How to Ask a Good Question

As many schools get into a new semester, this may be a good time to take a look at ways to use our service as effectively as possible.

What follows is an expansion of an entry in our Knowledgebase, which I wrote in the spirit of the 12 principles for writing a good answer that I posted in What It Takes to Be a Math Doctor last year. I wrote this, borrowing ideas from several other sites, based on our long experience with questions good and bad.

These are largely principles of good communication, and many will be applicable whenever you want to ask anyone for help. It’s important to be polite, to be cooperative, to have the right goals in mind, and to give them the information they need to help you.

Get our attention

In order to get a good answer from any site, you need to ask it clearly. Here are some keys:

1. Use a subject line that will get the attention of someone likely to have a good answer. It should be more specific than the category you specify: Don’t say “Math help” on a math site, or “Algebra” in the Algebra category, or “Help please!!!” anywhere, which tell us nothing; rather, say something like “Equation of a line” or “Rate problem” or “How can I factor a cubic?”. Briefly summarize the nature of your question.

On our site, we have a list of basic categories (Algebra, Calculus, …) into which to put your question. These don’t cover every possible topic, so don’t worry if you aren’t sure where it goes — we can move it if necessary. (Combinatorics questions, for example, often go reasonably under Probability, but may fit into Advanced Math too.) The title you give your question is more important, as it helps us decide which questions to read. Back in the days at Ask Dr. Math when we would get hundreds of questions a day, many were left unanswered, and those with clear titles would tend to get the attention. (I sometimes, though, deliberately looked at the ones with vague titles, figuring that those students might need help all the more.) Even today, the right title will often attract just the right Math Doctor.

2. Don’t omit important information from the body of the question and put it only in the subject line; sometimes we forget to read the subject. In particular, don’t start a sentence in the subject and continue it in the body. Similarly, do not include essential parts of the problem only in an attachment or picture without typing it in the body of the message.

Sometimes I have entirely missed the point of a question because the title was off my screen while I worked on it!

As for pictures, we may need to search for the content of a problem (e.g. to find previous questions about a current topic), and pictures can’t be searched for text; nor can we quickly scan for topics of interest. There may be someone who specializes in your topic, but he never sees it because he didn’t open the attachment!

Give us what we need

3. State the entire problem, in detail. If it is an exercise or assignment you were given, quote the whole thing verbatim (including the choices in a multiple-choice problem); and if you are asking only about a late step in a multi-step problem, tell us the earlier steps and your answers, so we can see if something went wrong there. Also tell us the context — what topic you are studying, or why you are asking.

Too often students have left out these details, resulting in wasted time until we realize that the key to a problem is a word that was omitted, or that the student misinterpreted an entire problem, so that the paraphrase we were given was nothing like what he had to do. You may think you are helping us by shortening a problem or focusing in on the one detail you are asking about, but seeing the full context actually saves us time.

Students often don’t realize how important the choices can be. Some problems really ask, “Which of these answers makes sense”, and don’t have a unique answer apart from the choices. In other cases, seeing the choices will help us understand what is being asked for – are they numbers or functions, for example? And quite often a student’s difficulty has been only that the correct answer is not in the list due to a typo, and we can’t tell that without them.

4. Show whatever work you have done, or at least tell us what you know that might be of use. This gives us a starting point in guiding you to a solution using what you already know. It’s important to understand that there are often several ways to approach a problem, and we will want to use the method you’ve been taught — which we can’t know unless you tell us. Also, tell us where you need help, and what went wrong.

For example, there are several different ways to factor a trinomial, so there are different kinds of errors you can make, and different kinds of advice we could give to avoid them. When you show enough work to let us see which method you are trying, we won’t be explaining how to do something you’ve never heard of, and don’t need to know. And if you have made a mistake in your work, we can focus our attention on that one step.

Have the right expectations

5. Don’t expect us to do your homework for you. Its purpose is to give you practice doing the math, not to see what someone else can do for you. (Would you go to gym class to watch a teacher do push-ups? No; it’s the teacher’s job to watch you do them, and give helpful advice.) In particular, we will not help you cheat.

We call ourselves “Math Doctors” because we like to observe you at work and “diagnose” your difficulty, then “prescribe” specific treatments for your particular problem. The treatment might be something to “eat”, or some “exercise” to do. But it’s up to you to do it.

We have too often been given an entire test without comment, or with a request that we provide solutions by a due date. All we can do then is to reply that this is not what we do! We can help you learn what you need to learn, but we will not earn for you the credits you need to earn.

6. Show that you have made an effort to learn; the more you say, the more effort we will put into helping you.

When you ask specific questions, that shows that you are trying to understand, and helps us be sure that our efforts will pay off. It also gives us more insight into your thinking, so we can more quickly focus on the help you need.

Stay focused

7. Keep a thread to one topic; if you have an unrelated question, don’t tack it on to your current thread. This not only makes our conversations easier to follow, but also gives you a better chance of getting an answer, because other Math Doctors who are available are more likely to help with a new question. A question in an existing thread is likely to be looked at only by its “owner”, who may not be available.

Sometimes we have had conversations that last for many days and up to a hundred messages. (Our old system couldn’t handle more than that.) Sometimes these can be useful, in that we get to know your needs. But after a while that becomes less effective, as we have to search for what you have previously said. It’s best to stay focused.

8. Don’t submit many questions at once, without waiting for an answer to the first couple; you are likely to learn how to do the later questions from our answers to the earlier ones. Especially, don’t ask the same question in more than one thread. If you want a different answer than we have given, tell us; someone else may join the discussion with a different perspective.

Submitting many separate questions can be as bad as submitting many questions in one message, because our answers to them may be redundant, and may unnecessarily tie more than one of us up. We are also happy to open a question to other Math Doctors, who can explain the same thing in other ways.

Make it clear

9. Ask your question in English; most of us don’t know most other languages. But if you have to translate a problem into English, it may help to also give the original form, so we can check its meaning. Also, avoid text-speak; abbreviations like “d” for “the” or “ur” for “your” don’t mix well with math symbols, and are likely to be misunderstood.

We often get questions from people for whom English is not their first language, and we try hard to work with them. I have found that often they are hesitant to say much (even though many of them use better English than many American students), but if you write more than you normally would, saying the same thing in multiple ways, we can understand you better. And when we see the problem in two languages, the same can happen: We (or Google) may not be able to translate it very well, but combining that with the student’s own imperfect translation can make it all clear. Redundancy helps in communication!

Math is a dense “language”, using symbols heavily, so a “d” or “u” in the middle of a sentence can look like a variable or an operation, and make it harder to read. We try to write the best English we can; you should do the same, for the sake of communication. (But don’t worry too much about spelling or grammar; just do as well as you can.)

10. Format symbols in a way that can be read easily. We hope to support LaTeX formatting in questions eventually, but don’t worry if you don’t even know what that is; see our article How to type math for standard ways to write formulas (such as “x^2” for x squared and “sqrt(x)” for the square root of x). Also, use parentheses to ensure that what you write means what you intend.

There are several kinds of formatting available, as shown in that knowledgebase article; choose the one you are most comfortable with. This includes a symbol button (Ω) and subscripts ($$x_2$$) and superscripts ($$x^2$$) on the edit toolbar, as well as images, which in some cases can be pasted in, while others may need to be attached. If necessary, upload an image of your handwritten work, as long as you also describe the problem in writing.

11. Be polite. Keep in mind that we are volunteers who are trying to help you. Help us to feel good about what we do. But if we goof, tell us (as gently as you can). We are also human!

Communication always works best between people who respect one another, and show it. We do the best we can, because we love doing this; but if we refuse to do something for you, or take longer than someone being paid would, please be patient. (And be aware that we may be in a different time zone than you, and sleeping!)

12. Feel free to ask any questions you have about math, not just about particular problems! On the other hand, sometimes an example can make it clearer what you are asking about, so be specific when you can, even about a general question. See the blog for examples of interesting questions we have been asked in the past.

For example, if you have a general question about polynomials, showing what you mean with a specific example will help us see what you mean.

For more good ideas on writing clear questions, see http://www.purplemath.com/modules/mathtext4.htm.

We look forward to hearing from you. Click on Ask a Question at the top or bottom of this page (or right here), and we’ll be waiting.

5 thoughts on “How to Ask a Good Question”

1. Hi, Precious.

This can be considered a 13th rule for asking a good question: Ask it in the right place, which is the Ask a Question page at https://www.themathdoctors.org/ask/. When you ask it as a comment, it’s harder to have the kind of discussion we like to have, and it’s a lot less private.

When you do so, be sure to also follow rules #3 and #4. A complete question will include instructions, which in this case is probably “Solve the equation,” and a careful copy of the problem, in which I think 0.5 is intended to be an exponent, so that the left-hand side is a square root. There may be additional information, such as a hint. In addition, I suspect that knowing the content of the section in which this problem was found might help both you and us find the best solution. I initially planned to square both sides, which looked like it would lead to a difficult equation; but as I wrote it out, I realized that the radicand is a perfect square. (That is an important hint, though it is not all the help you may need.)

Also, when you submit the problem, you should show whatever work you have tried, which will help me see whether you are on the right track, and what sort of help to offer.

I’ll be looking for your question in the Doctors’ Office.

1. PROBABILITY QUESTION:
What is the likelihood of, in roulette, NOT hitting a certain dozen of numbers for 20 times in succession please. This happened to me recently! I was playing on a European wheel containing 37 numbers (I.e. 1-36 (blacks and reds) and the green 0). The wagers were small but I was intrigued from a mathematical viewpoint! I thought it would (25/37)^20 or, in other words, (1- the probability of getting a hit from the dozen I wanted). I couldn’t get an accurate simplification percentage/fraction wise from my theory! If you could help, Dr.Math, I’d be very grateful! I did eventually get a ‘second dozen’ number on the 21st spin! Thanks. Steve.

1. This question really should have been submitted at our Ask a Question link (see my answer to Precious above). A partial answer can be found at another post, Should Rare Events Surprise Us?.

I agree with your calculation, which gives a probability of 0.0004, making it a rather unusual event. But such things do happen! Specifically, on average this should occur about once every 2542 attempts. I’m sure people play roulette often enough that what you observed happens frequently – but isn’t observed because no one is checking those 12 numbers!

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