Matching level of answer to level of question

So, I finally retired, got stuck at home by illness, and got some time to use this site more regularly. I have taught at all levels from kindergarten to university undergraduate. I tutor high school, college, and university.

Obviously the approach varies depending on where the person is mathematically. When a colleague in a tutoring center asked me why something didn't work (a moment of brain freeze as happens to us all after a long day teaching) my answer was three words "It's not linear." Other times it might be "Check the determinant" or "Is it abelian?"

On the other hand, when a high school or junior college student is floundering with a new concept, or when someone presents a tricky question that applies basic math in unfamiliar way, I take the time to demonstrate the working process. My answer may be several paragraphs in length. I'm not here to show off my flashy quick tricks, I'm here to lead people through new and challenging ideas. They may be well-worn roads to us, but they are new and sometimes difficult slopes to the learner.

When many of my answers get flagged as "best answer" I figure I'm on the right track here.

Also there's an issue about the quality of questions. In university level work there's an expectation that the writer can present a clear statement of what is going on, for example "I don't understand how this author found the matrix inverse". In high school and junior high school, if the student just posts the text question, as long as the post is literate that's pretty good.

I've been criticized a few times for my answer being too long, even though the questioner appreciated it -- these answers were checked and upvoted. Also one question which I answered was put on hold. It is a question on Euclidean geometry and trigonometry and has several issues in it that make it challenging for the high school student. The question was perfectly consistent and clear, and the student asked for any hints or help because he had no idea how to start. I was able to outline a system to start, show an inconsistency in the student's statement, and show the first part of the solution. Yet certain advanced users put it on hold because according to them the question is incomplete or unclear, which I do not understand. Another student was heavily criticized because an algebra question was given with no context; but as I commented there as well as here, junior high students are asked every day to solve equations without context and this is part of the problem in the curriculum. The student should be praised for trying to make sense of the work, not put down.

Obviously there is no hard and fast rule as to levels of questions and answers. But I would like to suggest to all users especially the most advanced users that they give a little extra leeway to beginners, both in how questions are posed and in the amount of detail needed in an answer.

• You raise some good points. Just one clarification, the information "I am a high-school student. I was told to solve this problem as preparation for the upcoming Algebra II test." would count as context. It ought to be possible for the asker to give this type of information. It can be a problem if this type of context is missing, among others, for the reasons you mentioned at the start.
– quid Mod
Feb 9, 2017 at 9:11
• Is there a question here, victoria? Feb 9, 2017 at 11:36
• @GerryMyerson not every post on meta must be a question. Specifically, posting a call for discussion that is not strictly speaking a question is usually considered as alright on meta. Anyway it would be trivial to insert a question if you insist on the formality. Now, strict adherence to SE customs could suggest to post a question and self-answer it. But, that you would insist on this given your recently displayed permissive attitude regarding answers is more than a bit surprising.
– quid Mod
Feb 9, 2017 at 19:55
• @quid, I don't see a call for discussion here, either. I see an airing of views, and a suggestion to users, and no indication of any interest in hearing other opinions. Feb 9, 2017 at 21:59
• @GerryMyerson now there is.
– quid Mod
Feb 9, 2017 at 22:07
• I would like to know whether victoria finds the edit to be in the spirit of the original post. Feb 9, 2017 at 22:10
• @GerryMyerson a user wanted to share their experience on the site. I cannot see anything wrong with this. It would be trivial to shoehorn it into a question. I prefer a post that is upfront about this, over a rhetorical question.
– quid Mod
Feb 9, 2017 at 22:21
• Certainly there is a question: What do other users think about this? Starting an argument about whether I asked a question or not is hardly helpful. Anyone is welcome to agree, disagree, or add suggestions of their own -- hardly a closed statement. Feb 9, 2017 at 22:37
• A particularly frustrating example of this is when the asker expects a simpler solution than the situation necessitates, and the correct answer is either not posted or ignored. Feb 12, 2017 at 8:44
• One thing to keep in mind is that many participants are not from North America, and thus may not be very familiar with certain terms. I don't know how many times (over 10?) I've seen a question by someone mentioning "prealgebra" or who otherwise provides context that suggests he/she is on shaky grounds with what is covered in a first course in high school algebra, and someone answers by recommending Hardy's Pure Mathematics or Velleman's How to Prove it. I wonder if they may have thought "prealgebra" means having not yet taken something like Herstein's Topics in Algebra? Feb 13, 2017 at 19:38
• @enthdegree Or when the answer is left sitting in the comments and the question feels dead? Yeah, I feel frustrated too man. Feb 18, 2017 at 17:41

Thanks for contributing to help folks who need help.

I think explicitly tailoring hints and answers to the OPs level and needs is entirely appropriate. I try to do that too.

I too like and write wordy answers.

Welcome to retirement. See https://tex.meta.stackexchange.com/a/7217/12496

• Hooray for wordy answers! They are my bread and butter, typically. Feb 14, 2017 at 3:09
• Meh, this post isn't wordy enough for me. :P Feb 18, 2017 at 17:31
• @TheCount Thankfully we also have users who post very concise answers (and hints) that strive to reveal the general essence of the matter, so readers have some hope of seeing not only the moss and the trees, but also the majestic view of the entire forest, Feb 19, 2017 at 17:46
• @BillDubuque some users politely elbow me over my use of verbosity, so i was voicing my support. Feb 19, 2017 at 18:15
• Right you are, Ethan. I hope that at least half the time, my offerings don’t merely answer, but instruct and maybe even improve the understanding. Apr 5, 2017 at 5:24

Let me tell you I completely agree with you.

Somewhere I feel that we do reject questions too early due to lack of clarity or context. However, each time one such question comes up, I use a bunch of diagnostic tests to see the interest of the student who has posted the question. They go as follows:

1) If the question is provided with sufficient context, then I usually answer it, inferring from the context the ability of the student, and his possible interest in the subject. Most likely, if there is an attempt on the question, then I rectify the attempt in my answer.

2) If I know the user well (I do maintain black and white lists of users) then I decide on the spot whether or not to answer the question. Some high school students are on that black list, of not providing context, of note replying to my first comment (read below),of waiting for answers etc.

3) Sometimes, like you say, students are unable to post questions complete with context. This would happen either because the students simply want an answer, or sometimes the students are interested, but are not informed enough to provide context. In this case, I run the diagnostics:

a) I ignore the question if somebody else has made a significant comment (in which case, my contribution is like a duplicate, which is worthless) or has answered the question (which happens quite often, mind you).

b) I ignore the question if I do not see activity for more than one hour on that page, because this suggests a lack of interest. I could be wrong (A student types a question and goes to math class immediately, for example, hence no reply).

c) If none of the above happen, I leave a comment that typically goes like : "Where are you stuck?", "Start from definition" (and stating the required definition), "Try contradicting the statement" etc. However, if I see the student is thoroughly confused about something, then I normally leave a link to an article capable of clearing his confusion.

d) Once the student replies, first and foremost, offer encouragement. A little bit of confidence can do wonders. Then, I comment at most once more, and then if a reply comes through, I answer the question outright.

However, there is one general principle that I hold while answering such questions:

Invite the student for introspection. Give him an answer that offers a little more. Give him a flavour of mathematics. I ensure all my answers are at least five lines each, and add additional reading material wherever possible.

In general, I entertain high school questions in this fashion. Of course, you are the teacher, you know better than me, but I always follow the above rulebook for these questions.

• Why the downvote? I cancelled it. Feb 10, 2017 at 17:56
• @EthanBolker Why? Cancellation votes just distort the signal.
– Did
Feb 10, 2017 at 22:30
• @Did I voted up because I like the question, not just to cancel the downvote. My comment should have been clearer. WIth high enough rep you can see the whole signal: right now it's 2 up 1 down. Feb 10, 2017 at 22:37
• @EthanBolker Please make up your mind: either you voted on this to counteract a previous vote (as your comment seems to indicate) and then you are actively twisting one of the mechanisms the site is built upon, which is bad; or, you voted on this post solely for the merits you see in it, and then why even mention a previous downvote and why proudly declare you "cancelled" it?
– Did
Feb 11, 2017 at 8:36
• Does it matter if it's both? Why can't it be 'I think this post has merit, and also feel that downvotes are not warranted, so due to the merit I see in this post, I will happily negate it?' We're really being pedantic on meta today.... Feb 13, 2017 at 19:23
• I would like to have a conversation with the person who has down voted this. I don't mind changing my views if somebody on the site deems the above unfit for good reason, but I can't please everybody, and five up votes ($6-1$) gives me the impression (may be false!) that most people think this attitude is fine. Feb 14, 2017 at 5:15
• a) Personally, if the question sits with the only content being in the comments, I recommend answering the question with a community post after about 24 hours. This way, you won't get the rep but you will finish off the question so that future viewers know that answer has been answered. Feb 18, 2017 at 17:28
• b) Did you mean if the user who asked the question has not been online? You can check this by clicking their profile, and on the right side, there will be a "last seen ____ minutes/hours/etc. ago", which helps me judge users :-) Feb 18, 2017 at 17:30
• For that ending part there, I find some users do best in chat rooms, where they can feel less pressured and whatnot. I don't know about you guys, but I felt a tad bit of pressure when I was starting out young. Feb 18, 2017 at 17:33
• @SimplyBeautifulArt Thank you for your input,especially on part b). Feb 19, 2017 at 3:18
• Looking back, I stuck to this pretty well across the next five years. Jul 1, 2022 at 8:34

I think there are a couple of reasons (at least) for answers that are above the level of expertise of the OP.

The first is just plain elitism. In any area of learning, there are folks whose primary goal is to show that they're better than the masses, and they belong to the "in crowd". They scoff at anything elementary, and say things like "everybody knows that ...". Typical answers are written in the style of a serious professional mathematician, the way you might write a research paper or an old-fashioned textbook. This style looks austere and unfriendly, to me.

A second (probably unrelated) reason is that some people don't even think that the purpose of this site is to provide the OP with a comprehensible answer. These folks say that our purpose here is to build a repository of knowledge, and if our answers succeed in helping the OP, that's merely a side effect -- a bit of icing on the cake. I don't subscribe to this view at all, myself. I'm not smart enough to contribute significantly to the the Grand Repository, and I regard my answers purely as an attempt to help an individual who asked a question. But that's just my view, and there are plenty of people around here who think differently. We're probably all going to have to agree to disagree on this point.

So, that's two reasons I see, and I'm sure there are others. But, whatever the reasons for them, I'd guess that overly sophisticated answers probably discourage some people. It's a bit depressing to receive an answer that you can't even begin to understand. So, when we write an answer that's intended for posterity, rather than the OP, maybe we should mention this.

Bottom line ... use the site however you want, and expect others to do the same. Be a personal teacher or a repository builder, make your answers long or short, abstract or concrete, focused or comprehensive, elementary or sophisticated. Whatever you do, it won't make everyone happy.

• Awfully kind of you to give us permission to build the repository, but could you dial down the personal insults just the slightest bit, please? Feb 12, 2017 at 10:30
• @GerryMyerson -- I did try to dial it down (this is much nicer than the first version). Apparently I did not succeed. Feb 12, 2017 at 10:40
• I did some more dialing. If you tell me which parts you think are insulting, I'm willing to reconsider. Feb 12, 2017 at 10:46
• Certainly, everything from "elitists" to "ugly head". There's no reason to call people names, no reason to use inflammatory language, to make your points. You don't think people should post answers the questioner can't understand. Everything else is just venting. Feb 12, 2017 at 12:02
• I think a good advice is : "If you don't like to read it then don't read it". It is highly probable that the answerer isn't aware of the level of the OP and answers as he would to anyone of his level. The OP is not the only one to read the answer and so others could profit from this answer. Feb 13, 2017 at 12:48
• I have met some awful elitists in math. One , supposedly my calculus professor, screamed at me for thirty minutes not even allowing me to speak, the day I got out of hospital; gave me PTSD and destroyed my career in math. Twenty years later I met another woman who quit her PhD and re-started to get away from him. Destroying careers in general and women's careers in particular for several decades. This kind of attitude helps no one. I haven't seen anybody quite this bad on SE, thank you, but yes, a few people have very good forgetteries. We all did level 1 some time, no need to be harsh. Feb 13, 2017 at 17:50
• It all depends on the interpretation. When I get a comment like "Do you know the Sylow theorems?" I'm inclined to take it as an insult, but after a moment I realize that it is very probable a genuine question and there was no intent to insult. Feb 13, 2017 at 18:10
• If somebody asks me "Do you know the Sylow Theorems" my answer is "Been a while; let me check them out again." On the other hand "Do you know how to multiply?" would be insulting to just about everyone on this site. Times and places :-) Feb 13, 2017 at 22:34
• This post certainly has it's fanatics and detractors. $4$ up and $4$ down. I've not seen that too often! Feb 15, 2017 at 12:30
• I somehow agree with you, but as an user who many times was helped by this website I'd say that in my own experience I'm glad the there were not only answers matched the OP's level, but also some other different answers giving another insight about the question.
– Xam
Feb 15, 2017 at 17:20
• @астонвіллаолофмэллбэрг If +4 and -4 seems unusual, you can find many more posts here on meta with similar voting patterns. SEDE query: Most controversial posts on the site. You can find even a post which is close to 40 upvotes and 40 downvotes, like this one. (Sorry for digression to voting statistics.) Feb 16, 2017 at 14:08
• @MartinSleziak I think some of these posts are astoundingly one-sided. Thank you for this list. I find some of the mails so surprising, that in some sense I think these were expected to be heavily up/downvoted. Feb 16, 2017 at 23:11
• I myself can't agree with this answer, and as others have said, it is a tad bit offensive. To me, there are three main reasons I love and use this site: I enjoy helping others learn, I get to learn and practice the skills I have/don't yet have, and it's a good challenge for me. For example, I knew how to do integrals two years ago, and I'm sure I could've managed all the integrals in the class I'm currently taking, but with a year's worth of time on MSE and I can scoff off my calculus homework as extremely trivial. (it's quite a nice thing) Feb 18, 2017 at 17:40

It's pretty hard to nail down what makes an answer or question good, especially here on MSE. There are many different views and many different scenarios, and I myself have tried to improve the "How to answer" page without too much success.

My opinion on the subject of answer quality (not necessarily the same as on my list of possible improvements question) is that you should try to match each user, just as you would anyone in IRL. While much harder, I take it to be a general rule.

My second rule/opinion is that answers should not be overly complicated. As my username suggests, I love the simplest answers, as they are often all that is necessary.

This is not the same as a hint. Hints and answers are two different things, and so while I may prefer the short route, there must always be a level of content in my answer. For example, in a limit problem, I might post a one line solution, something along the lines of

$$\frac{x+\sin(x)}{x}=\frac xx+\frac{\sin(x)}x$$

Both clear enough and done with enough content to qualify as a good answer.

As per new users, there is much discussion about that as you will find, and my personal opinion is to be "temporarily harsh" to them. Perhaps unlike many users, I repeatedly revisit questions I've already seen, so if I see a "bad" question i.e. lack of content, lack of effort, etc., I will downvote. If I come back and it's been improved, I will remove my downvote. If it hasn't, I may vote to close. If there is significant improvement on the OP's part, I will even upvote. This way, I am both punishing and rewarding without causing a negative impact in the long run on the OP (I hope).

• I hope that you provide a bit more than the single line of the solution? Otherwise it might come across as brusque. A sentence or two leading into your suggestion (e.g. "I suspect that you're making X mistake. Have you considered the following: <one line solution goes here>") goes a long, long way. Both mechanically, in that it helps the reader to frame the problem correctly, and emotionally, because very short answers often seem disinterested. Feb 19, 2017 at 8:31
• Of course, but I just made an exaggeration to prove a point. (Good point about the end with emotion and disinterest) Feb 19, 2017 at 11:44
• I like the dynamical aspect in the last paragraph ... at least, we're all sensing entities ... Feb 19, 2017 at 23:55

I take the view that besides an answer that's appropriate for the particular OP, there should also be answers given that would be appropriate for other people who could have the same problem but are at a different level. The OP will, after all, just read the answers within a day or so and leave, while the answers and question will remain here for a very long time for the benefit of the entire planet.

I do think that the given answers are typically biased in favor of using more advanced math. So, we need to do an effort to also include answers using primarily elementary methods that are suitable for children in school, even at primary school level if at all possible.

• The terms of service say one is supposed to be at least 13 years old to use this website, so I don't think primary school level comes into the discussion. Feb 22, 2017 at 2:37
• @GerryMyerson There are questions like "My son who is in primary school got problem X and could not solve it and I do not know how to explain this to him" So that level may come, though it is not common. Feb 22, 2017 at 6:34
• I started using this website at the age of twelve with adult supervision. Now I do not need it (I'm thirteen), but as far as possible I am extremely open to answering questions at the primary level in the most elementary fashion. We do encounter simple questions such as simplification of square roots and as @MalayTheDynamo has said, teachers have asked for simplified explanations of concepts on the website. If somebody took the effort to answer my questions in primary level, then it is only fair that I repay that faith, whether on Stack Exchange or outside. Feb 23, 2017 at 3:19
• Having said the above, if the question lacks context or reflects a lack of effort, then I certainly do not push myself to answer it. There is an etiquette to asking questions, and we have to adhere to it on the website, regardless of whether that question is at the primary level or at the post graduate level. Feb 23, 2017 at 3:20