Challenging Yourself to Answer Questions: How Often Should You Do It?

[JasonRox]

Alright, this is just a general question.

Most of the time in class, I always bring up interesting questions. Sometimes I figure them out in just a short while, or sometimes I just have strong evidence in favor of my statement (not a proof though...yet).

Anyways, most of the time the professor just challenges me into looking into it myself, which I occasionally do just for the sake of knowing or being more accurate. This is obviously good advice.

My question is, for students who experience this or who have experienced the idea of asking questions (mostly after class) and being challenged to answer them yourself.

How often do you answer them?

Some of the time, I just dismiss them without any need of knowing.

Should I answer them for my own sake?

 

[mathwonk]

hi jason,

that is a great question. i think you should always try to answer them yourself.


you may not always succeed, but if you do not, you then have a better reason to raise them to the teacher again, perhaps with reports of your partial success.


when this has happened to me, my teachers have sometimes ridiculed my interesting questions, making me angry, and sometimes answered them, thus depriving me of the chance to solve them myself, and sometimes simply sent me off to think about them as yours does. In fact the best teacher in our department for years was famous for never directly answering any question.


sometimes I have solved them myself, sometimes not. the ones that persisted for years are in fact the ones that gave me the most pleasure.

as to why a teacher would persistently fail to answer your questions, there are several possibilities.

best is they realize you will benefit from answering them, another possibility is that your question is over the heads of the rest of the class and inappropriate for class time, another is the teacher does not know.

but if they interest you enough to ask them,. they should interest you enough to think about them.

many questions on this forum are of the type: i have thought about this and come to the following conclusions, where am i going wrong? or am i on the right track?

of course many other questions are simply "please tell me what the answer is to this problem" which are less fun to answer.

 

[mathwonk]

if you continually pose questions for other people but do not choose to think about them yourself, you come across as intellectually lazy, or dilettanteish, and not inclined to work.
the correct answer to a question is actually an indication of what direction you should work into find an answer, not just giving you an answer.
many people on this website excel in giving such good partial answers to questions. one of my own failings is a tendency to completely answer a question myself, not having the patience to wait for the questioner to find his own way.
once in my office i answered a students question very clearly and carefully, and expected to be praised for making it so clear and simple.
instead the student seemed depressed and said, "gee i must be stupid not to have seen that." I had made it look so easy they thought they were to blame, instead of crediting me. so it was a poor answer for that student, since discouragement is not the desired result of an answer. and i did not get the thanks i wanted either.

 

[JasonRox]

Well, I do dismiss some of them as not being pleasant though.
Those that I do find interesting I usually stick to it.

It just doesn't seem possible to answer all of them. I have dozens everyday. I worked them out a lot of times and some of them I really do want to know, hence I think about them.

There is so many, I can barely even remember some of them. It would be impossible to write them all down to solve later. (They are uncountable. )

Now, it may seem like I never shup up with questions, but I only ask a few. A lot of them are kept to myself. Those that I ask are countable.

Anyways, I'll keep a bigger eye on solving interesting ones from now on.

 

[JasonRox]

if you continually pose questions for other people but do not choose to think about them yourself, you come across as intellectually lazy, or dilettanteish, and not inclined to work.
the correct answer to a question is actually an indication of what direction you should work into find an answer, not just giving you an answer.
many people on this website excel in giving such good partial answers to questions. one of my own failings is a tendency to completely answer a question myself, not having the patience to wait for the questioner to find his own way.
once in my office i answered a students question very clearly and carefully, and expected to be praised for making it so clear and simple.
instead the student seemed depressed and said, "gee i must be stupid not to have seen that." I had made it look so easy they thought they were to blame, instead of crediting me. so it was a poor answer for that student, since discouragement is not the desired result of an answer. and i did not get the thanks i wanted either.

I don't think I'm coming off as intellectually lazy because I occasionally asnwer them as we discuss about it.

Although I will certainly keep an eye on that too, I don't want to be considered intelletually lazy. That wouldn't be a good reputation at all.

I noticed that some students hate it when you make it sound easy. It's not their fault and I understand why one would feel that way. I learned not to feel this way though. I've learned to accept being wrong is completely normal. The important is to correct that wrong.

It'd be nice to have people to discuss all the interesting questions with, but at my school... no one is interested, which is sad because some are math majors. I'm thankful to have profs that give me 5 minutes after class though.

 

[VietDao29]

It'd be nice to have people to discuss all the interesting questions with, but at my school... no one is interested, which is sad because some are math majors. I'm thankful to have profs that give me 5 minutes after class though.

Then, why not to bring up some of your interesting questions, and have a little nice discussion here?

 

[JasonRox]

Then, why not to bring up some of your interesting questions, and have a little nice discussion here?

Sometimes they aren't easy to explain.

It can be a pain in the @$$ describing something too.

 

[honestrosewater]

I do that all the time and don't have any teachers, so unless I turn to the lovely people here at PF, I have to chase down answers myself. I don't think I've ever regretted following an interesting question on my own -- wherever it ended up leading me -- since I get to learn interesting things, which is often useful and always fun, and develop other valuable skills. But depending on how much time it takes, figuring out something on your own that ends up being addressed a few pages later in the book (or in the next class) might not be the best use of your limited time. I just write down questions as they come up, read through them (minutes or months) later, and follow whichever ones remain unanswered, are still interesting, and that I think I could learn something (or the most) from. I imagine the less time and energy you have, the more selective you need to be.

(In addition to regular note-taking, I love using 5"x8" note cards as bookmarks for this, jotting down the thought or question and the page number I was on when it occurred to me.)

How often do you answer them?

I don't think mine are usually the kinds of questions that have definite answers (isn't that what makes them 'interesting'?), or if I do wind up with a definite answer, it's not usually to the original question, but to some refinement of it.

Should I answer them for my own sake?

If you have the spare time, enjoy it, or want to be able to answer more questions on your own in the future, I'd say yes.

 

[JasonRox]

I don't think mine are usually the kinds of questions that have definite answers (isn't that what makes them 'interesting'?), or if I do wind up with a definite answer, it's not usually to the original question, but to some refinement of it.

Well, the subject I'm talking is about mathematics. The definite answers exists, usually.

A question can sometimes be well beyond the scope of the class when it comes to mathematics, however simple it may be. i.e. Fermat's Last Theorem.

I answer a lot of them. I seem not to bother with the obvious.

 

[honestrosewater]

Well, the subject I'm talking is about mathematics. The definite answers exists, usually.

Heh, yeah, I noticed that after I posted. Maybe keeping a list of them and reading it over every now and then could help you notice any (e.g. truth-functional) relationships between them.

 

[Dr Transport]

A famous dead physicist by the name of Paul Ehrenfest once said "The only questions worth solving are the ones you ask yourself", so keep asking the questions...

 

[JasonRox]

A famous dead physicist by the name of Paul Ehrenfest once said "The only questions worth solving are the ones you ask yourself", so keep asking the questions...

No need to include the word dead.

Wisdom doesn't accumulate after you die.

Yes, I totally agree.

I answer the ones that are worth answering. One day I'll post questions of what I mean.

 

[PRodQuanta]

I admit that I sometimes stray away from those challenging questions. I have found myself wondering so many things that I sometimes get too far off track from where I started.

Other than that, always figure your own questions out.

Paden Roder