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Famous Unsolved Math Problems as Homework

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Re: Famous Unsolved Math Problems as Homework

#41

Post by paulpauper »

ghshephard wrote: post #34
toothbrush wrote: post #28

Earlier quoted context omitted.

I can imagine the students now. All of them like, "omigod we're being forced to learn something by investigating things and being creative omigodomigod it has no known answer gasp". Yeah, that'd be embarrassing.

It's more like, "Student has a standard 15 credit semester, means 15 hours of classroom lecture + 45-60 hours of study/assignments outside of class. Student is micro-scheduling the number of minutes they have to answer each of the standard 20 Calculus questions (God, it was always 20 question) which they have to have in to the TAs before next lecture. 60 questions/week, every week, and you have about 12 hours allotte…

let it go, man. You keep belaboring the point

Re: Famous Unsolved Math Problems as Homework

#42

Post by kaitai »

ghshephard wrote: post #34
toothbrush wrote: post #28

Earlier quoted context omitted.

I can imagine the students now. All of them like, "omigod we're being forced to learn something by investigating things and being creative omigodomigod it has no known answer gasp". Yeah, that'd be embarrassing.

It's more like, "Student has a standard 15 credit semester, means 15 hours of classroom lecture + 45-60 hours of study/assignments outside of class. Student is micro-scheduling the number of minutes they have to answer each of the standard 20 Calculus questions (God, it was always 20 question) which they have to have in to the TAs before next lecture. 60 questions/week, every week, and you have about 12 hours allotte…

Students actually study that much these days?!

I don't see it!

Not being facetious or judgmental either. And there's strong pressure for calc profs these days to not assign more than 30 problems a week. Sensitivity about workload is very high at many institutions.

Re: Famous Unsolved Math Problems as Homework

#43

Post by ska »

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?

> but can you imagine what a freshman/sophmore student would do if faced with this situation?

Learn, in my experience.

Getting people to leave a mere "answer getting" mindset and engage with the "technique and problem understanding" mindset is one of the most important parts of the job of teaching freshmen and sophomores (particularly in mathematics). They've often been rewarded for this approach in high school and have trouble letting it go -- but it really constrains the ability to understand things.

The really sad cases are the ones who are really good at it, good enough to survive all the way to grad school sometimes. They aren't doing themselves any favors, and invariably get left behind by people who may have less innate talent but engage more. Hopefully recoverably.

Re: Famous Unsolved Math Problems as Homework

#45

Post by a_bonobo »

riffraff wrote: post #30
onion2k wrote: post #17

Earlier quoted context omitted.

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…

relevant: > When asked, "How could you possibly have done the first interactive graphics program, the first non-procedural programming language, the first object oriented software system, all in one year?" Ivan [0] replied: "Well, I didn't know it was hard." [0] http://en.wikipedia.org/wiki/Ivan_Sutherland

Or to quote Beyer's Grace Hopper and the invention of the information age:

>Common sense would dictate that the most experienced programmers should have been assigned to these difficult tasks, but, as Hopper glibly explained, young people did not know that they were supposed to fail.

Re: Famous Unsolved Math Problems as Homework

#46

Post by ghshephard »

paulpauper wrote: post #41
ghshephard wrote: post #34

Earlier quoted context omitted.

It's more like, "Student has a standard 15 credit semester, means 15 hours of classroom lecture + 45-60 hours of study/assignments outside of class. Student is micro-scheduling the number of minutes they have to answer each of the standard 20 Calculus questions (God, it was always 20 question) which they have to have in to the TAs before next lecture. 60 questions/week, every week, and you have about 12 hours allotte…

let it go, man. You keep belaboring the point

I was traumatized by my undergraduate calculus courses. And that was without the profs (who were all excellent) slipping in any "Unsolved Research problems." This entire thread has been like Trauma Trigger [http://en.wikipedia.org/wiki/Trauma_trigger]

I just want to make sure the undergraduate instructors reading this thread realize that doing this on the sly in a standard problem set would be a very, very bad idea. Not cool.

Re: Famous Unsolved Math Problems as Homework

#47

Post by ghshephard »

kaitai wrote: post #42
ghshephard wrote: post #34

Earlier quoted context omitted.

It's more like, "Student has a standard 15 credit semester, means 15 hours of classroom lecture + 45-60 hours of study/assignments outside of class. Student is micro-scheduling the number of minutes they have to answer each of the standard 20 Calculus questions (God, it was always 20 question) which they have to have in to the TAs before next lecture. 60 questions/week, every week, and you have about 12 hours allotte…

Students actually study that much these days?! I don't see it! Not being facetious or judgmental either. And there's strong pressure for calc profs these days to not assign more than 30 problems a week. Sensitivity about workload is very high at many institutions.

30 problems/week, 10/lecture would actually make calculus enjoyable, you could stretch out, and spend 20-30 minutes on some of the more challenging problems without freaking out.

Re: Famous Unsolved Math Problems as Homework

#48

Post by noja »

darkxanthos wrote: post #26
noja wrote: post #25

Earlier quoted context omitted.

Can you Google an equation?

You can to a degree. I've done it a bunch for my math classes. :) EDIT: Also wolfram alpha

So how does it look? Lots of parentheses? Are the special characters replaced with something?

Re: Famous Unsolved Math Problems as Homework

#49

Post by superuser2 »

This is great in class and for homework, but it can be taken too far. UChicago professors like to put open problems (without any indication that they are unsolved) on final exams. Half the battles is identifying which problems are unsolved to avoid wasting time on them.

Re: Famous Unsolved Math Problems as Homework

#50

Post by ColinWright »

ghshephard wrote: post #34
toothbrush wrote: post #28

Earlier quoted context omitted.

I can imagine the students now. All of them like, "omigod we're being forced to learn something by investigating things and being creative omigodomigod it has no known answer gasp". Yeah, that'd be embarrassing.

It's more like, "Student has a standard 15 credit semester, means 15 hours of classroom lecture + 45-60 hours of study/assignments outside of class. Student is micro-scheduling the number of minutes they have to answer each of the standard 20 Calculus questions (God, it was always 20 question) which they have to have in to the TAs before next lecture. 60 questions/week, every week, and you have about 12 hours allotte…

This sounds more like secondary school than university. Certainly for first year undergrad there are worksheets and a significant workload, but it sounds like you're describing what I think of as straight school-type work.
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