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Famous Unsolved Math Problems as Homework

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Re: Famous Unsolved Math Problems as Homework

#11

Post by ghshephard »

relet wrote: post #5
ghshephard wrote: post #3

The most important part of this was, "When I use these problems for in-class work, I will typically pose the problem to the students without telling them it is unsolved, and then reveal the full truth after they have been working for fifteen minutes or so." Any professor who handed out that assignment to an undergraduate class without fair warning, would likely face a full scale revolt, possible threats of violence,…

The important part of this was: * Students are forced to depart from the “answer-getting” mentality of mathematics. * Students are forced to redefine success in learning as making sense and increasing depth of understanding. * Students are able to work in a context in which failure is completely normal. If your class tends toward revolt, they have been way too far strayed from the first point, and that may be the pro…

Undergraduates (at least for the first few years) have to be in the "Answer Getting" mentality. I'm fine with curve balls being thrown at graduate students, and maybe, just maybe, fourth year students, depending on the course - but can you imagine what a freshman/sophmore student would do if faced with this situation?

Re: Famous Unsolved Math Problems as Homework

#12

Post by ghshephard »

pjc50 wrote: post #8
ghshephard wrote: post #3

The most important part of this was, "When I use these problems for in-class work, I will typically pose the problem to the students without telling them it is unsolved, and then reveal the full truth after they have been working for fifteen minutes or so." Any professor who handed out that assignment to an undergraduate class without fair warning, would likely face a full scale revolt, possible threats of violence,…

Cambridge used to do this routinely. Your university may vary.

What year of student? Freshmen/Sophmore?

Re: Famous Unsolved Math Problems as Homework

#16

Post by privong »

amelius wrote: post #14

While these problems are interesting, it would be nice to have a little background on them. Where did they come from? What other problems would be solved by solving these problems?

The post links to the wikipedia pages for two of the problms, so it is pretty easy to get the background on them. At any rate, the point of the post was not those particular problems, but how the instructor uses them to challenge the students. I think digressions into why those problems are mathematically or practically interesting would distract from the main theme of the post.

Re: Famous Unsolved Math Problems as Homework

#17

Post by onion2k »

geon wrote: post #6

As a student in 1939, the mathematician George Dantzig once arrived late to a lecture. He mistook the unsolved problems on the blackboard for homework, and solved two of them. http://en.wikipedia.org/wiki/George_Dantzig

I imagine being told that a problem is unsolved changes the way you approach it. You'll assume that 'obvious' things have been tried before. Without that psychological barrier you can try out ideas that are obvious to you that might not have occurred to anyone yet. Telling someone that a problem is unsolved implies they won't be able to solve it unless they're better than all the people who've approached it before in some way. That isn't necessarily true; "better" doesn't really apply at the level of people attempting these problems.

Re: Famous Unsolved Math Problems as Homework

#19

Post by ColinWright »

ghshephard wrote: post #11
relet wrote: post #5

Earlier quoted context omitted.

The important part of this was: * Students are forced to depart from the “answer-getting” mentality of mathematics. * Students are forced to redefine success in learning as making sense and increasing depth of understanding. * Students are able to work in a context in which failure is completely normal. If your class tends toward revolt, they have been way too far strayed from the first point, and that may be the pro…

Undergraduates (at least for the first few years) have to be in the "Answer Getting" mentality. I'm fine with curve balls being thrown at graduate students, and maybe, just maybe, fourth year students, depending on the course - but can you imagine what a freshman/sophmore student would do if faced with this situation?

I disagree - in my experience the "answer getting" mentality is the largest barrier to doing "proper" math that there is. The students are unwilling to just try stuff to see what happens, because they think there's one way to do it, and one answer to find. They think they need to find the right process, apply it without making any stupid errors, get the answer, and move on.

That's a huge problem when you've trying to teach them about proofs, and kicking them out of that mentality is the biggest challenge in first year under-grad. This idea of letting them work for a limited time on an unsolved problem seems a useful approach to changing their attitude.

Re: Famous Unsolved Math Problems as Homework

#20

Post by chris_wot »

cschmidt wrote: post #13

In grad school, I had a graph theory professor who assigned a research problem he was stuck on as homework. He didn't tell us that until later, after I had a wasted a lot of time trying to solve it. It wasn't very cool.

What, you call that a waste of time?
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