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My question is focused on thinking that MSE is a "temptation" for students, that is, many prefer to search or ask directly for the answers to their exercises here before trying it on their own.

MSE could affect the development of mathematicians? Do you think MSE helps more than it hurts?

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    $\begingroup$ Doesn't your argument apply to any resource where answers can be found though? Say... a library? Or an answer-set from a course provided by students who've already taken it? Why are you singling out MSE in particular for your question? $\endgroup$
    – postmortes
    Jul 20 at 5:02
  • $\begingroup$ It is not that it is pointed out or against MSE (on the contrary). I am only surprised by the number of solved exercises that can be found on the site, and I wonder if that does not encourage students not to try to do the demonstrations on their own (I say this because I have done it myself). $\endgroup$ Jul 20 at 5:09
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    $\begingroup$ Even before the internet age there are students who copied from their classmates every morning, and students who insists on working on their own. $\endgroup$ Jul 20 at 5:37
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    $\begingroup$ I was about to upvote based on your closing line says, "does MSE help more than hurt?", then noticed that your title has a contradictory thesis, "is MSE bad?". So I didn't vote, and can't tell what the first voter's position is. $\endgroup$
    – ryang
    Jul 20 at 6:12
  • $\begingroup$ I think the question is valid +1. As far as getting quick help with homework (which could deter students from struggling on their own, and thus learning deeply), in some contexts MSE is much more "effective" than other resources such as a library or classmates. $\endgroup$
    – Dan
    Jul 20 at 9:31
  • $\begingroup$ it happens that one usually finds himself with this type of question and it is obvious that it will not be the only case :math.meta.stackexchange.com/questions/2012/… $\endgroup$ Jul 20 at 16:23
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    $\begingroup$ You ended asking how math.se could affect future mathematicians. All the mathematicians I know jealously guard a good problem, and will take it to others only after they have gnawed off all the meat they could find on the bone. $\endgroup$ Jul 20 at 23:41

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Okay, I am just like an average learner but I'd like to share a piece of my mind on this. I think there is an element of truth when it is suggested that MSE usage should be abstained so one can think themself, but usually what comes in an exams or tests is not about how original one is but rather how well one can pattern recognize certain ways of solving questions/ proofs and repeat it .

In my personal opinion, if MSE makes the problems too easy for students, it may be time to trying giving problems to students which are more difficult and requires information of many different areas / MSE posts to answer.

Also, I don't really see the idea behind punishing a person by calling them a cheater because they are using every resource possible to them. In real world, the success would be measured by that instead of being able to blinding one self to search only in a textbook, right?

Anyways, big disclaimer: Just my opinion.

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    $\begingroup$ Don't mean to offend, but, I feel like people saying MSE is making things too easy is like those boomer memes where the grandparents which are like "Back in my day, I had to cross mountains by foot to reach school" and saying that it is a negative thing that one actually gets thing easily due to technology $\endgroup$ Jul 20 at 21:50
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    $\begingroup$ In the real world, using every resource can get you jail time, if those resources amount to theft, blackmail, insider trading, and so on, and so on. In academia, using every resource can get you in real trouble, if those resources involve plagiarism and such. $\endgroup$ Jul 20 at 22:49
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    $\begingroup$ Of course, this is in the context of tests and expanding human knowledge. I believe the idea of 'test' is in itself outdated and technology has developed beyond it. Imagine going back in time when calculators were discovered and the people saying one can't use calculator because it halts one's calculative ability growth... well I guess it does, but we have developed beyond that.. Nonetheless, I don't think there would come a point in real life wherea mathematics student would be asked to show a particular proof/ theorem offhand (excp. teaching, and there I've seen teacher themself see notes.. $\endgroup$ Jul 20 at 22:59
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    $\begingroup$ Schools use testing that disallows calculators precisely because one must understand intuitively and mechanically what is going on with the numbers, in order to understand those operations generalised to arbitrary objects. It is certainly defeating the purpose to use a calculator then, or to use "every resource possible" by Googling for the answers without actual effort. Similarly, trying to prove a theorem or solve a problem is to demonstrate how well the actual theorem problem is understood, and precisely where the person lacks; if it was as simple as using Google, we may as well not bother! $\endgroup$
    – Nij
    Jul 20 at 23:48
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    $\begingroup$ I really wish it was as you said, but most of the time it is just calculations for calculations sake rather than trying to find empiric number theory results or trying to figure out any general pattern. The point of challenging the student should be to push the student into a direction where they do stuff which is not done yet/ stuff they feel actually engaged about rather than repeating what has been said 100s of years before. This could involve asking difficult problems which students may need to discuss and work in groups to solve, and involve the students presenting the soltn (contin) $\endgroup$ Jul 21 at 1:41
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    $\begingroup$ in formats other than written. Perhaps a presentation / oral explanation or so. I think it does a student a long term harm to ask them to refrain using online sites for homework. Imagine in the long term they actually have a problem they need help on, should they just sit their and give up for the "virtues of math" or should they actually find the answer on SE and move on to something which interests them more..? $\endgroup$ Jul 21 at 1:41
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    $\begingroup$ Homework problems are not "real world problems" in the sense that they are not ends in themselves, only means to achieve something else. You don't solve them just to have them solved, but to make sure you read, review, and digest the material you just learned. So if a student is to "use every resource available to them", it should not be for "finding the answer", but learning the math, the nitty gritty details of definitions, the intricacies of the examples, the proof techniques, etc. These can't be gained by simply looking up an answer, not even if you can understand and reproduced the proof. $\endgroup$
    – Elliot Yu
    Jul 21 at 14:23
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    $\begingroup$ In a word, math is not a spectator sport. $\endgroup$
    – Elliot Yu
    Jul 21 at 14:24
  • $\begingroup$ On the other hand, I also don't believe punishment solves the issue. Ultimately it may not encourage the student to actually explore the math. Here are some better ideas from an answer (and its comments) in post linked by OP. $\endgroup$
    – Elliot Yu
    Jul 21 at 14:25

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