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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
by ghshephard 11y ago
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, and almost certainly a significant portion of the class immediately dropping him.
[Edit - to be clear, I'm commending the instructor for not hanging their students out to dry by giving a mission impossible homework assignment]
- toothbrush 11y agoI 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.
- ghshephard 11y agoIt'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 allotted, which works out to no more than 12 minutes per question. Any questions you go over that 12 minutes, you need to steal from other questions and somehow solve more quickly, and remember, this is all new material for the student. If you blow your budget on math, it either comes out of other classes, or sleep. That's the context in which being thrown a heretofore unsolved problem in calculus is not particularly amusing for an undergraduate.
- paulpauper 11y agolet it go, man. You keep belaboring the point
- ghshephard 11y agoI 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 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.
- Kalium 11y agoWith that in mind, what do you think is the acceptable way to get students out of the answer-getting mentality?
- ghshephard 11y agoI think what the professor did was exactly correct, have them experience something new mathematically, but give them the heads up that they weren't (likely) to be solving it, as it's a new pattern they hadn't recognized before.
- kaitai 11y agoStudents 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.
- ghshephard 11y ago30 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.
- ColinWright 11y agoThis 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.
- ghshephard 11y agoMaybe I was just a lazy student in high school, but I don't ever recall stressing over math homework. I'm struggling now to remember if I even had math homework -presumably I did, but it didn't lay down any memories. But SFU (a not so bad University in Canada), - Calculus 151 in Images theater, and Calculus 152. I recall the workload in those two courses very, very distinctly. Both first year courses. In hindsight, I think they served the purpose of filtering out students who weren't prepared to work hard...
- to3m 11y agoI had courses like this as part of my degree, though of course the ones I had could easily turn out to be something completely different. If you're any good at maths, it's very possible you just never noticed that these courses exist ;) They seemed to be designed for people who hadn't done (or had done poorly at, or mature students who had forgotten the material for) later secondary school maths exams. This was university maths, in that it was maths, and you were at university, but in terms of the syllabus it was pretty much later secondary school standard, and there was very little emphasis that I can recall on preparing people for further study of maths. So no proving anything. Just telling you how stuff worked, and then a zillion exercises for you to do to try to make it stick.
- rgcase 11y agoSeriously? You think students would revolt after being given an interesting problem to think about for 15 minutes?
- ghshephard 11y ago"Without fair warning" That's the important part of this - the instructor didn't give it as homework. And yes, I've seen students freak out on their instructor en-masse for far less than a mission impossible homework assignment.
- omaranto 11y agoI'm guessing you've never taught math to undergraduates. Unless they are math majors, for the most part they really don't like being given harder-than-average questions, let alone open problems.
- relet 11y agoThe 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 professors fault.
- ghshephard 11y agoUndergraduates (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?
- ColinWright 11y agoI 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.
- superuser2 11y ago>They think they need to find the right process, apply it without making any stupid errors, get the answer, and move on. Perhaps because they've been conditioned for 12 years to believe that this is what "math" is.
- Nadya 11y ago
- iamcurious 11y agoI have done that occasionally. They complain, but only in jest.
- ghshephard 11y agoYou've handed out a math assignment that was an open unsolved problem and not told your students what you had done prior to them leaving for the day?
- chris_wot 11y agoYeah, their "jesting" involved the lecturer, vaseline, a flagpole and lots and lots of string beans.
- iamcurious 11y agoIt strikes me that you expect students to behave that way for challenging them. Maybe it is a matter of cultural differences? In my university, at the most they would complain to the administration. And even then the problem would have to be tied to their grade so they could make the case of unfairness.
- chris_wot 11y agoYour imagination immediately jumped to only bad possibilities.
- ghshephard 11y agoMy university had a pretty liberal withdrawal policy if you did so prior to mid-terms. Instructors who weren't competent, or who acted like jackasses, didn't get complaints - the students just dropped the class and focussed their energy on instructors who were both competent, and not inclined to sabotage them.
- iamcurious 11y agoYou've handed out a math assignment that was an open unsolved problem Yes. and not told your students what you had done prior to them leaving for the day? No. As the comment I responded to says: I reveal the full truth after they have been working for fifteen minutes or so.
- pjc50 11y agoCambridge used to do this routinely. Your university may vary.
- ghshephard 11y agoWhat year of student? Freshmen/Sophmore?
- pjc50 11y agoThere were a few unsolved conjectures presented on the board on occasions. What was more common, as a first year maths student, was to be presented with homework that had 10 questions on of which one would be marked "hard" and one "very hard". Some of the "very hard" questions would be unsolved research problems. Some interviewers would present unsolved problems in interviews as well, if a candidate was happily eating their way through the regular material. Cambridge is a little unusual in that the only mark that people cite is the one on the final year exam. I believe US universities operate by continuous accumulation of marks? And that ongoing disputes over marking are more common because of this? It's also already working with a highly selected group of people from the far tail of the ability distribution, and looking for a way to identify the exceptional among the merely very high ability.
- ghshephard 11y agoWhat you are describing is entirely fair. The student has been fairly warned that they might not be able to solve the problem in the 8-10 minutes that their incredibly packed schedule allocates to it. They aren't being blindsided by an unsolved research problem masquerading as a standard question on a problem set. Fair game.
- pbhjpbhj 11y agoI think so long as they say it must be independent work and give a time limit then it's fair.