Matching level of answer to level of question

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.

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What do others think about this?

Answer 1

+1 for asking.

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.

Tastes differ here, so some of your answers will please some folks and displease others. Don't worry about it.

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

Answer 2

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 their 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 them an answer that offers a little more. Give them 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.

Answer 3

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).

Answer 4

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.

Answer 5

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.