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How do I ask a good question about a topic I am not completely familiar with?
Whats the best way to write mathematical preliminaries for physics papers?General question about mathematical thinkingDesigning a mathematical physics classIn What order should I Learn math in?What do you do when you are completely lost during a proof?Most efficient way to learn mathematicsHow to learn about the Rubik's Cube?How to take notes on Baby RudinReading textbooks: do we have to prove every theorem?Should I figure something out before learning how? SELF STUDYGraduate School (Can I be a Mathematician?)
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$begingroup$
In my classes, it is easy as my professor would correct my question if it bad, or ask me to re-state it and I would learn something new if my question was good or bad. However, in this site I have found people have a little less patience when dealing with questions like this. Often, I find myself being bombarded by irrelevant things in the comments below that have nothing to do with my question, no help to help me with where the problem is and such. It is kind of demotivating seeing all this negative feedback when posting a question while it would take the same amount of time to suggest a fix on the question its self and help me understand what I am doing wrong.
soft-question
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
$endgroup$
|
show 5 more comments
$begingroup$
In my classes, it is easy as my professor would correct my question if it bad, or ask me to re-state it and I would learn something new if my question was good or bad. However, in this site I have found people have a little less patience when dealing with questions like this. Often, I find myself being bombarded by irrelevant things in the comments below that have nothing to do with my question, no help to help me with where the problem is and such. It is kind of demotivating seeing all this negative feedback when posting a question while it would take the same amount of time to suggest a fix on the question its self and help me understand what I am doing wrong.
soft-question
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
$endgroup$
$begingroup$
Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ?
$endgroup$
– Peter
11 hours ago
$begingroup$
math.stackexchange.com/questions/3276243/…
$endgroup$
– bguner
11 hours ago
$begingroup$
and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such.
$endgroup$
– bguner
11 hours ago
1
$begingroup$
The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post.
$endgroup$
– Micah
11 hours ago
1
$begingroup$
To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely.
$endgroup$
– Micah
10 hours ago
|
show 5 more comments
$begingroup$
In my classes, it is easy as my professor would correct my question if it bad, or ask me to re-state it and I would learn something new if my question was good or bad. However, in this site I have found people have a little less patience when dealing with questions like this. Often, I find myself being bombarded by irrelevant things in the comments below that have nothing to do with my question, no help to help me with where the problem is and such. It is kind of demotivating seeing all this negative feedback when posting a question while it would take the same amount of time to suggest a fix on the question its self and help me understand what I am doing wrong.
soft-question
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
$endgroup$
In my classes, it is easy as my professor would correct my question if it bad, or ask me to re-state it and I would learn something new if my question was good or bad. However, in this site I have found people have a little less patience when dealing with questions like this. Often, I find myself being bombarded by irrelevant things in the comments below that have nothing to do with my question, no help to help me with where the problem is and such. It is kind of demotivating seeing all this negative feedback when posting a question while it would take the same amount of time to suggest a fix on the question its self and help me understand what I am doing wrong.
soft-question
soft-question
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
edited 11 hours ago
David G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
13.4k4 gold badges19 silver badges37 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
asked 11 hours ago
bgunerbguner
344 bronze badges
344 bronze badges
$begingroup$
Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ?
$endgroup$
– Peter
11 hours ago
$begingroup$
math.stackexchange.com/questions/3276243/…
$endgroup$
– bguner
11 hours ago
$begingroup$
and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such.
$endgroup$
– bguner
11 hours ago
1
$begingroup$
The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post.
$endgroup$
– Micah
11 hours ago
1
$begingroup$
To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely.
$endgroup$
– Micah
10 hours ago
|
show 5 more comments
$begingroup$
Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ?
$endgroup$
– Peter
11 hours ago
$begingroup$
math.stackexchange.com/questions/3276243/…
$endgroup$
– bguner
11 hours ago
$begingroup$
and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such.
$endgroup$
– bguner
11 hours ago
1
$begingroup$
The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post.
$endgroup$
– Micah
11 hours ago
1
$begingroup$
To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely.
$endgroup$
– Micah
10 hours ago
$begingroup$
Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ?
$endgroup$
– Peter
11 hours ago
$begingroup$
Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ?
$endgroup$
– Peter
11 hours ago
$begingroup$
math.stackexchange.com/questions/3276243/…
$endgroup$
– bguner
11 hours ago
$begingroup$
math.stackexchange.com/questions/3276243/…
$endgroup$
– bguner
11 hours ago
$begingroup$
and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such.
$endgroup$
– bguner
11 hours ago
$begingroup$
and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such.
$endgroup$
– bguner
11 hours ago
1
1
$begingroup$
The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post.
$endgroup$
– Micah
11 hours ago
$begingroup$
The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post.
$endgroup$
– Micah
11 hours ago
1
1
$begingroup$
To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely.
$endgroup$
– Micah
10 hours ago
$begingroup$
To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely.
$endgroup$
– Micah
10 hours ago
|
show 5 more comments
3 Answers
3
active
oldest
votes
$begingroup$
First, I want to praise you for asking a good question here!
Alas, teachers and professors generally only encourage students to ask "clarification questions," and don't otherwise instruct students how to ask good questions. (Of course every teacher answers questions... a different matter.) There are even cultures in which asking any questions is discouraged because it is considered an affront to the teacher ("who didn't explain the material well enough"), or the student him/herself ("who couldn't understand what everyone else understood").
At least your teacher and you realize that some questions are good, others bad.
A meta-technique: listen closely to the questions from other students and figure out what leads to good questions.
Here are guidelines:
- Ask about extremal cases (what's the most? the least? the farthest? the closest? the biggest? the smallest?...) as appropriate to the topic.
- Ask about how one knows some fact is true (how can one prove that? what is the evidence for that?...)
- Ask about analogies (is this similar to X? to Y?...) or ask for an analogy (what other thing is this analogous to?...)
- Ask how some fact is used in the real world. If the fact is about the real world, as about the theory that gave rise to it.
- Of course if there is a particular matter or step in a teacher's explanation ask a clear, cogent clarification question.
- Always make your questions clear, relevant, and well stated. Don't ramble, or mixup lots of questions (some good, some not, some related, others not...). Avoid discursive, rambling questions ("I was thinking about triangles the other day and wondered about right triangles and realized I was taught proofs of the Pythagorean theorem, I know there are many such proofs, so I wondered if anyone knows which is the shortest proof." Instead: "What's the shortest proof of the Pythagorean theorem?")
Finally, do a YouTube search on my name, "TEDx", and "How to ask good questions" to see a video on this topic.
Good luck!
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
$endgroup$
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
add a comment |
$begingroup$
I haven’t looked back over your previous questions, so this may not be one of your vices. But I will say it all the same because some other reader may benefit.
DO NOT ASK PEOPLE TO DO THINGS
Ask people to help you do something, and they will be delighted to help, because they know that at the end of it you will know more than you did, all thanks to them. Help them help you. Show them what you have tried. Even ask them what technique would be best for solving this problem or that one. But don’t say “Solve it for me!”. It makes people feel murderous.
And (again I don’t know whether you fall into this trap, and probably you don’t) - do read your question and see if it makes sense to someone far away who can’t see you and can’t see what you are doing. It is tragic to see people asking how to find the value of $x$ when the problem they have described doesn’t have an $x$ in it anywhere!
And do be encouraged by the answers to this question to ask more questions in future.
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
$endgroup$
add a comment |
$begingroup$
None of these are meant to directly relate to your own questions, but they're things I think about both when asking and answering questions online (although I can always do better).
Understand the social contract
This is a tricky one to express clearly, partially because it depends a lot on where you're asking the question. In some places, like this site, the social contract may be expressly written - there are guidelines in the help center that tell you about things like questions to avoid, or what to do if no-one answers your question.
In other contexts, you may have to interpret the social contract based on observation, questioning and/or experiment - you try asking a question in class, and your professor tells you to make an appointment to discuss it; or you notice that there's a green button on each desk and the professor somehow knows who wants to ask a question, you press the button and get called on so you realise it's a paging system.
Be humble
You've come to ask a question. That means that whoever answers it will, hopefully, know more about the subject than you. Or at least they know something about the subject that you don't, namely the answer to your question.
In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points. The person answering the question doesn't normally gain much of real value by giving you the answer, so be polite when they answer and take their response in good faith - particularly noting some of the things I write later about cases where you might have gotten something wrong or expressed things unclearly, don't get annoyed at them for trying to understand your question better.
Additionally, if you're asking a question that relates to a more esoteric aspect of mathematical theory, don't expect an answer immediately (or possibly at all) - if there's only one person in the world who knows anything about doubly-invertible homeopathic hyperfields, what even are the odds that they frequent this site? (Actually, probably quite high if they're the kind of person who compulsively searches for things where they can jump in and show off their expertise, but you can't always count on it.)
Provide meaningful context
There are a few reasons why context is important to your question
Giving relevant answers
Think about the mathematical rules you learned in school, and how they evolved. At some point you were probably told "You can't subtract a bigger number from a smaller one", but then a few years later got told about negative numbers. Of course "You can't take the square root of a negative number", until you get introduced to the imaginary numbers and the complex plane. And while back in your formative years the question "Why is $1+1=2$ and $1 times 1 = 1$?" gets little more than "Because that's the rule", several decades later you may be introduced to binary numbers, field theory, or the set construction of arithmetic (or maybe just the classic $1 + 1 = $ 田.
By providing sufficient context for your question, people can answer it within that context, so you get the answer you actually need.
Identifying mistaken or alternative assumptions
Think about the question "Why is $pi = frac227$?". We know it's not actually true, but it's an approximation that is used often enough in schools that some people might reasonably think that it is. And so, while there's no answer to the question (since it's built on a false premise), if we know why the asker thinks that it's true we can help show them the truth, and possibly discuss the topic of how these approximations come about and what a good approximation is.
Answering the real question
This happens a lot in tech support type forums, but it can also happen in mathematics. You're trying to do X, and you've worked out that it looks like you can use Y to do so, but you keep hitting problem Z. So you go to the forum, and you say "Why doesn't Z work?". Sometimes, the answer is because Z never works, especially when you try to use it for X, because Y is the wrong tool for the problem.
If you come along and say "I'm trying to do X. I looked at approach Y, but keep hitting problem Z. Is there a way to get around Z or is there maybe a better approach to X?" then it's a lot more likely that you'll actually get a working solution to X, which is what you really wanted in the first place.
Demonstrating effort
This relates a little bit to the whole "People are doing this out of good will and/or a desire to show off knowledge" thing - we often want to reward people who have tried to figure the answer out for themselves first. Sometimes this is because answering no-effort questions breeds more no-effort questions and drowns out the actually interesting ones. Sometimes it comes from a belief that trying to solve a problem for yourself gives you a better understanding than spoon-feeding you the answer, and I think a lot of people here think of ourselves as being educators to some extent.
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
$endgroup$
add a comment |
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3 Answers
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3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
First, I want to praise you for asking a good question here!
Alas, teachers and professors generally only encourage students to ask "clarification questions," and don't otherwise instruct students how to ask good questions. (Of course every teacher answers questions... a different matter.) There are even cultures in which asking any questions is discouraged because it is considered an affront to the teacher ("who didn't explain the material well enough"), or the student him/herself ("who couldn't understand what everyone else understood").
At least your teacher and you realize that some questions are good, others bad.
A meta-technique: listen closely to the questions from other students and figure out what leads to good questions.
Here are guidelines:
- Ask about extremal cases (what's the most? the least? the farthest? the closest? the biggest? the smallest?...) as appropriate to the topic.
- Ask about how one knows some fact is true (how can one prove that? what is the evidence for that?...)
- Ask about analogies (is this similar to X? to Y?...) or ask for an analogy (what other thing is this analogous to?...)
- Ask how some fact is used in the real world. If the fact is about the real world, as about the theory that gave rise to it.
- Of course if there is a particular matter or step in a teacher's explanation ask a clear, cogent clarification question.
- Always make your questions clear, relevant, and well stated. Don't ramble, or mixup lots of questions (some good, some not, some related, others not...). Avoid discursive, rambling questions ("I was thinking about triangles the other day and wondered about right triangles and realized I was taught proofs of the Pythagorean theorem, I know there are many such proofs, so I wondered if anyone knows which is the shortest proof." Instead: "What's the shortest proof of the Pythagorean theorem?")
Finally, do a YouTube search on my name, "TEDx", and "How to ask good questions" to see a video on this topic.
Good luck!
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
$endgroup$
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
add a comment |
$begingroup$
First, I want to praise you for asking a good question here!
Alas, teachers and professors generally only encourage students to ask "clarification questions," and don't otherwise instruct students how to ask good questions. (Of course every teacher answers questions... a different matter.) There are even cultures in which asking any questions is discouraged because it is considered an affront to the teacher ("who didn't explain the material well enough"), or the student him/herself ("who couldn't understand what everyone else understood").
At least your teacher and you realize that some questions are good, others bad.
A meta-technique: listen closely to the questions from other students and figure out what leads to good questions.
Here are guidelines:
- Ask about extremal cases (what's the most? the least? the farthest? the closest? the biggest? the smallest?...) as appropriate to the topic.
- Ask about how one knows some fact is true (how can one prove that? what is the evidence for that?...)
- Ask about analogies (is this similar to X? to Y?...) or ask for an analogy (what other thing is this analogous to?...)
- Ask how some fact is used in the real world. If the fact is about the real world, as about the theory that gave rise to it.
- Of course if there is a particular matter or step in a teacher's explanation ask a clear, cogent clarification question.
- Always make your questions clear, relevant, and well stated. Don't ramble, or mixup lots of questions (some good, some not, some related, others not...). Avoid discursive, rambling questions ("I was thinking about triangles the other day and wondered about right triangles and realized I was taught proofs of the Pythagorean theorem, I know there are many such proofs, so I wondered if anyone knows which is the shortest proof." Instead: "What's the shortest proof of the Pythagorean theorem?")
Finally, do a YouTube search on my name, "TEDx", and "How to ask good questions" to see a video on this topic.
Good luck!
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
$endgroup$
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
add a comment |
$begingroup$
First, I want to praise you for asking a good question here!
Alas, teachers and professors generally only encourage students to ask "clarification questions," and don't otherwise instruct students how to ask good questions. (Of course every teacher answers questions... a different matter.) There are even cultures in which asking any questions is discouraged because it is considered an affront to the teacher ("who didn't explain the material well enough"), or the student him/herself ("who couldn't understand what everyone else understood").
At least your teacher and you realize that some questions are good, others bad.
A meta-technique: listen closely to the questions from other students and figure out what leads to good questions.
Here are guidelines:
- Ask about extremal cases (what's the most? the least? the farthest? the closest? the biggest? the smallest?...) as appropriate to the topic.
- Ask about how one knows some fact is true (how can one prove that? what is the evidence for that?...)
- Ask about analogies (is this similar to X? to Y?...) or ask for an analogy (what other thing is this analogous to?...)
- Ask how some fact is used in the real world. If the fact is about the real world, as about the theory that gave rise to it.
- Of course if there is a particular matter or step in a teacher's explanation ask a clear, cogent clarification question.
- Always make your questions clear, relevant, and well stated. Don't ramble, or mixup lots of questions (some good, some not, some related, others not...). Avoid discursive, rambling questions ("I was thinking about triangles the other day and wondered about right triangles and realized I was taught proofs of the Pythagorean theorem, I know there are many such proofs, so I wondered if anyone knows which is the shortest proof." Instead: "What's the shortest proof of the Pythagorean theorem?")
Finally, do a YouTube search on my name, "TEDx", and "How to ask good questions" to see a video on this topic.
Good luck!
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
$endgroup$
First, I want to praise you for asking a good question here!
Alas, teachers and professors generally only encourage students to ask "clarification questions," and don't otherwise instruct students how to ask good questions. (Of course every teacher answers questions... a different matter.) There are even cultures in which asking any questions is discouraged because it is considered an affront to the teacher ("who didn't explain the material well enough"), or the student him/herself ("who couldn't understand what everyone else understood").
At least your teacher and you realize that some questions are good, others bad.
A meta-technique: listen closely to the questions from other students and figure out what leads to good questions.
Here are guidelines:
- Ask about extremal cases (what's the most? the least? the farthest? the closest? the biggest? the smallest?...) as appropriate to the topic.
- Ask about how one knows some fact is true (how can one prove that? what is the evidence for that?...)
- Ask about analogies (is this similar to X? to Y?...) or ask for an analogy (what other thing is this analogous to?...)
- Ask how some fact is used in the real world. If the fact is about the real world, as about the theory that gave rise to it.
- Of course if there is a particular matter or step in a teacher's explanation ask a clear, cogent clarification question.
- Always make your questions clear, relevant, and well stated. Don't ramble, or mixup lots of questions (some good, some not, some related, others not...). Avoid discursive, rambling questions ("I was thinking about triangles the other day and wondered about right triangles and realized I was taught proofs of the Pythagorean theorem, I know there are many such proofs, so I wondered if anyone knows which is the shortest proof." Instead: "What's the shortest proof of the Pythagorean theorem?")
Finally, do a YouTube search on my name, "TEDx", and "How to ask good questions" to see a video on this topic.
Good luck!
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
edited 8 hours ago
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
answered 11 hours ago
David G. StorkDavid G. Stork
13.4k4 gold badges19 silver badges37 bronze badges
13.4k4 gold badges19 silver badges37 bronze badges
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
add a comment |
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
No matter in which culture a teacher works, a serious teacher should answer sensible questions as good as he/she can , this is the job of a teacher. Instead of videos, I would suggest to read articles. Wikipedia is often a good start , more details can ususally be found in the suitable books.
$endgroup$
– Peter
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
@Peter: See revised answer. Teachers answering questions is not the matter at hand. Likewise, reading articles do not teach how to ask good questions. You're assuming the student reading an article will magically come up with good questions. Four decades of teaching in elite colleges and universities shows me that is not the case.
$endgroup$
– David G. Stork
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
$begingroup$
A good answer (+1)
$endgroup$
– Peter
11 hours ago
add a comment |
$begingroup$
I haven’t looked back over your previous questions, so this may not be one of your vices. But I will say it all the same because some other reader may benefit.
DO NOT ASK PEOPLE TO DO THINGS
Ask people to help you do something, and they will be delighted to help, because they know that at the end of it you will know more than you did, all thanks to them. Help them help you. Show them what you have tried. Even ask them what technique would be best for solving this problem or that one. But don’t say “Solve it for me!”. It makes people feel murderous.
And (again I don’t know whether you fall into this trap, and probably you don’t) - do read your question and see if it makes sense to someone far away who can’t see you and can’t see what you are doing. It is tragic to see people asking how to find the value of $x$ when the problem they have described doesn’t have an $x$ in it anywhere!
And do be encouraged by the answers to this question to ask more questions in future.
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
$endgroup$
add a comment |
$begingroup$
I haven’t looked back over your previous questions, so this may not be one of your vices. But I will say it all the same because some other reader may benefit.
DO NOT ASK PEOPLE TO DO THINGS
Ask people to help you do something, and they will be delighted to help, because they know that at the end of it you will know more than you did, all thanks to them. Help them help you. Show them what you have tried. Even ask them what technique would be best for solving this problem or that one. But don’t say “Solve it for me!”. It makes people feel murderous.
And (again I don’t know whether you fall into this trap, and probably you don’t) - do read your question and see if it makes sense to someone far away who can’t see you and can’t see what you are doing. It is tragic to see people asking how to find the value of $x$ when the problem they have described doesn’t have an $x$ in it anywhere!
And do be encouraged by the answers to this question to ask more questions in future.
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
$endgroup$
add a comment |
$begingroup$
I haven’t looked back over your previous questions, so this may not be one of your vices. But I will say it all the same because some other reader may benefit.
DO NOT ASK PEOPLE TO DO THINGS
Ask people to help you do something, and they will be delighted to help, because they know that at the end of it you will know more than you did, all thanks to them. Help them help you. Show them what you have tried. Even ask them what technique would be best for solving this problem or that one. But don’t say “Solve it for me!”. It makes people feel murderous.
And (again I don’t know whether you fall into this trap, and probably you don’t) - do read your question and see if it makes sense to someone far away who can’t see you and can’t see what you are doing. It is tragic to see people asking how to find the value of $x$ when the problem they have described doesn’t have an $x$ in it anywhere!
And do be encouraged by the answers to this question to ask more questions in future.
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
$endgroup$
I haven’t looked back over your previous questions, so this may not be one of your vices. But I will say it all the same because some other reader may benefit.
DO NOT ASK PEOPLE TO DO THINGS
Ask people to help you do something, and they will be delighted to help, because they know that at the end of it you will know more than you did, all thanks to them. Help them help you. Show them what you have tried. Even ask them what technique would be best for solving this problem or that one. But don’t say “Solve it for me!”. It makes people feel murderous.
And (again I don’t know whether you fall into this trap, and probably you don’t) - do read your question and see if it makes sense to someone far away who can’t see you and can’t see what you are doing. It is tragic to see people asking how to find the value of $x$ when the problem they have described doesn’t have an $x$ in it anywhere!
And do be encouraged by the answers to this question to ask more questions in future.
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
answered 9 hours ago
Martin KochanskiMartin Kochanski
2,4464 silver badges12 bronze badges
2,4464 silver badges12 bronze badges
add a comment |
add a comment |
$begingroup$
None of these are meant to directly relate to your own questions, but they're things I think about both when asking and answering questions online (although I can always do better).
Understand the social contract
This is a tricky one to express clearly, partially because it depends a lot on where you're asking the question. In some places, like this site, the social contract may be expressly written - there are guidelines in the help center that tell you about things like questions to avoid, or what to do if no-one answers your question.
In other contexts, you may have to interpret the social contract based on observation, questioning and/or experiment - you try asking a question in class, and your professor tells you to make an appointment to discuss it; or you notice that there's a green button on each desk and the professor somehow knows who wants to ask a question, you press the button and get called on so you realise it's a paging system.
Be humble
You've come to ask a question. That means that whoever answers it will, hopefully, know more about the subject than you. Or at least they know something about the subject that you don't, namely the answer to your question.
In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points. The person answering the question doesn't normally gain much of real value by giving you the answer, so be polite when they answer and take their response in good faith - particularly noting some of the things I write later about cases where you might have gotten something wrong or expressed things unclearly, don't get annoyed at them for trying to understand your question better.
Additionally, if you're asking a question that relates to a more esoteric aspect of mathematical theory, don't expect an answer immediately (or possibly at all) - if there's only one person in the world who knows anything about doubly-invertible homeopathic hyperfields, what even are the odds that they frequent this site? (Actually, probably quite high if they're the kind of person who compulsively searches for things where they can jump in and show off their expertise, but you can't always count on it.)
Provide meaningful context
There are a few reasons why context is important to your question
Giving relevant answers
Think about the mathematical rules you learned in school, and how they evolved. At some point you were probably told "You can't subtract a bigger number from a smaller one", but then a few years later got told about negative numbers. Of course "You can't take the square root of a negative number", until you get introduced to the imaginary numbers and the complex plane. And while back in your formative years the question "Why is $1+1=2$ and $1 times 1 = 1$?" gets little more than "Because that's the rule", several decades later you may be introduced to binary numbers, field theory, or the set construction of arithmetic (or maybe just the classic $1 + 1 = $ 田.
By providing sufficient context for your question, people can answer it within that context, so you get the answer you actually need.
Identifying mistaken or alternative assumptions
Think about the question "Why is $pi = frac227$?". We know it's not actually true, but it's an approximation that is used often enough in schools that some people might reasonably think that it is. And so, while there's no answer to the question (since it's built on a false premise), if we know why the asker thinks that it's true we can help show them the truth, and possibly discuss the topic of how these approximations come about and what a good approximation is.
Answering the real question
This happens a lot in tech support type forums, but it can also happen in mathematics. You're trying to do X, and you've worked out that it looks like you can use Y to do so, but you keep hitting problem Z. So you go to the forum, and you say "Why doesn't Z work?". Sometimes, the answer is because Z never works, especially when you try to use it for X, because Y is the wrong tool for the problem.
If you come along and say "I'm trying to do X. I looked at approach Y, but keep hitting problem Z. Is there a way to get around Z or is there maybe a better approach to X?" then it's a lot more likely that you'll actually get a working solution to X, which is what you really wanted in the first place.
Demonstrating effort
This relates a little bit to the whole "People are doing this out of good will and/or a desire to show off knowledge" thing - we often want to reward people who have tried to figure the answer out for themselves first. Sometimes this is because answering no-effort questions breeds more no-effort questions and drowns out the actually interesting ones. Sometimes it comes from a belief that trying to solve a problem for yourself gives you a better understanding than spoon-feeding you the answer, and I think a lot of people here think of ourselves as being educators to some extent.
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
None of these are meant to directly relate to your own questions, but they're things I think about both when asking and answering questions online (although I can always do better).
Understand the social contract
This is a tricky one to express clearly, partially because it depends a lot on where you're asking the question. In some places, like this site, the social contract may be expressly written - there are guidelines in the help center that tell you about things like questions to avoid, or what to do if no-one answers your question.
In other contexts, you may have to interpret the social contract based on observation, questioning and/or experiment - you try asking a question in class, and your professor tells you to make an appointment to discuss it; or you notice that there's a green button on each desk and the professor somehow knows who wants to ask a question, you press the button and get called on so you realise it's a paging system.
Be humble
You've come to ask a question. That means that whoever answers it will, hopefully, know more about the subject than you. Or at least they know something about the subject that you don't, namely the answer to your question.
In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points. The person answering the question doesn't normally gain much of real value by giving you the answer, so be polite when they answer and take their response in good faith - particularly noting some of the things I write later about cases where you might have gotten something wrong or expressed things unclearly, don't get annoyed at them for trying to understand your question better.
Additionally, if you're asking a question that relates to a more esoteric aspect of mathematical theory, don't expect an answer immediately (or possibly at all) - if there's only one person in the world who knows anything about doubly-invertible homeopathic hyperfields, what even are the odds that they frequent this site? (Actually, probably quite high if they're the kind of person who compulsively searches for things where they can jump in and show off their expertise, but you can't always count on it.)
Provide meaningful context
There are a few reasons why context is important to your question
Giving relevant answers
Think about the mathematical rules you learned in school, and how they evolved. At some point you were probably told "You can't subtract a bigger number from a smaller one", but then a few years later got told about negative numbers. Of course "You can't take the square root of a negative number", until you get introduced to the imaginary numbers and the complex plane. And while back in your formative years the question "Why is $1+1=2$ and $1 times 1 = 1$?" gets little more than "Because that's the rule", several decades later you may be introduced to binary numbers, field theory, or the set construction of arithmetic (or maybe just the classic $1 + 1 = $ 田.
By providing sufficient context for your question, people can answer it within that context, so you get the answer you actually need.
Identifying mistaken or alternative assumptions
Think about the question "Why is $pi = frac227$?". We know it's not actually true, but it's an approximation that is used often enough in schools that some people might reasonably think that it is. And so, while there's no answer to the question (since it's built on a false premise), if we know why the asker thinks that it's true we can help show them the truth, and possibly discuss the topic of how these approximations come about and what a good approximation is.
Answering the real question
This happens a lot in tech support type forums, but it can also happen in mathematics. You're trying to do X, and you've worked out that it looks like you can use Y to do so, but you keep hitting problem Z. So you go to the forum, and you say "Why doesn't Z work?". Sometimes, the answer is because Z never works, especially when you try to use it for X, because Y is the wrong tool for the problem.
If you come along and say "I'm trying to do X. I looked at approach Y, but keep hitting problem Z. Is there a way to get around Z or is there maybe a better approach to X?" then it's a lot more likely that you'll actually get a working solution to X, which is what you really wanted in the first place.
Demonstrating effort
This relates a little bit to the whole "People are doing this out of good will and/or a desire to show off knowledge" thing - we often want to reward people who have tried to figure the answer out for themselves first. Sometimes this is because answering no-effort questions breeds more no-effort questions and drowns out the actually interesting ones. Sometimes it comes from a belief that trying to solve a problem for yourself gives you a better understanding than spoon-feeding you the answer, and I think a lot of people here think of ourselves as being educators to some extent.
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
$endgroup$
add a comment |
$begingroup$
None of these are meant to directly relate to your own questions, but they're things I think about both when asking and answering questions online (although I can always do better).
Understand the social contract
This is a tricky one to express clearly, partially because it depends a lot on where you're asking the question. In some places, like this site, the social contract may be expressly written - there are guidelines in the help center that tell you about things like questions to avoid, or what to do if no-one answers your question.
In other contexts, you may have to interpret the social contract based on observation, questioning and/or experiment - you try asking a question in class, and your professor tells you to make an appointment to discuss it; or you notice that there's a green button on each desk and the professor somehow knows who wants to ask a question, you press the button and get called on so you realise it's a paging system.
Be humble
You've come to ask a question. That means that whoever answers it will, hopefully, know more about the subject than you. Or at least they know something about the subject that you don't, namely the answer to your question.
In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points. The person answering the question doesn't normally gain much of real value by giving you the answer, so be polite when they answer and take their response in good faith - particularly noting some of the things I write later about cases where you might have gotten something wrong or expressed things unclearly, don't get annoyed at them for trying to understand your question better.
Additionally, if you're asking a question that relates to a more esoteric aspect of mathematical theory, don't expect an answer immediately (or possibly at all) - if there's only one person in the world who knows anything about doubly-invertible homeopathic hyperfields, what even are the odds that they frequent this site? (Actually, probably quite high if they're the kind of person who compulsively searches for things where they can jump in and show off their expertise, but you can't always count on it.)
Provide meaningful context
There are a few reasons why context is important to your question
Giving relevant answers
Think about the mathematical rules you learned in school, and how they evolved. At some point you were probably told "You can't subtract a bigger number from a smaller one", but then a few years later got told about negative numbers. Of course "You can't take the square root of a negative number", until you get introduced to the imaginary numbers and the complex plane. And while back in your formative years the question "Why is $1+1=2$ and $1 times 1 = 1$?" gets little more than "Because that's the rule", several decades later you may be introduced to binary numbers, field theory, or the set construction of arithmetic (or maybe just the classic $1 + 1 = $ 田.
By providing sufficient context for your question, people can answer it within that context, so you get the answer you actually need.
Identifying mistaken or alternative assumptions
Think about the question "Why is $pi = frac227$?". We know it's not actually true, but it's an approximation that is used often enough in schools that some people might reasonably think that it is. And so, while there's no answer to the question (since it's built on a false premise), if we know why the asker thinks that it's true we can help show them the truth, and possibly discuss the topic of how these approximations come about and what a good approximation is.
Answering the real question
This happens a lot in tech support type forums, but it can also happen in mathematics. You're trying to do X, and you've worked out that it looks like you can use Y to do so, but you keep hitting problem Z. So you go to the forum, and you say "Why doesn't Z work?". Sometimes, the answer is because Z never works, especially when you try to use it for X, because Y is the wrong tool for the problem.
If you come along and say "I'm trying to do X. I looked at approach Y, but keep hitting problem Z. Is there a way to get around Z or is there maybe a better approach to X?" then it's a lot more likely that you'll actually get a working solution to X, which is what you really wanted in the first place.
Demonstrating effort
This relates a little bit to the whole "People are doing this out of good will and/or a desire to show off knowledge" thing - we often want to reward people who have tried to figure the answer out for themselves first. Sometimes this is because answering no-effort questions breeds more no-effort questions and drowns out the actually interesting ones. Sometimes it comes from a belief that trying to solve a problem for yourself gives you a better understanding than spoon-feeding you the answer, and I think a lot of people here think of ourselves as being educators to some extent.
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
$endgroup$
None of these are meant to directly relate to your own questions, but they're things I think about both when asking and answering questions online (although I can always do better).
Understand the social contract
This is a tricky one to express clearly, partially because it depends a lot on where you're asking the question. In some places, like this site, the social contract may be expressly written - there are guidelines in the help center that tell you about things like questions to avoid, or what to do if no-one answers your question.
In other contexts, you may have to interpret the social contract based on observation, questioning and/or experiment - you try asking a question in class, and your professor tells you to make an appointment to discuss it; or you notice that there's a green button on each desk and the professor somehow knows who wants to ask a question, you press the button and get called on so you realise it's a paging system.
Be humble
You've come to ask a question. That means that whoever answers it will, hopefully, know more about the subject than you. Or at least they know something about the subject that you don't, namely the answer to your question.
In a place like this, answers are given out of some weird combination of actual altruism and an addiction to meaningless internet points. The person answering the question doesn't normally gain much of real value by giving you the answer, so be polite when they answer and take their response in good faith - particularly noting some of the things I write later about cases where you might have gotten something wrong or expressed things unclearly, don't get annoyed at them for trying to understand your question better.
Additionally, if you're asking a question that relates to a more esoteric aspect of mathematical theory, don't expect an answer immediately (or possibly at all) - if there's only one person in the world who knows anything about doubly-invertible homeopathic hyperfields, what even are the odds that they frequent this site? (Actually, probably quite high if they're the kind of person who compulsively searches for things where they can jump in and show off their expertise, but you can't always count on it.)
Provide meaningful context
There are a few reasons why context is important to your question
Giving relevant answers
Think about the mathematical rules you learned in school, and how they evolved. At some point you were probably told "You can't subtract a bigger number from a smaller one", but then a few years later got told about negative numbers. Of course "You can't take the square root of a negative number", until you get introduced to the imaginary numbers and the complex plane. And while back in your formative years the question "Why is $1+1=2$ and $1 times 1 = 1$?" gets little more than "Because that's the rule", several decades later you may be introduced to binary numbers, field theory, or the set construction of arithmetic (or maybe just the classic $1 + 1 = $ 田.
By providing sufficient context for your question, people can answer it within that context, so you get the answer you actually need.
Identifying mistaken or alternative assumptions
Think about the question "Why is $pi = frac227$?". We know it's not actually true, but it's an approximation that is used often enough in schools that some people might reasonably think that it is. And so, while there's no answer to the question (since it's built on a false premise), if we know why the asker thinks that it's true we can help show them the truth, and possibly discuss the topic of how these approximations come about and what a good approximation is.
Answering the real question
This happens a lot in tech support type forums, but it can also happen in mathematics. You're trying to do X, and you've worked out that it looks like you can use Y to do so, but you keep hitting problem Z. So you go to the forum, and you say "Why doesn't Z work?". Sometimes, the answer is because Z never works, especially when you try to use it for X, because Y is the wrong tool for the problem.
If you come along and say "I'm trying to do X. I looked at approach Y, but keep hitting problem Z. Is there a way to get around Z or is there maybe a better approach to X?" then it's a lot more likely that you'll actually get a working solution to X, which is what you really wanted in the first place.
Demonstrating effort
This relates a little bit to the whole "People are doing this out of good will and/or a desire to show off knowledge" thing - we often want to reward people who have tried to figure the answer out for themselves first. Sometimes this is because answering no-effort questions breeds more no-effort questions and drowns out the actually interesting ones. Sometimes it comes from a belief that trying to solve a problem for yourself gives you a better understanding than spoon-feeding you the answer, and I think a lot of people here think of ourselves as being educators to some extent.
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
answered 52 mins ago
ConManConMan
8,15714 silver badges24 bronze badges
8,15714 silver badges24 bronze badges
add a comment |
add a comment |
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$begingroup$
Usually, showing an effort (even an incorrect effort) is not bad received here. Basically, the community should have some evidence that the questioner has tried something. Of course, downvotes and closevotes are not always justified. Can you link particular such questions where you have the feeling this happened ?
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– Peter
11 hours ago
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math.stackexchange.com/questions/3276243/…
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– bguner
11 hours ago
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and a few more such as around 3 days ago, I asked why can a reducible Holonomy representation be indecomposable and asked what the meaning for reducible and indecomposable when talking about Holonomy representations and why we use two words to mean you can decompose the representation into irreducible subspaces. And the comments after 1 hour of waiting went something like: well of course we use two, and such.
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– bguner
11 hours ago
1
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The point of providing context is not (only) to show effort or to prove that you deserve to get an answer. It is (also) to specify what you're looking for precisely enough that random people on the internet who've never met you will be able to provide a helpful answer. I'd guess that people are downvoting the question you've linked because it's fundamentally impossible to answer without knowing a lot more detail about your paper than you've provided, and quite possibly more detail than it's possible to give in a forum post.
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– Micah
11 hours ago
1
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To put it another way, the set of questions which are good in a classroom or academic setting is larger than the set of questions which are good on the internet. Requests for "context" are generally intended to shrink that gap, but they cannot remove it entirely.
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– Micah
10 hours ago