Are we answering questions or teaching people how to answer their own questions?

Question

In this answer to another meta thread, Bill Dubuque raises the following point:

We should strive not only to give solutions to problems but also to teach how to solve problems. One of the important things to stress in that regard is that to succeed in mathematics requires sustained effort attacking problems. If students don't spend enough time chewing on problems before they post them here then they will not learn essential problem solving skills that are crucial to succeed as a mathematican.

Matt E comments:

Another comment: the question you raise could sensibly stand as the topic of its own thread, where it could be discussed more fully. It is related to, but not the same as, the older threads on homework. I think (but might be wrong) that there could be some tension between those who view this site purely in Q&A terms and those who have a more academic view of things, in which there are teachers and students, who stand in a particular relationship to one another. For this reason, I'm not sure that discussing this issue will be conclusive; but it may well be productive.

I think this is an interesting topic worth discussing. It seems to me that question askers on this site can roughly be divided into two categories:

• A student (say an undergraduate) asking about a topic which confuses her.
• A professional outside of mathematics asking about a topic which has come up in her work.

It is fairly easy to tell the two types of askers apart, and this particular discussion is about the first type of asker. In the long run, it is not necessarily a great idea just to answer all questions by an asker of the first type for precisely the reasons stated above. (Admittedly I have been somewhat guilty of this.) What should our policy be with respect to such askers? Should something go into the FAQ?

(Askers of the second type should, of course, be directed to appropriate resources as much as to a solution to their problem.)

Answer 1

My experience in other mathematical forums at this level leads me to believe that opinion will vary greatly on this topic. There will be some students who highly desire to learn problem solving techniques and others who simply want an answer. Likewise there will be some experts who truly care about teaching and others who are content simply serving complete answers on a silver platter.

Unfortunately the SE software does not lend itself well to teaching, since this requires more extended dialogues, starting with hints, etc. Moreover, inconsistency in the type of answers supplied can often lead to tension. For example, I often give hints rather than complete solutions. Sometimes these are not well-received because students expect the full answers supplied by other teachers. But others are reluctant to supply a full solution once they see a hint posted, so this leaves the student having no choice but to spend some real effort on the problem - as opposed to having that answer handed to them on a silver platter.

Such problems don't really arise to the same degree on SO because the subject matter is quite different. When one asks a question about how to do such-and-such in some programming environment one does really desire a direct answer. But in mathematics, the point of solving problems (esp. at this level) is not the answer but, rather, the learning experience - which often provides new insights. Indeed, in mathematics textbooks, the questions are explicitly designed to provide certain types of learning experiences, which is not the case for questions on most other SE sites. Unfortunately many students don't yet have the experience to realize how important it is to earnestly practice their problem solving skills on these well-crafted problems. Hopefully we can encourage them not to use this site in a way that robs them of these essential learning experiences.

Answer 2

I think this discussion is not framed right. Two of the core stackexchange principles are

1. the audience is the internet community at large, not the asker, and
2. the goal is to create definitive, high quality, timeless answers.

If you find a question interesting, answer it as best you can regardless of who asked it. If not, no worries, just move on.

These principles have been explicitly stated by the stackexchange and stackoverflow founders. Furthermore you see these principles in the design of the software at every level and how it differs from other online communication mediums.

A couple examples are that comment threads that get too long are hidden to discourage back and forth conversation (eg., the hint, attempt, hint, attempt, back and forth style), and answers can be edited and improved by different users than the original poster.

In his answer above, Bill Dubuque suggests these sort of things are flaws in the software - if only stackexchange was set up differently, then it could be a little online office hours session with all the academic cultural implications that entails. They aren't flaws, and this isn't a university classroom. They are intentional design decisions made to encourage a certain culture and posting style that sometimes conflicts with the traditional academic model.

Answer 3

I think answering questions and teaching can coexist. I cannot see why not. If the OP does not want a full answer, he can ignore it.

EDIT Let me summarize the situation.

(1) There are people who think giving a full answer is pedagogically harmful.

(2) There are people who think getting a full answer is pedagogically harmful.

(3) There are people who expect a full answer.

(4) There are people who would like to know various good answers to a question.

(5) There are people who would like to provide a full answer.

The people of (1) and (2) may or may not overlap and the people of (3) and (4) and (5) may or may not overlap. Please note that a question in this site is a public asset. It's not just used by the OP alone.

Please also note that there may be all the five kinds of people on almost every question. For example, suppose someone asks about the proof of the the Pythagorean theorem. I think there may be the people of (1), (2), (3), (4), (5) on this question. I think the situation is the same for a more advanced question.