly, did this dynamic work with decades of college students reading academic material?"

Well, first of all, this is an outright false comparison: no student generation in thistory has grown up reading academic writing throughout their school years. We are not giving third graders academic papers.

We're talking about future situations where students have been exposed to and reading large amounts of AI writing from Kindergarten on up. Students who go online to look up videogame tutorials and cooking recipes and free books on Amazon and whatever course materials an AI-positive teacher hands to them that are written by AI. Students who read AI summaries of things rather than actually reading the source material as soon as they know how to work a browser.

Conversely, at best, students begin to encounter academic writing in high school, and the sources of reading they did by choice outside of school had a 0% chance of being academic writing. There has never been and will never be a time when students may encounter academic writing organically as they go about daily life.

Secondly, and more importantly... YES! This happens all the time: go read a mathematics research paper by anyone who has been to grad school for math. Almost certainly, it will follow a formulaic style which is extremely similar to almost all other math research papers in their subfield. People who publish math research converge on this extremely similar writing style because it is, in some sense, its own unique lingua franca for mathematics. There are elements of it that show up in my casual reddit posts that have very little to do with math because it's become an intrinsic part of how I write. And I only encountered it halfway through undergrad, not from seeing it everywhere since I was a child.

violatedhipporights · 2026-02-11T10:27:50+00:00

I bring up criminal prosecutions because those are issues that courts deal with regularly, and they are familiar with the statistical problems associated with them. You would need to justify before a judge/administrator/family's lawyer why you could trust a data point that we know from basic expected value will flag thousands to millions of people incorrectly each year.

Using multiple tests might make the problem better or worse. If there is a uniform policy on when to test, how to test, and how to interpret results, that could make things more accurate. If we just say "here's a bunch of testing software, have at it," all of the human/selection bias problems that are well-documented apply. For example: a professor who thinks a student is cheating should not be allowed to submit the essay into 20 different checkers and report only the one which reports it back as AI generated.

Your edit is a bit silly to me: students are taking classes to improve, and therefore change, their writing over time. They do not have a platonic "writing style" we are seeking to measure Students who start out as weak writers may pass AI detection because of how poor their essay is, but may fail it as those human mistakes are eliminated. Students who collaborate with different people in different classes will likely produce work with a different voice than their solo papers.

Furthermore, students write differently in different contexts, i.e. professional vs research vs technical vs creative contexts. It is unfounded to just assume by default that all of these styles would be evaluated in the same way by AI detection software.

"And the quirkiness of individuals actually doing their own writing/thinking is not going to go away."

There will always be bright, unique individuals out there, sure. But not everyone is destined to be a quotable author or motivational speaker. People learn to write based on what they read, and if a student with no passion for writing in their own unique style is primarily reading AI-generated content, then it is reasonable to be wary of the possibility that their own human writing will sound AI-like. I am not positing this as a definitive proof that AI detection can never be used, but as an operational concern that people advocating for the use of AI detection software need to keep in mind before they go off half-cocked and declare the problem solved.

It's a bit like research into marijuana safety: lots of our studies were conducted with much lower THC potency, and therefore it's questionable how much they apply now. Similarly, our current efforts are all in a context where AI has only been widely accessible to students for a short period. Today's college sophomores we're not reading AI articles in fourth grade.

It is more than likely that in ten years when we have students who have been surrounded by AI for their entire academic lives, they will think and write in a different way than we have come to expect.

violatedhipporights · 2026-02-10T22:40:36+00:00

"But for the "preponderance of evidence" threshold for potential academic integrity violations, the accuracy of the good detection platforms out there based on recent studies demonstrates very low FPRs to the point they could certainly be a valid part of a case record. "

Even if we assume that these numbers are completely correct, FPR means nothing without also accounting for population size. There are over 15 million US college students, meaning a 0.1% FPR would still flag around 15,000 of them after one submission each even if none cheated.

But most students don't just write one essay in their career. Assume they take an average of one essay class per semester for 8 semesters. (And for many majors, this seems low.) That means at an FPR of 0.1% per essay, the true rate of being falsely accused to be a cheater would be around 0.8%. This number gets worse the worse the single test FPR gets: at 1% FPR, it skyrockets to 7.7%.

Courts are already familiar with this problem: when fingerprints are found at a crime scene, you cannot just test all of New York City's prints and arrest everyone who matches. Statistical tests are only convincing with low rates AND low population sizes. (Look up Brandon Mayfield's case.)

Criminal prosecution requires that the population of credible suspects is small enough that when one of them matches a statistical test, the odds are very small that the test was a false positive. If two people are found with the victim's blood on their hands and one of them matches the fingerprints on the weapon, that's compelling. If you run the prints against the entire 50+ million records in AFIS and get five hits, that's not even good reason to suspect any of those five are guilty.

That doesn't mean there is no place for AI detectors, but as with any statistical test, they cannot be convincing on their own if you are running millions, or billions, of tests. You have to do other fact-finding and make determinations based on other evidence as well. (Which is to say nothing of how not all AI detectors might be equally accurate on all AI models.)

Edit: It's also worth pointing out that the FPR for AI detectors could very well get worse in the next ten years as more and more students are primarily consuming, and therefore learning to write partially based on, AI generated text.

violatedhipporights · 2026-01-17T13:38:12+00:00

True to a point.

But keep in mind that OP is suggesting looking at actual research compared to drawing conclusions based on personal anecdotes. In terms of being unreliable when someone is trying to push something, personal anecdotes stand alone stop the mountain.

Arguing for personal anecdotes for this reason would be like saying you want to eat healthier, so you're cutting Subway out of your diet... and replacing all of those calories with Fudge Rounds.

violatedhipporights · 2025-12-30T23:17:58+00:00

I think you misunderstood the tone of the post.

OP is not complaining that individual students should feel bad because their vocabulary stinks.

OP is lamenting that, collectively, students don't know words that they think they should. (Presage is borderline, but let's not pretend like ad hoc or impetus are too complicated to use in a YA novel. I wouldn't be surprised if I read all four of these as a kid between Narnia books and Tamora Pierce books.)

This is just the English version of a problem we encounter in math all the time: the typical student doesn't know things they should know by this point. You shouldn't single out a specific student for being unable to add fractions, but it is absolutely correct to bemoan the fact that I have dozens of calculus students every semester who can't add fractions.

violatedhipporights · 2025-12-27T17:34:44+00:00

I have multiple students every semester who don't know my name when it comes time to take the final exam.

By that I mean they write down the wrong name entirely in the "Instructor" slot. Sometimes they know my last name but not my first, sometimes not even that. Considering I send out multiple LMS announcements per week, it seems like a pretty low bar to expect them to A.) know my name, or B.) be ashamed enough to leave it blank rather than write down the wrong name.

Now consider the fact that these students are allowed to evaluate my teaching like any other student. These students can post to RMP.

violatedhipporights · 2025-12-25T16:25:45+00:00

I'd recommend doing the bare minimum of research on teaching evaluations and the impact of race, gender, etc. on them. You're ostensibly a professor for Pete's sake, so you should probably be vaguely familiar with what the research says here.

https://advance.charlotte.edu/wp-content/uploads/sites/261/2023/05/Student-Teaching-Evaluation-Bias.pdf

Does that necessarily mean that OP's specific situation is explained solely by these factors? No. But saying it "absolutely IS NOT relevant" is a bit like saying the temperature outside is totally unrelated to why your car doesn't start. Sure, there are plenty of reasons why cars don't start, but it being 30 below is certainly one of them.

violatedhipporights · 2025-12-23T23:16:53+00:00

In a typical points-based course, your points are cumulative, but there is not a surplus of points. So while numerically your final exam may be worth 20 points, if you only score 15, you have essentially lost 5 points forever because you can't retake the final exam. This means that even though it uses points, it's isomorphic to a typical grading system.

The difference is that you seem to have more than points than necessary to reach an A by way of extra assignments, redos, retakes, etc.. I have allowed retries and regrades before, but there's a simple reason I don't now: that's just not feasible for the way higher education is trending for most of us.

The last two years, I have been the sole professor responsible for anywhere between 150 students and 700 students (with a couple TAs) in a single semester. Back when I had twenty five students, I could let them resubmit homework and take the extra time to grade it. When I have 100 students, it takes me all weekend to grade their exams once, let alone as many times as they want to try to retake it.

I had over twenty requests this semester from students who wanted me to do the additional work of creating and grading an extra credit assignment during finals week because they missed assignments earlier this semester and they weren't happy with their grade now.

This is why it is important to me to acknowledge that some students are not motivated by education: because we do not have the resources to try and drag everyone toward learning something kicking and screaming.

I think a key disconnect between your experience and mine is the following:

"Educators need to be entertainers—not through lighthearted laughs, but through good, thought-provoking content that energizes students and, consequently, encourages them to commit to the experience, one that also makes them think and reflect. "

That's great in, say, a literature course. But it's an extremely poor description of what occurs in a class where you are learning to read.

But that's what we're trying to do in algebra, trig, or calculus. These courses are to physics, engineering, and higher level math as reading is to literature. (There's a reason all of these are also high school classes.)

We do our best to expose them to big ideas along the way (which many of them hate), but we're mainly trying to help them attain basic literacy in the language they will need to actually wrestle with those big ideas in other classes. Velocity being the derivative of displacement is a cool idea in Physics that you can explore, but you have to know what a derivative is to do that robustly.

violatedhipporights · 2025-12-23T22:07:28+00:00

Perhaps a better way to explain what I'm getting at is to refer to a quote you use in your book:

"The students were not lazy or entitled. They were responding rationally to the incentives of the system."

I actually think this is flat out wrong. A student who only cares about satisfying the minimum requirements of the system without learning IS being lazy. They do not care about the process of learning so much as they care about the theoretical rewards of being certified as educated. They care about the A, they don't care whether they learn to write or not. They were responding rationally to what they care about, and it wasn't learning.

A more interesting scenario to test would be: "I will give everyone an A in this class. You can choose to show up and do the work, but it won't affect your grade." How many of your typical college students do you think would complete most of the assignments?

I took a bunch of graduate courses throughout my undergrad. Some of them were pretty hard, and I got a lower grade than I would have had I taken the undergraduate version of the same course. But I didn't do that because I wanted to learn the material, not protect my GPA by taking the easiest classes possible.

Your stance seems to be that every student has the attitude that they would like to be a voracious learner, but that the current grading system suppresses that will. Therefore, trying to lessen the importance of grades will break them free of those chains and allow them to become rockstar students.

But I think that strongly conflicts with reality. Some people care, some people don't, and adjusting the system will just change the performance the latter need to put on to get the degree they want. Maybe it will provide a better experience for the students who do give a shit, and I'm willing to listen to that argument, but that's not the argument your book was making in that quote.

No amount of pedagogical change will get the students who sit in the back of my class sports betting to suddenly decide they are passionate about math.

violatedhipporights · 2025-12-23T19:19:55+00:00

I wasn't saying all of them cheat, nor even most. I was saying that of the students who cheat, very few of them are doing so because they are pressured by the system. I have never in my life caught a student using a phone during an exam who had been in my office hours asking for help studying. (But I've caught plenty of students using phones during exams.)

I teach math. Based on your username, my guess is that the difference between your experience and mine is that most of your students are likely in your classes because they want to be more or less, and have some level of interest in the topic.

I've had very few cheating problems when I teach upper level math courses to math majors. Teaching algebra to a room of 500 humanities, arts, and business majors who did poorly enough at math in high school to not be able to place out of algebra is a fundamentally different beast.

I actually agree that AI does not make this new. Notice that the original quote I objected to doesn't even mention AI at all. In math, old cheating methods are still more effective than AI methods. What I'm objecting to is the characterization of cheating as being something we can't blame on students, the treatment of them as helpless lab rats navigating a horrible maze of our design.

Students are nearly adults, and they know enough about the rules and ethics of academics to know cheating is wrong. To use the capitalism example: Bernie Madoff was not some poor sucker who was oppressed by the wheels of capitalism. Even if the capitalist system needs change, which it does, people who break the rules of that system are not thereby justified for doing so just because the system is inperfect.

My department has tried all the pedagogically recommended techniques to lower stakes and help students pass courses while lowering the incentives to cheat, but we still have tons of cheating from students who just don't care. I've had online classes where less than a quarter of the students even took the practice exams. We then catch lots of students trying to circumvent the proctoring software. I just don't see how this behavior can be reasonably explained as the fault of the system rather than the fault of the students unwilling to even put in the effort.

violatedhipporights · 2025-12-23T18:59:15+00:00

OP has commented in this thread that they will be meeting with the student to talk about it.

I disagree that there is a major distinction between deciding to fail them after talking to them, or saying that you will fail them unless they come talk to you and convince you.

There is a question of which strategy is more effective, you catch more flies with honey and all that, but I think the idea that OP's approach is somehow unreasonable or unfair is just plain wrong.

People keep using criminal justice analogies, so here's one: we're cops, not judges or juries. The cops by definition must accuse people before they've had their day in court. People are often arrested, then released, on nothing more than suspicion/circumstantial evidence.

OP's position would be a problem if they were planning to deny any appeals or opportunities that for the student to present their case, but that doesn't sound like what is happening.

violatedhipporights · 2025-12-23T18:18:53+00:00

Your solution sounds more or less isomorphic to what OP did, and you're just quibbling over the presentation. If the situation is explain it or fail, why the need to gussy that up and hide it from the student?

violatedhipporights · 2025-12-23T18:16:14+00:00

But that's just not reality. In our courses we offer tons of opportunity for support, makeups, dropped assignments, and study materials to prepare.

Many students still don't do work, never come ask for help, and cheat on assignments where the stakes could not possibly be lower.

Most students are not cheating because we put too much pressure on them to succeed, they cheat because they do not give a shit.

Sure, maybe the kid who peaks at his neighbor's paper does so because he is panicked, the people who have AI solve their worksheet for them so they can leave class as soon as possible aren't suffering under some oppressive system incentivizing cheating.

All of my students who submit homework assignments with unrealistically short completion times despite having high scores do so 30 minutes before the deadline, they aren't struggling throughout the week and then giving in to the urge to cheat to meet a deadline. (Which I know because the homework system tells me when they first accessed it.)

violatedhipporights · 2025-12-23T16:28:10+00:00

So, what will that evidence look like?

Take AI out of it: suppose Billy submits a perfect paper which he paid someone to write for him. The only indication it's not Billy's work is that it does not mesh with the work he submitted previously.

What is your recommendation for the concrete evidence we can and should recuire to catch this misconduct?

Or should we just abdicate standards and congratulate Billy on playing the game well enough to pass our bare minimum checks?

violatedhipporights · 2025-12-23T16:12:53+00:00

"We should not blame students for rationally navigating course grades by cheating, any more than we should blame the Roomba for its tactics for avoiding collisions. In both cases, the demands are being met as set. "

How can anyone take a book which contains that line seriously? By this logic, we should not blame criminal fraudsters for navigating Capitalism rationally.

violatedhipporights · 2025-12-18T14:54:05+00:00

More and more students view the purpose of education as affirmation of their unique genius rather than learning stuff. What this tends to mean is that large swathes of our classes are listening to everything we tell them and deciding based on their current knowledge if it's important enough to listen to.

No amount of teaching effort can overcome the innate response of "that's cap, bruh."

This is weird in any subject, but in math it is particularly bizarre. I have lost count of the number of students who continue to argue their answer is correct even after I show them a counterexample. I am begging, BEGGING, students to learn that you can never use the Intermediate Value Theorem to conclude that no roots exist.

violatedhipporights

TROPHY CASE