Suggested Guideline for "I Don't Know Where to Begin" Questions

Question

We've all seen them: posts that ask the community members for help regarding a homework problem, lacking in any previously attempted work. Sometimes you can't blame the asker for not knowing where to start- most, if not all of us, have ran into these issues often enough at some point.

Having said that, I do suspect that there's a good deal of posters who have simply copied and pasted their assignments (sometimes in the form of an image file) to the post, without putting much- if any at all- effort into solving the problem. I think it's pretty reasonable to make this claim; however, it can be tricky to differentiate who really didn't know where to begin than who is just trying to dump a homework assignment on the community.

Thus, I write this post to pose a suggestion: Math.SE could petition its askers to at least write out a definition or two pertinent to the problem if they really don't know where to begin. After all, knowledge of the terms' definitions are (usually) a great starting point to understand just what the homework problem has given you, and what the homework problem wants back. If the asker doesn't know the definition (at times, it's just too obvious that's the case) then the help one offers isn't really enriching the asker's knowledge of mathematics. All one ends up doing is making the asker a poorer student.

If the asker did know the definitions, it would be easier for the community to highlight a proof or computation strategy, and would imply that at least the asker is learning something.

What do you think?

Answer 1

Tim Gowers has a series of blog posts on this topic and related topics. In one, he says:

Let me introduce a notion of fake difficulty. Every pure maths supervisor at Cambridge has had conversations like this:

Supervisee: I found this question rather difficult.

Supervisor: Well, what were your thoughts?

Supervisee: Erm … I don’t know really, I just looked at the question and didn’t know where to start. [By the way, never say that. Ever.]

He goes on to say:

This is a fake difficulty because it is not a legitimate reason to get stuck on a question. If you don’t know a definition, you can look it up. “I didn’t know where to start” is a well-known euphemism for “I was too lazy even to work out what the question was asking.”

That's how I read it too; I find the remark intensely annoying. Unfortunately, I don't think we are well-equipped to help these people, except perhaps by doing their homework for them. Someone who is faced with a question asking if $[0,1]$ is compact, and who is too lazy or disorganized to look up the definition of compactness, or even to ask a sensible question along the lines of “how can I understand compactness better?” is probably not going to benefit from gentle prodding or helpful suggestions.

If I had one of these three people in my office, I would ask them to write down the definitions, and we could proceed from there to have a discussion about it. On this web site, the users most in need of this kind of back-and-forth discussion are those least likely to participate in one, so I don't think we can usually help them. In the past I have often left comments 1 2 3 4 suggesting that the writer should start by writing down the definition of compactness; these comments are almost never answered. (Item 3 is a happy counterexample.) My current practice is usually to downvote the question (as a warning to other readers) and move on quickly.

I wish I could be more optimistic.

Answer 2

I think that one of the issues here is that we (professors, teaching assistants, private tutors) sometimes expect that by solving one problem, the student could deal with the same type of problems immediately.

But we forget that the underlying approach to a problem is something that have to be taught as well. Especially with abstract problems. This is why I always tell my students to work with the class notes near by, to begin by writing down the definitions, etc. and then see what exactly you have to do.

Back to the website. Depending on whether or not I can feel confident in my ability to assess the OP's difficulty, I might post a hint suggesting to verify the definitions with or without an additional hint as to how to proceed. If I'm less certain about how much the OP understands I might just leave a comment.

Sometimes, however, when I have the time and energy, I might write a longer answer showing how to verify the definitions and so on. You know, the sort of thing that in order to "copy-paste the answer" you'd have to work in order to extract a submittable answer, so you end up writing your own.

Of course it can be expected that other people have asked the OP in the comments what seems to be the issue, and this may affect the outcome. I could decide to vote to close, or I could better understand the difficulties of the OP.

Answer 3

I (like Asaf, it seems) try to base my behaviour on the site the way I teach in classrooms - this can be more or less straightforward depending on the situation.

One thing I stress in my classes is that it is a standard situation to be given a problem and not know where to begin, and I encourage students to tell me when this is the case. So I certainly don't want to discourage these kinds of questions on the site. However, rather than simply stating the problem, the question should ask specifically for help getting started, and the answers should provide this kick-start, rather than a complete solution. (I still maintain, although I know some other users disagree, that in most cases where the question is about an exercise from a book or a class, that the asker will learn more from answers that leave them something to do.) I guess I can't avoid talking about the "no-context" controversy, so I'll mention it briefly - I'm in favour of this close reason existing, and use it, but my requirements for context are fairly minimal, and can be met by the OP merely saying how much of the problem they could do before they got stuck, even if it was nothing.

Usually the first thing I ask in this situation, as you suggest, is whether the student knows the definitions - so I also tend to do this in a comment on the site. This also helps to establish the conventions being used in the asker's book/course (which one of several equivalent definitions are being used as a starting point, do rings have units, etc.) and adds more context to the question.

Once the definitions are established, I would usually give a hint on how to get started, and nothing more, so that the student has a chance to try something out and see if the problem clicks for them - they are always invited to come back to me for more help if they need it. This is a little harder to do on MSE, and can occasionally result in long threads of comments with the OP getting increasingly confused - particularly if my hint wasn't as good as I thought, as sometimes happens - but usually I think it works well.

Answer 4

This idea is emphatically not new. And has been repeated. This is why sometimes questions are closed as off-topic with the reason "Missing context": the prompt specifically directs the OP to visit the second link above to find out how to improve the question.

Its success, however, is debatable.