you're taught to recognize the question that will test that skill.
There's a relevant anecdote in Surely You're Joking, Mr. Feynman, about some students in Brazil.
Are these students required to take Calc II? What are they majoring in? I wonder what motivates someone to take calc 2 if they don't understand calc 1.
1: Every Brazilian I've talked to thinks the volume of a cylinder is πr^3h.
2. I think most of the ones who made Cs or below are being forced to take it for their major - engineers, CS, physics, maybe a BS in chemistry.
Cs or below [...] engineers
Aaaaahh.
you're taught each skill in isolation, and you're taught to recognize the question that will test that skill
There was an article about that the other day in the NYT.
Now I have a justification for all the classes I skipped!
4: I got through Calc (with an A, thank you) by studying with engineering students.
From the link in 6:
The findings can help anyone, from a fourth grader doing long division to a retiree taking on a new language
What's the justification for still teaching long division? Don't get me wrong, I'm not saying don't teach it, and in fact I've done some literal back of the envelope calculations using long-division as an adult,* but not for a few years, but is there any non-school test context where one would need it nowadays?
*I don't remember why, but I didn't have much scratch paper, didn't have a calculator, and wanted to work out something or other right then. It took me a while to work out how to do long division again.
My ninth grade teachers made us learn how to do everything using log tables. My parents were amused.
I think people should start describing the techniques suggested in that article as "brain-fartlek."
The NYT writer should have been given a test on this before going to press:
This article has been revised to reflect the following correction:
Correction: September 8, 2010
An article on Tuesday about the effectiveness of various study habits described incorrectly the Heisenberg uncertainty principle in physics. The principle holds that the act of measuring one property of a particle (position, for example) reduces the accuracy with which you can know another property (momentum, for example) -- not that the act of measuring a property of the particle alters that property.
Speaking of higher ed:
Argh the university was supposed to tell us if we were allowed to go back on Monday at 5.00 and it's 6.02 now and nothing and argh.
Forgive me if this sounds stupid, but why would one want to make the grade for a course not dependent on the completion of earlier courses? Is the grade independence of courses supposed to be desirable? It seems mystifying to me.
If you are taking Some-sort-of-maths 3, surely one would naturally expect [nay, desire!] that people who'd done Same-sort-of-maths 1 & 2 would do better?
Well, we go back Wednesday but!
The [Library] building has been certified as structurally sound. However, the collapse of book stacks on all floors means it will not be available for accessing books for the remainder of this semester.
Holy fuck.
re: 16
Man, someone is going to have a hard job reshelving.
Oh yes. You can see pictures here (the first picture's the library) and video here and here.
13: The correction itself is wrong.
19: yes. It's actually more wrong than the wrong sentence, which at least was factually accurate even if it wasn't a statement of the uncertainty principle.
9: it's not that you are going to use long division so much as that you will have a hard time moving on to algebra if you don't spend many a weary hour burning the relations between numbers into your brain. I've mentioned this before, but I re-invented "short" division in 6th grade after interminable long division assignments. I've forgotten it but I assume I can re-learn it when my daughters do long division. I wrote the remainders as subscripts or something? my teacher made me not do it even when the answers were all correct. I found this very tedious. I got the fucking answer! what do you want?!
but is there any non-school test context where one would need it nowadays?
IME it comes in handy for metric/neaderthal measurements conversion.
21- assimilation, I guess - resistance being futile & all that.
19, 20: It looks correct-ish to me, although it would be clearer if "you can know" were to be changed to "you can simultaneously know". There's a not-very-interesting (to me) argument going on over on Scienceblogs at Uncertain Principles about the article's statement and the history of the uncertainty principle. I would prefer for it to be stated without reference to measurement, but that was what Heisenberg's original paper did, apparently.
OT: Phone meetings with Australians are nice because it's been a long time since I've heard somebody call me "mate."
This is partially exactly what you say: the consequence of a curriculum where every course is taught as an isolated experience. The sciences build sequences in, but they leave it to the students to do whatever mysterious things are necessary to retain command over the previous content as they put their hands on the next rung of the ladder. We don't talk to them about why the curriculum has the sequences that it does, or how these things all connect, except to promise somehow at the end of the road (when they're us) it will all make sense. But here I am, decades later, with much more interest in curricular issues, interdisciplinary connection and so on than many of my colleagues, and I still can't tell students entirely what the structure of the curriculum is, or why Department A asks you to take a particular class first and then take another class second.
We don't tell students that when they've gone from introductory microeconomics to introductory cognitive science or psychology, they've very likely gone between two increasingly rivalrous ways of understanding human motivations, agency, etcetera--the econ professor almost certainly didn't tell them that there's anything else out there, and the psychology professor probably won't address the other paradigms either. We leave that up to them, whether they even understand that what they learned in one place has implications for what they learned in another.
I'm parroting a bit of what Gerald Graff wrote in Clueless in Academe, but that's because I think he's basically right--the students who retain or apply knowledge from one class to the next are those who already have the social capital or training to do that; we don't do shit to help the students who don't understand how to do that and have absolutely no road map of a curriculum. We don't explain ourselves because it's too much fucking effort and it would take being at least partially responsible to other peoples' courses when it often seems difficult enough to be responsible for our own.
15
Forgive me if this sounds stupid, but why would one want to make the grade for a course not dependent on the completion of earlier courses? Is the grade independence of courses supposed to be desirable? It seems mystifying to me.
You don't want a course to have too many prerequisites (or courses that are to be taken simultaneously) if they aren't really needed. Physics II might provide good Calculus II problems but do you really want to require every student taking two years of calculus to also take two years of physics? A math requirement for other courses makes more sense but if you make it too stringent you will severely limit your enrollment.
9
What's the justification for still teaching long division? ...
The same as for teaching many other things of limited (at best) practical value. It helps identify the smart students which is one of the main purposes of school.
I second Sifu's terror.
This actually really bugs me. I don't know that it's helpful or wise to approach poor student performance from the perspective of "what do I need to do to help them" as it can only reinforce maladaptive patterns of behavior. Why is this something heebie has to fix? What about just...failing them? This is college, right? They're adults, for all intents and purposes? With their own agency, responsible for their own paths in life?
I don't subscribe to this kind of thing with elementary students, bc they're freaking children, but really...college? There is something to be said for failure. It's instructive. And getting an A when you've been coached to it, or given several do-overs, doesn't provide quite the same mastery experience that might lead to an increase in, say, self-efficacy and accomplishment later in life, as a B+ in a class where you got your ass kicked in the first week.
I can see where this kind of thing might lead to a sense of entitlement, is what I'm saying, and I see that... everywhere.
Why teach division if you can spend your energy in making people come together?
Why teach division if you can spend that same time multiplying?
Why teach division if you can spend your energy in making people come together?
The remainder is love. Just love.
18: For a moment, I forgot that there was a massive earthquake in that part of the world, and I sat here stunned, trying to imagine what kind of Benny Hill/Wyle E. Coyote/Mr. Bean conflagration could have caused such devastation.
Sorry. Hopefully they build you a better one.
(Yes, nosflow, I know the general usage of conflagration; this is how I want to use it.)
Long division is v. helpful in algebra sometimes. It doesn't really matter tho if they teach it to you at primary, 'cause by the time you use it you've forgotten it again, in my experience.
'cause by the time you use it you've forgotten it again, in my experience.
Really? You never divide by 2.54 (cm to inches), 2.2 (Kg to pounds, for practical purposes), 1.8 (Km to miles, roughly)? I do that sort of thing more or less every day.
And then you don't have the euro yet. Or no, that's going to be at parity, by the time you stop dividing Europe ;-)
32.1: under the circumstances, you would have to assume the Tasmanian Devil was involved somehow.
I've never given this much thought, but I think if I do unit conversions in my head I always multiply rather than divide. Multiply miles by 1.6 to get km, multiply km by 0.6 to get miles. That sort of thing.
I just go to google and type "miles to kilometers" or whatever. Because I'm an internetist.
34, 37: like toilet swirls, use of unit conversion operators is very neatly divided by hemisphere.
... which, okay, doesn't precisely explain chris y. Get over to the other side of Greenwich, would you?
NZ's pretty metricised, to be honest, especially at school.
You're in Texas right? It's the Corexit in the Gulf moisture drenching the students reducing their ability to function. Obama gets a million dollars in Bahrain-laundered Afghanistan money for every white cracker student who passes a higher math course without true understanding. I have links!
I suppose Britain's position may be fairly unique - you never know what measurement system you're going to encounter from moment to moment - but I'm interested that NZ is that much more settled. When did they start converting?
Forgive me if this sounds stupid, but why would one want to make the grade for a course not dependent on the completion of earlier courses? Is the grade independence of courses supposed to be desirable? It seems mystifying to me.
If you are taking Some-sort-of-maths 3, surely one would naturally expect [nay, desire!] that people who'd done Same-sort-of-maths 1 & 2 would do better?
I'm not clear on what you're asking.
NZ went metric in the early seventies. I think NZ switched quite quickly, and everything's in metric (including road signs etc.)
Switching quickly was wise. Britain tried to switch by degrees over a generation - "Oh, the old people will be confused if we go too fast" - and completely fucked it up.
43: I think it is the general proposition that inherent in something like a 300-level course should be mastery of prior material--you can't (and shouldn't) try to make it a level playing field for someone trying to enter the math sequence at that level of course.
It's all about the levels!
Oh. In the OP I was addressing two different points - courses where there is an explicit prerequisite (Precal to Cal to Cal II), but also how students do not integrate knowledge between courses when there isn't an explicit dependence. That second point was pretty well dealt with by Burke and Shearer, though.
Maybe standards have declined since my day, but I thought of Calc I as your basic entry-level college math course that shouldn't have prereqs. (Or rather, not meeting the prereqs puts you in a remedial group.)
You kids get off Moby's prairie.
48: Varies between schools. Recently I read an article that I keep meaning to blog about, which asserted that higher ed schools have become incredibly localized* with respect to academic ability. I mean that in 1980, most schools had a vast range of talent, and now most schools have a surprisingly narrow range of talent.
So there are plenty of institutions where nearly everyone enters, ready for Calculus, and plenty where nearly nobody could take Calculus their first semester, because the filtering process has become so precise.
*Can't find the right word
My son's first night of homework for the year (9th grade) - some easy algebra problems, some basic spanish worksheets, and signing a bunch of "I will follow the Rules" sheets.
My daughter's first night of "homework" for her senior year (her 2nd of 4 years as a senior!) - Reading Neil Gaiman's Wolves in the Walls, complete with howling for effect. BR and my son chimed in with some howls from downstairs for added benefit.
50: I think my undergrad school used Calc to discourage/flunk out large numbers of entering freshmen. It was required for nearly every B.S. major and by state law they couldn't not admit graduates of in-state high schools.
re: 29
I've argued something similar in previous education threads, but I think I came down at the fairly harsh bastard end of the philosophies of education spectrum as represented on Unfogged.
re: 26
Yeah, I think perhaps I'm thinking much more in terms of the Scottish system, which is more tightly structured in my experience.
"You do Ordinary X, and then you do Higher Ordinary X, if you do OK then you'll get admitted to Honours X, where you'll have a choice of y options from a total of z, and where prerequisites or companion courses will be clearly indicated."
Know what pisses me off? I can't listen to music and do much of anything.
My suggestion is to move to a better University. I'm currently at a top-100-in-the-world Uni. We have a 2nd year Cambridge undergrad as an intern and he blows all our undergrads away and a good portion of the postgrads. That power law drops off fucking fast.
I'm teaching this year. It is going to be interesting.
That power law drops off fucking fast.
Quick! Someone light the Cosma-Signal!
I've gotten the impression that it is actually harder to transfer mathematical knowledge from one context to another. As I remember the curriculum, I basically was taught algebra every year from sixth to tenth grade, each time approaching it like it was brand new.
It would be ironic if math is harder to transfer between contexts, because it is the most general form of knowledge. But that might be the problem. You can't use any of your concrete, social cues to create analogies between contexts.
Canada is less metricized than I expected, in some areas. I've been looking at furniture and different stores show the dimensions in both systems, or only in one (it would be nice if the stores that did only one did the same one). And I convert temperatures since I still haven't worked out a "natural" sense of Celsius.
I haven't done any long division though. Just rough estimates, or like essear, I do multiplication. If I'm not doing the calculation in my head, I use a calculator. I can't say the justifications for long division in elementary school given above are very convincing.
54: the English system too. Where I went, everyone on the degree course did the same first year classes, and then in second and third year you picked a few term-long modules from a fairly short list and did those, along with a few compulsory modules. The US system seems rather more pick and mix.
58. You can do long division in your head if you can do long division.
And I convert temperatures since I still haven't worked out a "natural" sense of Celsius.
I know that 45 C is very, very hot b/c of the lyrics to Midnight Oil's "Beds are Burning." Zero is freezing, so you can extrapolate between those two points.
I think 29 is pretty much entirely wrong. And here's why:
I believe Sifu's 5 was meant to express dawning recognition.
Also, if you think that the point of higher ed is to separate the wheat from the chaff, Shearer-style, then sure fail and punish away. If the point, however is to teach people, then you have to a) monitor how effective your teaching methods are (Heebie-style), and b) balance not wasting the smart kids time against giving those kids who are not dumb and can eventually get it the chance to get it. The importance in b) of the former concern over the latter increases the further you get in higher ed, but it's always a balance.
I don't see second chances or alternate methods of instruction and testing as increasing a sense of entitlement in themselves. In my limited experience (but which includes teaching at both an elite school and a state school) entitlement is primarily combatted by having the second chances be on your terms rather than those of the students, and by having an administration that backs up its faculty (within reason). Students often give up on themselves long before they should. Judicious use of second chances can sometimes get them past those blocks and allow them the chance to push themselves and take on the material.
re: 59
Yeah. They are fairly similar in most respects, I think. Studying philosophy at Glasgow there were, if I recall correctly, 3 different first year philosophy courses* any one of which was sufficient as a prerequisite for 2nd year philosophy, where there was, iirc, only a single course. You didn't get admitted to 2nd year without achieving a certain standard at 1st year level, and didn't get admitted to honours without achieving a certain standard at 2nd year level, and so on. It's restructured now, I think, to accommodate a semseter system.
* one general course, one with more a philosophy of science/epistemology emphasis, and one with a more ethics/moral-theory/'continental' bias. But all three overlapped a fair bit, I think.
61: A reasonable room temperature in summer is sort of low-mid 20s. Cleaning staff at the hotel I was in last week kept resetting the thermostat in my room to 15. I didn't fully appreciate the craziness of this until I did the conversion.
Roughly, 5 is seriously cold, 10 is cold, 15 you need a sweater, 20 is comfortable, 25 is warm, 30 is too hot unless you're a sun worshipper, 35 is too hot, period, 40 is potentially injurious unless you're dressed right and carrying a lot of water.
32: (Yes, nosflow, I know the general usage of conflagration; this is how I want to use it.)
High school English teacher (with PhD): Can anyone define the word conflagration?
Me: (eagerly) It's a really big fire!
English teacher: Uh, no, that's a very interesting try, but it means a collection of objects.
I'm not sure I understand all this animus towards teaching long division. I mean certainly it's stupid to make people do a lot of it (after all google is much faster at it) but I'd find it rather embarrassing not to know how to do one of the four basic operations myself. I mean there's only four of them!
In the google/wolfram alpha age I wish we stopped emphasizing computation and moved towards a deeper conceptual understanding. For an example of a conceptual question involving long division, it'd be great if people knew that the number of digits in a/b is roughly the number of digits in a minus the number of digits in b (that is log(a/b) = log a - log b).
5 is seriously cold
That has to be nearly 40 degrees, regular temperature. If you call that "seriously cold" you should probably toughen up or move somewhere subtropical.
Without long division, rational numbers seem like just an abstraction. There's a lot more to numbers than figuring out prices.
re: 62
I agree with much of that, to be honest, I don't even think it's necessarily incompatible with actually failing people when they deserve it or fail to reach an appropriate standard (given reasonable levels of support for students and a system that doesn't reward assholes).
There's often different types of student and different types of failure under discussion in these topics. I've had students who really struggled with the material (despite a desire to learn) and I think those students deserve as much help as is practical. I've had other students who were failing because they were arrogant irresponsible pricks who thought they were pretty much entitled to pass whatever they wanted. Helping the former without giving an easy out for the latter seems the right way to go, I'd have thought?
re: 68
It's not seriously cold, but you'd want some fairly warm clothes on if you were spending much time in it. As someone who lives in the north of England I expect chris is fairly familiar with chilly and/or damp and miserable weather.
I am surprised to hear that so many people don't remember how to do long division. I've forgotten a whole lot of things, but that one is not ever going away. It's second nature.
For quick in your head conversions F≈2C + 30 works pretty well (is a bit off when it gets hotter).
C, 2C + 30 approximation, 1.8C+32 (exact)
5, 40, 41
10, 50, 50
15, 60, 59
20, 70, 68
25, 80, 77
30, 90, 86
35, 100, 95
40, 110, 104
Seriously cold as in, time to take measures like breaking out your winter coat, not seriously cold as in "am I going to leave the heating on low overnight?" But cold enough not to ignore it.
In the google/wolfram alpha age I wish we stopped emphasizing computation and moved towards a deeper conceptual understanding.
If I were teaching low-level math and not chained to a predetermined curriculum, I would be tempted to require students to do some numerical programming, as an alternative to some of the repetitive pen-and-paper computation. Teaching a computer how to do integrals or to solve equations by Newton's method, for instance, is a useful exercise that helps build understanding, I think. Running into cases where algorithms fail is also often useful for understanding.
70:
No, I'd agree with that. It's why I disagree with my colleague who think that in order to be "fair" you have to treat all of the students exactly the same. I think that's an abdication of pedagogical responsibility rather than an expression of it. But yes, failing students sucks, but they should be able to fail.
Yeah, making people program the math they learned would be a great improvement on making them do it themselves over and over again. And they'll learn the valuable lesson that if you understand something well then you can teach a computer and then *you'll never have to do it yourself again*. I think that's a lesson even a lot of mathematicians could learn from.
To convert between F and C I tend to use the fact that they're equal at -40. I'm not sure if it's actually faster, but it somehow makes more sense to me than pausing to work out where to put the 32. So e.g. 15 C is 55 C above -40, 55 deg C times 9/5 is 99 deg F, 99 more than -40 is 59 F.
Taking the Celsius temp, doubling it, then adding 30 gives a good and fast approximation of the Fahrenheit temp for the weather/room temperature range.
72: Yeah, I do long division all the time, sometimes for unit conversion, other times to figure out percentages. It's faster than carrying whatever numbers I'm working with to a calculator.
For quick in your head conversions JP Stormcrow + 6 works pretty well too.
62: Is this a set of circumstances that is likely to be repeated anywhere else in life besides academia? Honest question. My own experience leads me to believe that the answer is a resounding "No."
I've already outed myself as having gone to MIT, I might as well use this info now: MIT graduates go on to become successful entrepreneurs at an astounding rate. Yes, there are confounding factors, but the data was still eye-catching enough that they (Cambridge University and MIT) spent 5 yrs researching why (I helped with this). The data they collected and available research suggested that this had more to do with MIT's teaching culture than what they actually taught, which can pretty much be summarized in the following:
1.1 I once had a professor who informed us that he didn't believe in undergraduates, as though we were pixies or something, and he wouldn't act as though he did. He didn't.
1.2. An outside researcher: "This is the only place I've ever been where faculty seem determined to make life as difficult as possible for undergraduates."
2. IHTFP = I Hate This Fucking Place is on every class ring (the brass rat).
3. "It's like trying to drink from a fire hose." "It's like ordering a ham sandwich and getting a pig and a loaf of bread." Both of these things are true.
I wouldn't argue that this is necessarily the best approach, as many MIT graduates (I'm speaking of the undergraduate experience) leave incredibly traumatized (this is pretty hilariously obvious if you ever work the phone banks of recent grads looking for donations). And actually, I would include myself among them. But there's something to creating an attitude of self-reliance. I think to a large extent (and perhaps this is a classic behavioral modification perspective; I'm not really familiar enough w it to know) teaching philosophies prepare students to face circumstances that mirror the ways those philosophies manifest in pedagogy. I'm not saying one shouldn't have office hours, or resources, or what have you -- I really, really think you should, and, in case this isn't clear, I think heebie's desire to help every student she encounters actually learn as much as they possibly can is awesome and commendable -- I just think there's a kind of meta-preparation that goes on that might not be optimal. One can learn the material accurately while learning inaccurate things about life in general.
Switching quickly was wise. Britain tried to switch by degrees over a generation - "Oh, the old people will be confused if we go too fast" - and completely fucked it up.
I wonder if the habit described here - using Fahrenheit for hot temperatures and Celsius for cold - is generally true or just a bit of occasionally-true observational humor. (At 4:44)
Is this a set of circumstances that is likely to be repeated anywhere else in life besides academia?
Probably not, but why should it be?
On reshelving (16): it seems it shouldn't take a whole semester if you get all the students involved. From a page on the 1989 earthquake at Stanford,
Green East, the new wing built about ten years ago, was virtually unharmed, except for several hundred thousand volumes that were dumped unceremoniously on the floor. A massive volunteer effort got the books back on the shelves in about 3 days.
82.1: My experience is frequently "Yes". Maybe not the culture of entrepenuers.
I'm actually pretty fine with that being the culture of a place like MIT--as long as they really make incoming students and their families aware up front--but do not think it works as a general rule.
84: Because of this bit: "teaching philosophies prepare students to face circumstances that mirror the ways those philosophies manifest in pedagogy." Maybe you don't agree with that point, but that's the reasoning behind my concern.
86: Oh my, they are not up front about it at all. But the students you encounter when you visit are. When I was there I knew a few people who couldn't restrain themselves from interrupting tour groups with "the truth."
MIT graduates are, in my experience, the most insanely productive people I've ever met in my life. My theory is that anything seems basically easy after MIT undergrad, and they're perfectly used to working 80 or 90 hour weeks. Even the ones I've known who are fuckups are incredibly productive fuckups -- why just take drugs when you can make them, as well, and then write up elaborate descriptions of how to make them and post them online? That kind of thing.
87.2: they're pretty up-front about it at the orientation speech, no? With the "look to your left, look to your right" thing?
88.1 specfically refers to people with MIT undergraduate degrees, by the way. MIT grad students seem basically normal. MIT professors are also insane, but that's another story.
I once had a professor who informed us that he didn't believe in undergraduates, as though we were pixies or something, and he wouldn't act as though he did. He didn't.
Could you elaborate on this? If I held similar beliefs I wouldn't even be at the class to say this :)
I've already decided I don't belief in lectures. I'm going to attempt more participatory/interactive learning.
Adverse circumstances, like boot camp, definitely fulfill a purpose. But there's got to be a middle ground between endless do-overs and a high suicide rate.
Something I found noticeable about my short and ill-fated MIT tenure is that while the faculty may have been making the undergrads' lives as difficult as possible, the administration wasn't -- dealing with administrative issues there was surprisingly forgiving and responsive. Dropping out and back in again was facilitated, financial issues tended to get smoothed out supportively and so on; you could focus all of your panic on the literal academic problems, rather than on real-world difficulties. Don't know if that had any pedagogical effects.
With the "look to your left, look to your right" thing?
Which hasn't actually happened in a couple of decades, but there was awareness of it anyway, at least in my era.
anything seems basically easy after MIT undergrad
There's some of this, but the culture also promotes doing lots of extra things - making things more difficult than necessary, really - even at the expense of your sanity. "Sure, I'm taking six classes, but this'll be a fine time to work in a lab, direct a musical, and put a top hat on the dome!"
82:
I think profs like the one you describe are lazy-ass jerks. They're smart people who don't know how to teach undergrads and so decide to valorize their own ignorance.
Look, I'm all about cultivating personal responsibility and treating college students as transitioning into full adulthood. I don't why that need to translate into "The world is harsh and cold and you have to scratch and claw for any crumbs you can." The MIT culture you and others describe is what I like to call a culture of ordeal. If you want to be an entrepreneur, then maybe it is very good training (or maybe it just preselects for folks with those inclinations, or maybe it makes it too painful to work for someone else ever again). It might, however, also give some inaccurate lessons about life in general, ie, student may fail to learn "It doesn't have to be this way."
All the best math classes I ever took were throw-you-in-the-deep-end style classes that pretty much treated undergrads like grad students (which is what I think of when I read "didn't believe in undergraduates"). This worked very well for those classes, and maybe is similar to the style at MIT, but I wouldn't expect it to work at more than ten or twenty institutions in the world.
The thing that surprised me about my undergrad education was that one week of a typical math class was like two or three of a typical physics class; the math professors packed in much more material and were never apologetic about it.
My own experience of studying was of having a fairly easy time at undergrad level and the culture of ordeal* bit being at the graduate level. That seems to me to be a bit healthier -- the grad students being old enough and ugly enough to not be entirely unaware of what they are in for.
* by 'ordeal' you mean, lots of work and a real chance of failing [rather than out and out abuse].
88.2: Orientation, when you're already THERE.
90: I think he found undergraduates boring, which I can understand, as we don't know as much math and thus aren't very interesting to talk to. So he blew through most of a year long sequence (arguably the hardest undergraduate sequence at MIT; aero astro and physics (16 and 8) offer some good contenders) in the first 2/3 of the first semester and then proceeded to go on to the things he thought were more interesting. The first time he taught the sequence he reportedly tried to fail all but 5 people. Best class I ever took. Started with 120 kids, ended with 22. 2 of them women.
91: Yeah, there's been a lot of litigation about that. My experience is that the issue was a lack of mental health resources -- they just didn't have enough money or enough people -- combined with a student population that was not necessarily culturally inclined (as in, the country they originally came from) to seek help. Of course, the academic culture of sink or swim (also, figure out a brand new, hyper efficient way of swimming, while you're at it) did not help. That's why I think fraternities, sororities, and living groups are so prevalent at MIT -- you need SOMETHING to hold you together.
95:
I'm unapologetic about my typos, except in so far as I apologize for them.
Perhaps he meant "-pants" but it came out as "-graduates."
94: He struck me as kind of Aspy, honestly, which was the case with a majority of the math faculty. Watching them deal with unexpected events -- like a squirrel suddenly trapped in building 2 -- was often awesome. I found a lot of it endearing, because their joy in the math (and in some cases physics) was so obvious, and often infectious. You can't not smile at a grown man who gets so excited by an equation that he breaks his chalk on the board and the proceeds to rub the chalk dust on his face, hair, and shirt, giggling the whole time. (That was a different prof, actually, but the principle applies.)
There are exceptions, obviously. Assholes are everywhere. But my experiences were largely positive on a personal level.
Also, LB is right about administrative stuff. This is a source of frustration for me to this day when encountering bureaucracy at other institutions. "What? Why do you do it that way? That's so...inefficient! WHY WOULD YOU DO THAT?"
Which is sort of the flip side of the point I was trying to make.
96: By "culture of ordeal" I mean something more general: the priciple that because the previous generation went through this unpleasant but character building rite of passage, it's important that the next generation go through it as well. It's never all of what's going on; it's bound up in ideas of effective pedagogy or evaluation or trasition to adulthood. The rites that it's bound up with can be in fact useful, but the idea of traditional forms of suffering are often distorting not particularly usseful. For example, some form of comps just makes sense as part of graduate training, but the six hours alone in a room form that I went through I think primarily had the appeal of a traditional ordeal rather than a useful evaultion of professional skills.
And now I'm chuckling to myself imagining that squirrel story play out.
There's a prof here who reportedly tried to fail everyone (I believe) when he taught an undergrad class, and now he isn't allowed to teach undergrads anymore.
re: 101
Yeah, that too, at grad level. I sat in a meeting where one of the senior faculty said, "this is the hardest course of its type in the world;* I'd like it to stay that way".
What is a 'comp'?
* I expect there's some hyperbole in that ...
my short and ill-fated MIT tenure
I kept telling you, tenure or no tenure, they're going to find a way to kick you out if you start defending the Holocaust, but you didn't listen.
You can't not smile at a grown man who gets so excited by an equation that he breaks his chalk on the board and the proceeds to rub the chalk dust on his face, hair, and shirt, giggling the whole time.
Oh god, this brings back memories of the worst math class I ever took. The guy was apparently a good researcher, but in front of a blackboard he became incapable of proving the most trivial statement, getting tongue-tied and reversing the directions of implications and getting more and more confused, then he would just suddenly go into a hysterical high-pitched giggling fit for a few minutes, before calming down enough to tell the class to look up the proof in the book.
101: Absolutely true. I forget what Cialdini called it, but it's a thing. Rites of passage to cement membership in a group, etc. Serves to enhance group cohesion, identity, what have you.
I think, as with all things, it's useful, practical, and good within moderation. I think when promoting membership in an exclusive group is the only purpose a rite of passage serves, it's time to throw it in. E.g., can anyone think of a reason doctors are still expected to pull 36-48 hours shifts during residency? Aside from preventing residents from having a social life, isn't this more likely to actually kill people?
102: ... and the maths professor looks out of the window, sees another squirrel in a tree outside and says "Wonderful! A solution exists!"
107,103: Yeah, not exactly punishment...
can anyone think of a reason doctors are still expected to pull 36-48 hours shifts during residency?
It's cheaper to have one person covering that shift than 4 or 5?
104:
"Comprehensive exams," also know as "prelims/preliminary exams." In the US they usually follow graduate course-work and one is required pass them to move on the the ABD stage. There are different formats and different expectations depending on the discipline and the institution.
my lower level classes
Quashing students' self-esteem. Again.
108, 111: My sister says that it really is about minimizing handoffs -- that there's a substantial benefit to having the same doctor monitoring very ill patients for longer continuous chunks of time. I don't know if she's right or if she's been co-opted by having to go through the system herself, but it's a rationale.
I call my students "Lowlies" just to drive the point home.
108,111:
THere was an npr piece on this a couple years ago and the best positive argument anyone could make for it was, "What if there's an earthquake or a war? The doctors have to be prepared to keep working without sleep when the bodies keep piling up," as if you'd retain a muscle memory from your interning days, lo those many years ago. Even they, however acknowledged that ttaM's explanation was more the thing.
114. May be true, but I've heard of established consultants justifying it on the basis of "culture of ordeal" to junior colleagues.
Similarly, there was a discussion at FSP recently along the lines of "should we penalize people with tenure-track jobs who appear to actually enjoy life?"
Oh my God, alameida was right: I am so a rat in a skinner box with this refresh button. This is helpful, actually. Haven't thought much about the ex in a few hours.
Ha!
114: The importance of minimizing handoffs goes together with the entirely inadequate record keeping and lack of electronicization in much of medicine. If doctor's kept track of what was going on, and computers ran through the data automatically to flag danger signs then we wouldn't be so worried about keeping everything in one doctor's head.
118: Wasn't the discussion "are they penalized" not "should they be penalized"?
I was doing long division (in my head) to work out how many litres of diesel we'd used on our holiday, given that I knew how much I'd spent on it.
The trouble with long division is that people don't realise it's just the same process as short division.
Yeah, it gets much worse when you're actually commenting. During short periods where I've sworn off for work reasons, I'll still mostly read all the comments, but it'll be ten minutes once a day. Any thread I'm commenting in, I'm a rat on crack.
Would it help to know that there is an actual rat in a box at the other end which has an orgasm every time you hit refresh.
The trouble with long division is that people don't realise it's just the same process as short division.
This bemuses me. What else would short division be, except a shorthand way of writing out the same process as long division? I can't really conceive of how the confusion would work.
"should we penalize people with tenure-track jobs who appear to actually enjoy life?"
Do such creatures exist?
125: Agreed, but the rat in 123 has died happily of a stroke by now anyway.
died happily of a stroke
IYKWIMAITYD
124. It's about presentation. You're taught short division (small divisors, piss easy) one year, then the next year you're taught OMG long division (humungous divisors, scary), in an atmosphere that says "this is hard, you couldn't have done it last year". Of course if elementary school teachers were capable of explaining the principles involved everybody could do mental long division at the age of seven. But they mostly aren't.
And then they make another song and dance out of fractions.
129: I agree, but I also think it's true that not everyone is capable of understanding the ...
HOLY CRAP I HAVE STUFF TO DO. HOW DO YOU PEOPLE MANAGE THIS.
129: I agree, but I also think it's true that not everyone is capable of understanding the ...
HOLY CRAP I HAVE STUFF TO DO. HOW DO YOU PEOPLE MANAGE THIS.
I don't even know what "short division" is.
Oops.
Also, now I'm imagining a Morris Dance about fractions.
134. Division that's easy enough that they don't make you show your working. In elementary school, usually defined by divisors up to 12, so that the kids can mentally recite their multiplication tables till they get to the answer.
So "short division" is "knowing the answer"?
I was taught a shorthanded method of showing work that was called short division. Setup like a long division problem, first step the same, but then subtract in your head and scribble the intermediate remainder inbetween the digits of the dividend to go to the next step, if you see what I mean.
I'll still mostly read all the comments, but it'll be ten minutes once a day.
Wow, you read quickly.
Thanks for asking, neB. I was just wondering that myself.
I don't know shit about math. And I have a tiny penis.
132: Primarily by ignoring my work. Your tax dollars at play...
HOW DO YOU PEOPLE MANAGE THIS.
How did you manage without? I'm on deadline, missy.
I don't think it's really called short division, I was just contrasting it to long division. It's just fucking division. (Sorry, am in bad mood due to other fucking idiots, so irritation may spill over.) But basically, 'short' division 1001 ÷ 7 , long division 1001 ÷ 13 .
Sorry, am in bad mood due to other fucking idiots, so irritation may spill over.
If we're allowed to do that, then fuck all of y'unz.
Nope. Didn't help my mood in the slightest.
144: Primarily by ignoring my work.
Ah, that's very efficient. I don't ignore my work, I just don't do it.
Oh c'mon, I could do with an argument about division or something equally trivial, to distract me from these fucking cows I have to deal with. Someone tell me 13 doesn't even GO INTO 1001, or something.
But really, your fucking cows.
There are worse things to be, presumably.
152 S/B 153
I'd be interested to see your proof.
152 = 153 for unusually large values of 152.
160, 161: HEY I"M DYING HERE!
On the OP: I have developed the habit of showing students the distribution of grades for whatever assignment they've done. The main reason I do this is that I think it discourages grades complaints. I imagine someone getting a poor grade, seeing that plenty of people got A's, and transfering blame to themselves, rather than thinking the test is unfair. I also show the distribution curve when it is very bimodal, to launch a discussion about why the curve wound up that way.
No one did this when I was a student, though. Is there a reason why I shouldn't do it?
163: Drift towards the mean. Students just above the mean will be all, eh, it's good enough, unless you also provide them with some type of positive reinforcement. The example I'm familiar with is a smiley face.
We're (sort of) herd animals.
Close enough to cows, in other words. Go on, asilon. Don't let society's expectations keep you from happiness.
...Too much?
163: I always liked it when teachers provided that sort of information, when I was a student.
I also show the distribution curve when it is very bimodal, to launch a discussion about why the curve wound up that way.
"Something approaching 1/2 of you suck. I'd provide more information about how you suck, except for the fact that you got so little correct, it is easier to list everything you do know. Which is basically nothing, because you suck. Furthermore, the fact that there is nobody in the middle of this distribution here suggests the problem is you suck at learning, not that I suck at teaching. So, if you promise me you'll try to suck less, I'll promise you that I'll continue to my best to reach the stupid half of the class."
A high school teacher put up a stem and leaf chart of our grades on the front board, then walked across it and drew lines for the curve. The groupings were pretty indisputable when it was presented like that.
166: That wasn't exactly my approach. Importantly, the main class where I get bimodal distributions is baby logic. There I give a little speech about the material clicking or not clicking, and how much you have to practice to jump from one group to the other.
168: No one wants to buy my motivational tapes.
No one wants to buy my motivational tapes
UR doin it rong
169, 170: "Undaunted, I knew the game was mine to win. Just like in life, all of my successes depend on me. I'm the man who has the ball, I'm the man who can throw it faster than fuck. So that is why I am better than everyone in the world. Kiss my ass and suck my dick, everyone. "
I'm buying dona's - do you think I can just go for cows straightaway, or work up to them via cats, dogs, and goats?
Careful, asilon. You fuck one goat...
I believe herding cats is considered...difficult?
I just opened my throat and fellated a goat ...
I can't believe I typed that whilst admiring my 9 year old's latest card trick.
OT: Apparently, I'm not the only person in Pittsburgh who uses species as a determinant of animal rights.
"At one point, animal control officers tried to lure the dog out with a cat."
At my institution, we use grading software that lets students see their scores online. It also tells students the mean score. The trouble is that there are frequently very low outliers who will generally withdraw from the class, and these drag the mean scores down considerably. So a lower-performing student will see that his score is "above average" and consider that permission to slack off.
For this reason I always try to discuss the distribution of grades in more detail.
A farmer and his wife were lying in bed one evening; she was knitting, and he was reading the latest issue of Animal Husbandry. He looked up from the page and said to her, "Did you know that humans are the only species in which the female achieves orgasm?" She looked at him wistfully, smiled, and replied, "Oh, yeah? Prove it." He frowned for a moment, then said, "Okay." He got up and walked out, leaving his wife with a confused look on her face. About a half hour later, he returned all tired and sweaty and proclaimed, "Well, I'm sure the cow and sheep didn't, but the way that pig is always squealing, how can I tell?"
I can't believe I typed that whilst admiring my 9 year old's latest card trick.
Careful, asilon, you're venturing close to b territory.
teaching philosophies prepare students to face circumstances that mirror the ways those philosophies manifest in pedagogy
I don't actually agree with that, but even if I did, how is drinking from a firehose a useful or desirable skill?
Oh my God that linked comment is a gem.
180: I hear careers in adult film are becoming much more socially acceptable.
In the real world, I've definitely been more surprised by how many chances you get than how many times the axe drops. Obviously some of these are white/middle class/etc privilege.
But a lot of it - how many times someone can be fucking terrible at their job without losing their job - just seems to be how our society functions.
For example, a colleague builds idiotic little GOTCHAS! into her syllabus, so if you don't read the whole (gigantic) syllabus outside of class, you don't know to email her with a smiley face message, and you get a zero on some embedded assignment. I'm really not clear where in life you get totally screwed for not immediately consulting the fine print when you receive it, as opposed to waiting until some situation calls for you to double-check the details within.
178: Wow. The "Coolidge effect" actually seems to be a term of art based on the old joke. Results seem to be mixed for simultaneously hermaphroditic species.
I'm really not clear where in life you get totally screwed for not immediately consulting the fine print when you receive it, as opposed to waiting until some situation calls for you to double-check the details within.
184. True Fact:
Back when their band was known as Mammoth, Van Halen played a concert on my wife's family tennis court.
My wife remembers David Lee Roth doing several wardrobe changes, which she thought odd for a high school dance. No M&Ms were harmed.
At some point during the meet-up this past weekend we were discussing how Unfogged has been around long enough now that no matter what the topic of conversation, there's at least one relevant archive link.
108,111
Surgeon-to-be friend of mine claims that it's simply because there is no way to learn the material, or develop the muscle memory, in a reasonable number of years without doing it that way. Plausible, but maybe she's just got Stockholm syndrome.
Oncologist friend used to be on 24/7 call for his patients, since the cases were complex enough that even with electronic records (which they had) there were too many things that could go wrong if the patients were handed off between doctors. Or so the hospital insisted.
Saying they had electronic records doesn't mean the electronic records are useful. I've heard horror stories about circumstances where a patient has several incomplete sets of electronic records in different systems that don't intercommunicate (records from when they're hospitalized, records from outpatient treatment for the same problem, etc.), supplemented by a set or sets of paper notes.
175: Sounds like adult-rated Dr. Seuss. Do people read Dr. Seuss in Britain?
Do people read Dr. Seuss in Britain?
Only for the articles.
So, do we require parental notification before a hospital can provide delivery care? (So sorry dear, but before you can have a kid you're either going to have to get a signed note from your mom or a waiver from a judge)
Wrong thread, not that I needed to say it, but it's a tradition.
191: We're going to need your parents permission before we can transfer you to another thread.
We also need an apostrophe, stat!
I'm sort of surprised that people think that doctor's would do a better job at diagnosis than computers. The setup where you have a ton of different rare conditions and lots of possible treatments really seems like the sort of thing where a giant smart database would do better than a person. Of course, you'd want people trained to have good bedside manner and to be good at getting info out of people, and you'd still want surgeons. But I'm kinda baffled that doctoring has stayed so done by humans rather than robots.
I think the cause is probably that people don't have a single insurer their whole life, so there's no upside to getting a good system in place. Also that the financial incentives for everyone are all wrong. But at some point some country is going to get this right and they're going to have better health outcomes for way cheaper.
We also need an apostrophe, stat!
doctor's
That was fast!
195.1:You don't watch House do you?
The problem is that difficult diagnoses often require exotic, expensive, invasive, or even destructive tests and procedures. Perhaps the computer would do better at narrowing the options, but as likely it would just demand them all.
I imagine this would lead to some nightmarish expected value calculations.
Wait, insurers already do this, don't they?
I've read that medical doctors (not to be confused with *real* doctors) perform best at diagnosis a few years out of university. Long enough to have some experience, but not long enough to forget all the rare problems. Programs routinely perform at human expert level or higher at diagnosis in restricted domains. This stuff is as old as AI; Mycin and Oncocin were some of the first programs for this task IIRC.
From Wiki on Mycin:
"[I]n tests it outperformed members of the Stanford medical school faculty."
http://en.wikipedia.org/wiki/Mycin
198 - yes, we love Dr Seuss!
I was on a train with my kids today and was treated to 3 renditions of "I know an old lady" by the about-to-be-8 year old. Hence farmyard animals being more on my mind than usual.
(Train to Cardiff and back, to collect my son from my mum, Cardiff being halfway between us, and the train being cheaper for me than driving.)
huh - I typed 198 and then 'corrected' it to 198 again. Should have been 189. And I totally wasted a Kobe moment.
and the train being cheaper for me than driving
You live in Heaven.
202: Yep, you don't need no baggage, you just get on board.
Well, it's a mixed blessing, fuel is quite expensive. And the toll bridge into Wales costs £5.50. But I have a family railcard which gives a decent discount, and booking ahead works well - lots of cheap singles available, and it cost me about £23 to get there and back.
lots of cheap singles available
I beg your pardon. I may be unmarried, but I'm certainly not cheap.
Of course, you'd want people trained to have good bedside manner
So you don't want doctors involved in that part of the process either.
I'm not sure I understand all this animus towards teaching long division.
Eh, I think it's just me. I love how comments threads can make it seem like a whole bunch of people are arguing one point when a whole bunch of people argue against it. Anyway, I mostly withdraw my objection because I can't come up with a way to clearly distinguish long division from division, and I think you obviously have to teach division.
As for the temperature calculations, I was thinking more in terms of precise-ish numbers in the middle range. I'm generally fine with knowing below 15 is cool to cold and above 25 is warm to hot, but 15-25 I don't know as well as, say 55-75 (which is not the equivalent range, but I haven't run the numbers). Basically, friends who don't know Fahrenheit were wondering how cold or warm it was this summer where I was, and I figure it's my responsibility to convert it to their system.
In my first years in Europe I ended up memorizing the conversions by intervals of ten and going from there by multiplying by 9/5 (-10=14, 0=32, 10=50, 20=68, 30=86, 40=104). Eventually both became second nature but I'm still able to convert very quickly.
On the prerequisites question, the policy in my current program is to give automatic Fs to anyone who tries to take a course out of sequence. This seems a bit extreme.
I haven't followed this thread in any detail, but I'm finding 195.1 quite strange. Surely the bit about getting information out of patients is rather central to any subsequent robotic processing of said information.
On the real world question, I found that in my first job after college, it was much more acceptable to do half-assed work, goof off at the office (in acceptably unobtrusive ways), and miss deadlines than it had been in school. I felt very welcome in the real world. Poorly paid, though, and the company later went out of business.
207.2, 208: I just wrote out a quick little two-column conversion chart and taped it near my monitor, which is where I usually checked weather and temperatures anyway. Pretty soon it became second nature.
205 has clearly *never* been to Wales.
I just wrote out a quick little two-column conversion chart and taped it near my monitor, which is where I usually checked weather and temperatures anyway. Pretty soon it became second nature.
Just now?
I'm really not clear where in life you get totally screwed for not immediately consulting the fine print when you receive it, as opposed to waiting until some situation calls for you to double-check the details within.
Any dealings with financial services companies? Or insurance companies? Landlords? Mobile phone operators?
Gasping along in the wake of this dead thread... I'm TAing a lab in modeling simple equations this term, and I'm dubious about adding numerical programming to anyone's first exposure to long division or higher. Even with two out of three of { math, population dynamics, programming }, my students are losing track of what the Knowns and Unknowns are at a given point.
Also, we're using a program written here some time ago and in the last throes of bit-rot, so they're afraid to make programming mistakes because it will hand. BADBAD.
...What would it take to have programming be a useful addition? Programming itself would have to be a vaguely familiar non-scary thing, maybe something everyone had done a little game in. Like how the XOXO is supposed to work.
That is a weird outcome. I took calculus an ungodly amount of times because I wanted a passing grade and gave up on the pre-med. (and KU would let me take incompletes).
BUT I took a biological statistics class while I was in the midst of the calculus debacle, I begged into the class. The published requirement was to have passed Calc 1 and I hadn't. I got an A in that particular class, I understood the equations and etc. but didn't in the theoretical classes.
I took me about six semesters to finally take a C grade. Seriously. And that was the end/edge of my math education. Asimov's theory of everyone having a maths level that they cannot rise above is right.
The other piece of the parts is that I would be going to class, doing the homework and understanding until, at a progressively later date in each class, I'd come to class and it appeared to my brain that the teacher was speaking a wholly different language than the day before.
It did stop me from ending up a medical student. but at this point in my life (50s) I don't regard that as a loss;
\
Asimov's theory of everyone having a maths level that they cannot rise above is right.
Maybe, but I'd bet almost no one ever reaches theirs. My (completely unfounded) theory is that we just aren't very good at teaching brains, and with the right techniques and feedback I could teach my cat not just calculus, but how to discover calculus.
Aaaand I should probably go to bed now.
9: What's the justification for still teaching long division?
Well, for one thing, knowing long division greatly helps you understand polynomial division, which you need for a whole bunch of algebraic simplifications. Just like I had one of my algebra students this summer practice his fraction arithmetic techniques so he could better understand how to work with rational expressions. There's a fair amount of algebra that is best understood by "you already know how to do this with arithmetic expressions - now let's generalize that to a symbolic context."
Other applications: understanding why any rational number is either a finite or repeating decimal (the remainder you get in each long division step can only take on a finite number of values, which have to repeat after at most size-of-divisor steps). Working with and calculating remainders. Converting between improper fractions and mixed numbers (see fraction arithmetic techniques, above).
Math shouldn't just be learning a bunch of facts and techniques for their own sake, but for what they can help us understand about other facts and techniques. So the point isn't how often you will use long division as an adult, but what you can learn from understanding the technique.