Timeline for Is there evidence whether undergraduate math courses improve problem-solving?
Current License: CC BY-SA 2.5
21 events
| when toggle format | what | by | license | comment | |
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| Feb 11, 2011 at 16:46 | vote | accept | Anna Varvak | ||
| Feb 11, 2011 at 11:47 | history | edited | Greg Kuperberg |
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| Feb 11, 2011 at 7:48 | comment | added | Yaakov Baruch | there is evidence that mathematicians lag in practical problem solving skills, for which they overcompensate by doing rock climbing. | |
| Feb 11, 2011 at 7:01 | comment | added | Harry Gindi | @Arnav: "not infrequently"... If George Orwell were alive to see this, he'd rolling in his grave (simultaneous George Orwell and Black Dynamite reference. Probably the first ever!). | |
| Feb 11, 2011 at 6:48 | answer | added | JRN | timeline score: 5 | |
| Feb 9, 2011 at 2:34 | comment | added | Deane Yang | Steven, agreed! | |
| Feb 9, 2011 at 1:51 | comment | added | Steven Gubkin | Generally the sort of mathematics courses which are required for graduating are calculus courses where memorizing a list of rules are all that is required. I do not think such courses contribute to problem solving or logical reasoning skills at all. They do contribute to intellectual stagnation and an attitude that you should believe what authorities tell you. Of course not all calculus courses are like this - I would not be in grad school if I had such a course as a high school student. For some reason it seems like most of them are this way though. | |
| Feb 8, 2011 at 23:04 | comment | added | Michael Lugo | Kevin: perhaps math majors tend to do well on the LSAT. But is that mean that math courses give someone the sort of intelligence needed to do well on the relevant section of the LSAT, or that the sort of person who has that sort of intelligence already is likely to become a math major? (I'm guessing it's some combination of the two. I'd like to think it's at least partially the first, because I like to think that some of what I'm teaching is problem solving.) | |
| Feb 8, 2011 at 21:04 | comment | added | Deane Yang | This claim can be established only by studies that evaluate students' problem solving skills both before and after taking the course. I am not aware of systematic studies like this. I think such studies would be very valuable, both for establishing the value of math courses and for helping us teach math better. | |
| Feb 8, 2011 at 20:21 | comment | added | Andrew D. King | Kevin, the section on the LSAT that math types tend to do particularly well on is "analytical reasoning". I can tell you from experience that if you have a fair amount of experience working through mathematical proofs, you should find this section incredibly easy. | |
| Feb 8, 2011 at 18:24 | comment | added | Kevin Ventullo | I have heard that math majors tend to do well on the LSAT, though I suppose this is more a test of logical reasoning than problem solving. | |
| Feb 8, 2011 at 17:15 | comment | added | dvitek | Anna: I just saw your post as I submitted my comment. Several more things: that's a mission statement for the mathematics major, not for the department as a whole. Still, at least in reference to Duke, you may want to look at the 149S course, which is undergraduate problem-solving and has an enrollment of about 20 each year, not all of which end up being math majors. It's also taught by upperclassmen with some guidance from a professor, which is slightly unusual but works rather well. | |
| Feb 8, 2011 at 17:10 | comment | added | dvitek | Anna: I would be surprised if there was any high-quality research on this, simply because "problem-solving" as a general skill -- as opposed to mathematical problem-solving, which has some overlap, but is definitely distinct -- is very hard to define or measure across-the-board. You might try specific situations or something like Raven's Progressive Matrices -- which I would suspect would correlate decently with mathematical training -- but you're running into a definition problem, especially as "problem-solving" is nowadays being used as a sort of catch-all term in education-speak. | |
| Feb 8, 2011 at 17:06 | comment | added | Anna Varvak | @Mariano: here's an example: Mission statement of Duke University math.duke.edu/undergraduate/mission7.pdf | |
| Feb 8, 2011 at 16:58 | comment | added | Mariano Suárez-Álvarez | I have never read "problem-solving" listed as an objective of a math course (except those that are specifically targeted at that, very few) | |
| Feb 8, 2011 at 16:26 | history | edited | Anna Varvak | CC BY-SA 2.5 |
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| Feb 8, 2011 at 16:23 | comment | added | Anna Varvak | @Arnav: I am certain that if you take a look at the stated goals of the math department at your university, "problem solving" would come up in some form. Good point about logical reasoning. I would be interested to learn on any studies about that too. | |
| Feb 8, 2011 at 15:38 | history | edited | Deane Yang | CC BY-SA 2.5 |
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| Feb 8, 2011 at 15:11 | comment | added | Arnav Tripathy | ...for, at least at the very basic level that we're talking about when we discuss "courses required for graduating", is being able to easily see flaws in reasoning, gaps in arguments, things that follow 'tautologically', and so forth. | |
| Feb 8, 2011 at 15:10 | comment | added | Arnav Tripathy | I'm surprised to hear that cited as the justification -- in my humble opinion, learning mathematics, especially at an undergraduate level, is less about developing problem-solving skills and more about honing logical acuity. For example, I am not infrequently asked which courses exactly one should take to develop skill at the Putnam (presumably one of the most elementary examples of mathematical problem-solving), to which I hem and haw and then say to just take some standard classes so you know the material and then go work some problems instead. What I think a mathematics education IS good... | |
| Feb 8, 2011 at 14:53 | history | asked | Anna Varvak | CC BY-SA 2.5 |