Timeline for What should we teach to liberal arts students who will take only one math course?
Current License: CC BY-SA 2.5
24 events
| when toggle format | what | by | license | comment | |
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| Jun 27, 2010 at 18:18 | comment | added | Noah Snyder | @Jeffrey: I think you're right about upper level classes for majors, but I was just talking about the first intro class (which is often mostly non-majors). | |
| Jun 25, 2010 at 3:57 | comment | added | Harry Gindi | @Neel: I'm of the opinion that close reading is nothing more than reading your own thoughts into a book. If you read closely enough, that is, you can find anything you want. | |
| Jun 22, 2010 at 20:14 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Jun 22, 2010 at 11:07 | comment | added | Jeffrey Giansiracusa | @Noah: Actually, I'm often surprised by how close undergraduate history comes to the cutting edge of history research. My wife lectures history here in Swansea. I admit that the first year intro courses aren't up to the professional research level, but they do have an entire lecture course on 'what is history?', and by the second year students are certainly 'doing history' in a real sense. By their third year, it is possible for good students to produce publishable research. In the humanities they have the concept of 'research-led-teaching' that we mathematicians are unable to adopt sadly. | |
| Jun 21, 2010 at 12:28 | comment | added | Michael Lugo | To extend Noah's last comment: we probably think that intro level courses in other subjects bear some resemblance to how those subjects are practiced in the wild because our own experience with those subjects is limited to the intro level courses. | |
| Jun 21, 2010 at 12:23 | comment | added | Neel Krishnaswami | @Harry: Pick up a copy of Wayne C. Booth's The Rhetoric of Fiction for a (very accessible) example of the kind of thing professional scholars in the humanities do. Observe that the amount of close reading you have to have done in order to to be able to make the kinds of observations he does, easily exceed the total amount of reading-unqualified that most incoming freshmen have done. What humanities people do isn't science, but it is scholarship, and calls for the kind of expertise which unavoidably takes a lot of time and effort to develop. | |
| Jun 21, 2010 at 9:01 | comment | added | Harry Gindi | I don't include the social sciences in the humanities (I rather agree with the list on Wikipedia). Aside from the classics, I still think that my statement holds for the rest of the subjects on that page (I'd also probably add political science to the humanities because it doesn't really seem like there's any attempt at actual science there). | |
| Jun 20, 2010 at 23:07 | vote | accept | Michael Hardy | ||
| Jun 20, 2010 at 23:07 | |||||
| Jun 20, 2010 at 16:47 | comment | added | Noah Snyder | I don't really grok what scholarship in English means, so I'll avoid comment on that. But other subjects say History, Classics, Linguistics, Economics, Anthropology, Psychology, Sociology, etc. the intro level classes have almost nothing to do with how the subject is practiced in the field. Intro level classics classes are learning greek not doing research, intro level linguistics is stuff like learning what a phoneme is not doing research, intro level history is learning about the basics of some historical period not digging around in old books in some obscure library in France. | |
| Jun 19, 2010 at 23:00 | comment | added | Harry Gindi | Why not? The humanities, unlike the sciences, are not built hierarchically, unless there's some kind of "tiered obscurantism" that I've never heard about. | |
| Jun 19, 2010 at 20:52 | comment | added | Noah Snyder | I'm a bit skeptical that intro level courses in the humanities have much exposure at all to "how they're practiced in the wild." | |
| Jun 19, 2010 at 18:57 | comment | added | Harry Gindi | I'm not saying that these thing shouldn't be taught, perhaps even by mathematicians. I'm saying that mathematics students are required to take humanities and writing courses, where they are exposed to subjects the way they are practiced in the wild. I say then that a basic numeracy/statistics course (or even a calculus course (the way it's taught to non-majors at least)) should not count as a fulfillment of some requirement for exposure to mathematics. Mathematics is unique among the subjects in that most standard courses do not even expose students to how mathematicians think and what they do | |
| Jun 19, 2010 at 18:47 | comment | added | Noah Snyder | Of course, if numeracy and basic statistics were covered in highschool (where they should be taught!) then we wouldn't need to teach them in an intro college class. In a perfect world this would be highschool material, and then an intro college class could be more geared towards interesting mathematics. | |
| Jun 19, 2010 at 18:46 | comment | added | Noah Snyder | Although I think Andy's argument has some validity, the reason I lean more towards covering numeracy/statistical numeracy is the moral reason (it's more important for us to teach knowledge that's valuable to the students) more than a practical reason (if we just teach classes for our own fun we'll all be out of jobs). | |
| Jun 19, 2010 at 18:25 | comment | added | S. Carnahan♦ | Harry, I think your claims rest on a few shaky assumptions, most importantly that applied math, statistics, and heuristic reasoning aren't part of mathematics as mathematicians do it. The fact that these topics are uninteresting to a vocal subset of mathematicians doesn't imply that teaching them is a waste of time. Regarding the use of rigor, I think an analogy is most appropriate: My own experiences with required survey classes in non-math departments is that they can be quite enlightening when organized and executed well, even if they don't show me their day-to-day practice. | |
| Jun 19, 2010 at 17:06 | comment | added | Andy Putman | (continued). I recommend googling to see what happened to the University of Rochester's math department. It's an important cautionary tale for us all... | |
| Jun 19, 2010 at 17:05 | comment | added | Andy Putman | @Harry : But our students don't understand the basics. This needs to be corrected, and if we are too cool to correct it, then who will? My fear is that some other dept will get fed up and start offering such a course. At some universities, depts that use math (eg : physics and various types of engineering) were unsatisfied with how calculus was being taught by the mathematicians and decided to offer calculus classes themselves. This causes math dept enrollments (and math dept budgets) to drop. It's in our discipline's best interest to teach what students need rather than what we enjoy... | |
| Jun 19, 2010 at 9:36 | comment | added | Harry Gindi | I totally disagree with you. I think the whole point of such a course would be to show that mathematics is not all computation. The problem with the course you're describing is that it wastes time on the pedestrian and boring parts of mathematics, which takes time away from "mathematics as mathematicians do it". I think that the class should be taught with rigour, but perhaps at a slower pace. It's not the math department's job to teach basic numeracy and basic statistics, and if it somehow was left up to the math dept. to teach them, it surely shouldn't count as a legitimate math course. | |
| Jun 19, 2010 at 5:16 | comment | added | Noah Snyder | On the other hand, I agree with you that it's likely to be forgotten quickly, but that's true no matter what the class covers. But I think that by concentrating on a few simple things (1 million dollars isn't very big) you can get people to remember those few things. The very very easy evolutionary biology class I took in college did a very good job of only making a few points but doing to very forcefully (namely evolution by natural selection requires variation, heredibility, and selection; and using small amounts of antibiotics on livestock will lead to resistance and destroy civilization) | |
| Jun 19, 2010 at 5:13 | comment | added | Noah Snyder | Wait, what about this approach presents it as amusing tricks and games? 75% of the class is about concrete real-life applications of math. The rest is one real math topic. What about the classification of platonic solids is a trick or a game? | |
| Jun 19, 2010 at 2:23 | comment | added | The Mathemagician | @Noah The problem with this approach is it presents mathematics as a set of amusing tricks and games-and it's likely to be forgotten just as quickly since it's being taken with the same degree of passing importance. | |
| Jun 19, 2010 at 2:20 | comment | added | Qiaochu Yuan | John Allen Paulos would definitely agree: amazon.com/Innumeracy-Mathematical-Illiteracy-Its-Consequences/… | |
| Jun 19, 2010 at 1:21 | vote | accept | Michael Hardy | ||
| Jun 19, 2010 at 2:35 | |||||
| Jun 19, 2010 at 0:51 | history | answered | Noah Snyder | CC BY-SA 2.5 |