Is "playing dumb" considered un-helpful?

Question

It is fairly common for someone to post a question with an easy-to-fix notational error, for example, writing an integral and forgetting to put $dx$ at the end. Some users will just edit the post and fix the notation, but others seem to prefer commenting something like, "I don't understand what you've written. Is there meant to be a $dx$ at then end of that integral?"

This strikes me as disingenuous and rude. The user commenting this way almost certainly does know what the OP means, and what they're really trying to say is, "hey, you forgot part of the notation." I understand that this particular form of disingenuousness is common enough in the mathematical community - certain teachers like to use it - but is it fair to say that it does not create the type of atmosphere we wish to maintain at a site such as this?

Thanks in advance for your thoughts on this matter.

EDIT: It's apparent this question has produced a good deal of misunderstanding. I'm not asking how to respond to a commenter who I think is "playing dumb". I'm not asking if, or suggesting that, I can distinguish it from honest questioning. I'm asking whether doing it is a good idea. Is it helpful, or does it do more harm than good? I know that it happens sometimes, and I wonder if it is sound pedagogy.

Answer 1

Having been on the Internet a while now, I know that no matter how genuinely confused I am, and no matter how politely I try to phrase my question, there can still be someone who thinks I am just trying to be a jerk. Wikipedia has a policy, not observed as universally as it should be, that one should assume that others are acting in good faith. I think this is a good policy, not just on Internet message boards but in life.

Here is one of many examples. The querent had used the symbol ≤ to compare two groups. I asked for clarification:

What do you mean by ≤ here? Does that mean that (group A) is a subgroup of (group B)?

I would have been very unhappy if the reply had been some variation on “of course it means that, stop being an ass”. (It wasn't; the reply was flawless: “Yes, that is what I meant”.)

Even if I had intended to be an ass, nothing would be gained from a rude or defensive response. Simply replying “Yes, that is what I meant”, as the querent did, is always superior. This was a successful interaction. I think we both got it right.

Summary: On the Internet, it can be hard to tell sometimes if people are trying to be jerks. Sometimes they are trying to be jerks. But it is nevertheless better to act, as much as possible, as though they are not. Haters gonna hate; we don't have to let them bring everyone else down too.

Answer 2

I'd say it's completely down to the particular tone the user uses. Using "playing dumb" to point out user mistakes, on its own, is not bad in my opinion.

I think, so long as it isn't taken to the extreme of making fun of the OP, this is a good way to teach the OP to be exact when using mathematical language. Often, if a user learns how to properly use mathematical language, he has learnt a much more valuable lesson than just how to solve some particular integral - and after all, this site is here to help people be better at math moreso than solving their homework. Naturally, if the OP then edits and improves his question, the answer must either be deleted or edited - if not, it certainly is un-helpful.

I think it is related to providing "technically correct" answers, such as if a user asks "Prove there is no number $x$ such that $x^2=2$", and the first answer will be "We cannot prove that, because $x=\sqrt{2}$ solves that equation".

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TL;DR:

No, I don't think the practice is bad in itself, however overdoing it can prove unhelpful. Going overboard and doing it when someone forgets a $dx$ is taking it too far, but that doesn't mean the whole concept is bad.

Answer 3

"Playing dumb", as you put it, is a principal and important method of teaching, not restricted to mathematics. I've found it works well when used correctly. I use it in my office hours, and I use it on math.stackexchange.

The situation where it applies is where a little error signifies to me a principle point of misunderstanding. In such a situation, I ask a simple question about the format or meaning of the original question, either to the student in my office hours or in a comment/answer here on math.stackexchange. My intent is to force the asker to ponder what they actually meant to ask, and sometimes this is all that it takes for them to reach understanding.

Now, this can be hard to judge, and sometimes it doesn't work. But often it does, as is proved on math.stackexchange when various answerers miss the point and post answers which go over the OP's head, whereas I "play dumb" and my comment/answer hits the point.

Answer 4

Sometimes these things can be borderline as written, and it's necessary to ask for clarification. Because of the differences in our backgrounds, something like "Is there meant to be a $dx$ at then end of that integral?" could be intended in all good faith.

But also much hinges on presentation. Text on the internet is, in general, a notoriously ambiguous mode of communication.

As a matter of courtesy, one should try to soften such corrections. Actually, I don't think the example you gave is so very bad. It's certainly within the limits of slack which you cut people you don't know very well.

On the other hand, I have seen things where posters, who should have known better, have said things along the lines of "Your question about conditions on a set $X$ to be a group is utterly wrong because what if $X=\emptyset$?" when there was, in all likelihood, an innocent omission on the poster's part. That sort of obtuse comment is counterproductive, but it could be presented in a better way.

Answer 5

I have very frequently added the $dx$ and done similar things. If I were to see $\displaystyle \int f(x,y)$ then I might ask whether that was intended to be $\displaystyle \int f(x,y) \, dx$ or $\displaystyle \int f(x,y)\, dy.$

There are actual cases where I don't know what is meant and I ask. If someone asks what is intended I would not start from the assumption that it's sarcasm. Once on Wikipedia someone said they objected to the existence of a certain Wikipedia article on the grounds that a mathematical equation should not be the subject of a Wikipedia article unless it's an earth-shaking new discovery. I expressed some objection to that position and he allowed that I had a point, but then added: "but you know what I meant." I didn't know what he meant. Further discussion revealed that he thought it was obvious that a mathematical equation should not be the topic of a Wikipedia article, and he assumed that would be obvious to me, and that he didn't know what an "equation" is. It would have been easy for me to think he was being sarcastic, and maybe he thought I was being sarcastic. Sometimes someone who claims not to understand what you meant does not understand what you meant.

Answer 6

I think some principles apply:

1. It's incumbent on people seeking help to make their questions clear

2. Careful use of notation is very important in mathematical questions. Sometimes even tiny changes can radically alter what is being asked.

3. We have a role not just in answering questions but in helping people learn and understand, and in being able to ask better, more precise (well-formulated) questions.

4. A better formulated question is often more readily answered by the asker. Numerous times I have been preparing to ask a question and have found that proper preparation in asking the question (care over notation and definitions, clearer expression of the issue etc) has quite a few times led to me answering it myself. Helping people improve their ability to do this -- to formulate questions properly, with all the benefits that brings -- is crucial to helping them get better, faster answers and with their own development as users of mathematics. That is, helping people to arrive at better questions is definitely part of helping them.

5. There are numerous aspects of doing that; part of it will be editing (at least if it's obvious what the intent is), part will be commenting to explain the issue. Part of it can include "playing dumb" in that comment, as long as it's not done in a rude way - it's a form of instruction with a long history and is at least sometimes quite effective. It does, for example, make it clearer that the responsibility for the question is their own - they should not post any old nonsense and expect others to do all the lifting to make it work as a question.

So I think playing dumb - at least in some situations - is fine, as long as we keep in mind the point: firstly to help the user end up with a good question and secondly to help them write better questions in the future. If it's doing that without putting posters off, I think it's completely fine.

In terms of the original question, it's disingenuous by the ordinary dictionary definition of the word ("not candid or sincere, typically by pretending that one knows less about something than one really does") but I don't think it's automatically rude.

Sometimes it's actually useful to approach it that way because sometimes at least what it seems the user is asking is not what they actually wanted to ask, and presuming you know less than you think you do may - in some cases - be more accurate, and perhaps less rude.

Answer 7

In math, I know that there is a lot that I don't know. If I make an assumption about something, I could very well be wrong.

For example, I think I understand the basics of calculus, but I'm not secure enough in that knowledge to teach it to someone else nor even to correctly guess what is meant when something is omitted.

In your integral example, I wouldn't be sure whether $dx$ or $dt$ is meant. Without Michael Hardy's answer, I wouldn't have even thought of $dy$ as a possibility.

For basic arithmetic, I might be more confident if I think the asker is unaware of operator precedence, but I still would not assume that someone who writes a - b/c meant (a - b)/c.

On the other hand, I think it would really be playing dumb if I were to say I honestly think $$\prod_{i = 1}^n 1 - \frac{1}{p_i}$$ could possibly mean $$\left(\prod_{i = 1}^n 1\right) - \frac{1}{p_i}.$$

Although of course coming from someone else that could be a genuinely sincere query that is misunderstood as sarcastic.

Maybe instead of saying "I don't understand X" it would be better to say "I think you meant to write Y rather than X." Then hopefully the response is either "I really did mean X" or "You're right, I'll change it accordingly," not "What the hell is your problem?"

Answer 8

Some people are not comfortable telling directly to others they are wrong. It can be because they are afraid to sound rude. Or simply because there is still a small possibility of they are the one that are wrong and are don't want to loose face. Then, "playing dumb" is not a snarky way to dismiss the OP and point out an obvious mistake, but a polite way to speak and a form of etiquette.

A real-life example: A highly reputed Japanese professor told me about his PhD student in that way: "He is really brilliant and very passionate. In life, he will always respect me and stay polite, but when we do maths together, he has no hesitation telling me directly when I am wrong".

A SE example: on another SE site about language with many non-native English users, someone answered one of my question starting by "I was trolling on the web to find an answer..." and I commented something like "There is probably a typo. You meant strolling I think". It appeared that I was wrong and the use of to troll here was correct. I would have felt embarassed if I had made a more direct comment like "Hey, you meant strolling on the web"

My opinion is that we should not think too much about people playing dumb. Most of the time, the OP will get the content of the comment, understand (s)he is wrong and correct the question. Or someone else will do it.