tag:blogger.com,1999:blog-1466552513513999074.post7874802353207826077..comments2015-06-13T15:07:47.396-07:00Comments on Even More Grumbine Science!: Teaching Women Sciencequasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-1466552513513999074.post-67948627728359778632008-12-15T13:09:00.000-08:002008-12-15T13:09:00.000-08:00I think it depends on what's forgotten. If one has...I think it depends on what's forgotten. If one has no idea what a derivative or an integral means, one should probably take calculus again. If one can't recall which trig substitution to use for e.g. int(sqrt(1+x^2)), one should do a few problems in the relevant section of a calculus text. If one doesn't recall the exact formulation of Green's Theorem, one can use the Google.<BR/><BR/>As far as the actual doing of the math, most things (including symbolic differentiation and integration of anything that can be done comfortably by hand) can be done with a calculator. Virtually everything can be done by computer. The key though, in both of those, is that you have to know how to set up the problem, which requires a not-insignificant level of understanding and skill. Having learned how to do a decent amount of math by hand and by computer, I have to say it's actually <I>harder</I>, in a lot of ways, to do calculus by computer if you're only doing it once (unless you're doing iterated integrals of nauseatingly complex multivariable expressions clearly never intended for human consumption). The main advantage is that if you want to run the same sort of procedure over and over using different functions or constants or whatever, or if you want to do relatively simple numerical computation on large quantities of data, the process is automated.<BR/><BR/>I'd be distinctly surprised, in other words, to find out that a significant number of scientists whose field of work involves doing symbolic math on a regular basis have forgotten how to do it. Not only did most working scientists grow up before the technology to do this sort of stuff was widely available, but the technology in its current form just doesn't have any advantages for one-off problem-solving unless the problem involved is hideously complex. Of course, many modern scientists deal mostly with statistical analysis of large amounts of numerical data, but then even without computers their calculus skills might still get rusty without practice.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-43816986716931114772008-12-14T23:56:00.000-08:002008-12-14T23:56:00.000-08:00Much of math post-calculus level you simply lose i...Much of math post-calculus level you simply lose if you don't use it enough. I'm sure a lot of scientists forgot many of the "integration techniques" such as trig. substituions, integration by parts, etc....the vital part is that they know what an integral means and why they or someone else should use it. "Solving for x" can be done with a calculator. I wonder what the recommended approach is for someone who forgot some of the stuff that is assumed in higher-level courses.Chris Colosehttp://www.chriscolose.wordpress.comnoreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-47059509347455542042008-12-11T06:22:00.000-08:002008-12-11T06:22:00.000-08:00I have to second your notion that too much math in...I have to second your notion that too much math instruction falls into the "rote" mode of cranking out problem after problem with no real application attached.<BR/><BR/>Higher math is not my strong suit to begin with, but undergrad Calc II made no sense whatsoever to me until I took my first Graduate Physical Oceanography class, and we started doing motion equations for water parcels in differing sized basin. I still claim no math expertise as a result of that, but at least then I could see how it all came together. Perhaps we should have folks from non-math disciplines ( who are never the less trained in math) teach the calc I and II classes - if only so students don't get lost in the letters.kcsphilhttp://www.blogger.com/profile/12049875206738422083noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-57737008200097241252008-12-06T14:03:00.000-08:002008-12-06T14:03:00.000-08:00The problem I've seen a lot of is not so much what...The problem I've seen a lot of is not so much what I'd call a math weakness, but a math applications weakness. Many math instructors and most math textbooks seem to try very, very hard to teach specific skills in sequence and in isolation. They are also generally very artificially consistent with notation, using the same letters for the same things almost every time. Applications problems in math classes are almost invariably a matter of "take the formula, theorem, or process you just used on the last 50 problems, figure out where the given information fits into it, and crank the problem out in exactly the same way." <BR/><BR/>This does help students remember the processes well enough to progress in math courses, but it's not what's needed as preparation for science courses. When dealing with a science problem, one has to have one's math memories cross-referenced, not just sequentially ordered; one has to be able to reach back and pull out some techniques from pre-algebra, some from calculus, some from trigonometry, and some unique to science, and one has to be able to decide how to put them all together. In the process, one has to deal with scientists' peculiar notation habits and different variable names and moving coordinate systems, which tend to fail to "trigger" the correct process in students who have been well-conditioned by math departments.<BR/><BR/>Now, obviously this isn't the main problem for your students in intro astronomy courses who are barely functioning at a pre-algebra level. It may, however, have been an issue for your grad school office-mate.quasarpulsehttp://www.blogger.com/profile/08762550806982089851noreply@blogger.comtag:blogger.com,1999:blog-1466552513513999074.post-83185344647885911322008-12-06T08:29:00.000-08:002008-12-06T08:29:00.000-08:00My first inkling about the importance of not makin...My first inkling about the importance of not making too many assumptions came when I was in grad school. My office-mate was having a hard time with a homework problem that was a simple (if you understood multivariate calculus -- which one does rather assume of graduate students in math-heavy sciences) matter of integrating terms that were given to us in the problem. Her comment "Just because I passed a class doesn't mean that I learned the material."<BR/><BR/>On one hand, it rather <I>should</I> mean exactly that. On the other, reality intervenes and even if a student has had a course that I as a teacher of some later class would think sufficient to understand my stuff, I really should not assume that it is the case.<BR/><BR/>I had a more extensive introduction the last time I taught astronomy (100-level at a local community college). Though the class did have a math requirement, and my nominal expectations were well below that, I wound up giving my own in-class math placement test. I made a number of changes after discovering that few in the class could operate at a jr. high to high school pre-algebra level. <BR/><BR/>Next time I teach, whenever and whatever that is, I'll have some math and other in-class placement (or maybe I should call them warning?) tests in hand.<BR/><BR/>For the non-math sides, I've also started looking at the cultural assumptions. That, for instance, students will know what the path of a ball through air looks like. (I already know that this can't be assumed.) There are many such things. Some lend themselves to being labs (ok, go toss some balls, drop some and see how high they rebound, ...).Penguindreamshttp://www.blogger.com/profile/10783453972811796911noreply@blogger.com