From Daniel Davies:
In particular, I’m not in the market for arguments which rely on, say, a physics exam being “more difficult” in the past because it used to require the memorisation of a list of formulas. The same exam could be made even more difficult by turning out all the lights and making candidates wear boxing gloves, but this would not have much to do with the standard of physics learning either (I don’t believe that standards of driving have declined due to the obsolescence of double-declutching, or that standards of football have declined due to the invention of laceless balls)
I like to point out that I had to learn a hell of a lot more physics to get my degree then Einstein did. He got to skip stuff like the photoelectric effect, brownian motion, reletivity etc. That makes the "easier" exams totally justified.
I've seen the results of contentless education, and it's not pretty. There was a reason for memorizing all those formulae, and it was because you have to have a foundation of knowledge to build upon. You can't think without having something to think with. We spend all our time trying to teach "critical thinking skills," but don't teach students anything to think with. We give them learning strategies, but don't tell them what's out there that they need to know (this has everything to do with the postmodernists' objection to "colonializing" the students' minds). Now students know nothing, but, because of all the self-esteem education they received, they are confident about it. But don't worry -- so long as educated immigrants keep coming here to work, we native-born Americans who are ignorant because we do not get any kind of education anymore can just go on welfare and have them all support us.
On the other hand, when I was in college (it wasn't here either...), we were supposed to be able to derive our formulas from basic laws, complete with proofs. And the exams were all a free-form interview with a lot of "opportunity" to do the above. I remember spending 5 hours doing just that in my senior year on the subject that wasn't even anywhere near my major. You actually end up remembering the formulas that way... just not by rote memorizing them from a sheet ;-)
No matter. In measly 20 years or so I have all of it safely forgotten :-D. I think the thinking pattern [of a physicist] is the only thing I have actually retained. Not at all sure I could have internalized it without all that "unnecessary" work on formulas, proofs and problems.
Sometimes it's appropriate to provide formulas, sometimes it's not. Obviously an E&M student should be expected to know Maxwell's eqns backwards and forwards, but in the context of another course, providing them is a reasonable precaution to save people from wasting their time with a sign error or the like.
I guess I was the opposite of Max in that I didn't stress about internalizing formulas because, in a pinch, I could re-derive most of them. But by now I've forgotten how to do that as well. So I'm out on both counts. Books come in very handy nowadays...
"Not at all sure I could have internalized it without all that "unnecessary" work on formulas, proofs and problems."
This is what our professor meant by he was giving us the formulas. We got the very basics and had to derive everything else out of them. The idea was to encourage students to not depend so heavily on memorization. It was possible to just memorize all the derivatives too but the people who did this studied far more and did worse than those that just learned the concepts.
D^2 is talking through his hat: the standard of physics and maths that British children learn at school is miles below what it was 30 years ago. Evidence: (1) I've taught Uni students over that period, so I bloody know. (2) My daughter did GCSE physics and showed me some of the pathetically thin stuff she was taught, poor mite. (e.g. Ohm's Law taught as three separate results, because it's now assumed that the pupils can't rearrange a line of algebra. And, three results being really really hard to remember, they are then taught a geometric mnemonic for them. N.B. so it now also requires more rote memorisation than it used to. Bloody brilliant.) (3) Some departments have used the same test for new freshers over two or three decades and so can demonstarte the jaw-dropping decline in knowledge and skill. One is (if memory serves) Computer Science at York. Or rather, it was; the recent freshers did so badly that the department gave up the test as having become useless.) D^2 remains an utter plonker.
Football has laceless balls? Then what is that white lacey thing Tom Brady grips when he throws touchdowns?
I think a case can be made that standards of driving declined with the eclipse of stick shift. In fact, I tried to make it once. I can't speak to double declutching, which must have been really hard.
Now students know nothing, but, because of all the self-esteem education they received, they are confident about it.
Naw, that's just a sign of getting old.
Meanwhile, Davies seems to be conflating two related, but not causal, points in all of that. The first is whether the standards have changed, the second is whether it is possible to make the standards more difficult without imparting added value to the education.
The latter is not only possible but regularly occurs. My engineering alma matter, for example, tends to run its Differential Equations curriculum in seven-year cycles, where for four or five years it is used to pare the goats out of the sheep flock, and then for a couple years they tone it down because too many students are scoring below a C in the course (often well below) and tighten up one of the other courses to compensate for the lost sorting function. This repeats like clockwork.
That Davies uses such an argument as the second to serve as a lateral refutation to the first is probable evidence that he hasn't looked very deeply into the first, and needed something glib as a substitute.
Self-quoting but exclusively for the sake of clarity:
Not at all sure I could have internalized it without all that "unnecessary" work on formulas, proofs and problems
"It" in this sentence referred to the thinking pattern, not the formulas. The former is still useful, the latter ceased to be even before I graduated (changing the major helped).
The topic of standards can be batted around a bunch, which is why D^2 doesn't want to argue it. I wouldn't necessarily agree with him, but there's not world enough and time to discuss all the relevant issues. One point is whether it would be necessarily useful to have various lost skills (such as in driving), or whether the importance of knowing more things (but vaguely and having to look them up) is better than knowing fewer things better, particularly, as noted, in the sciences where more has been discovered in the last 100 years.
Physics presumably has it a little rougher than mathematics (my field) in that all the modern results are expected to be covered by an undergraduate. That necessitates skipping some things or covering them less well. By contrast, math still tends to teach the same mathematics to undergrads that it always has. As a result, you can't do math research when you become a grad student-- you generally only know math up to, say, 1900, though if you're advanced you'll have gotten a bit farther and seen Lebesgue integration (1902), measure-theoretic probability (1930s), the Riesz representation theorem (1906?), or maybe some early 20th c. modern algebra. You steadily work forward in grad school until after a few years you can work with your advisor to learn about new work so that you can do research. OTOH, at least physics can discard discarded theories, whereas math is built up on itself.
It's begging the question, really, that paragraph. Of course in some sense the standards of driving has declined because it's easier, but surely that's an advantage of civilization, not a problem. Standards decline in some things because those talents are considered no longer as useful as other things.
It may well be that easy access to books and the Internet mean that memorizing formulas is no longer as useful. However, I have definitely seen occasions where ability to instantly recall formulas, and even from simple rote memorization, has help mathematical research and understanding. Whether it's of enough use to make up for learning more material, or other aspects of things, is always a matter of debate-- though it may well be other peoples' problem if you're not an educator. I fail to see how taking a test in boxing gloves would ever be useful, so his comparison is pointless and useless.
I remember with fondness one of my EE engineering classes where, during each test, you could bring in a 3x5 card with whatever formulas you wanted written on it (front and back). For the first test, I had a lot of formulas written down. By the last test, not so many, because I had managed to learn the ones I used the most.
I thought that it was a good system for several reasons. (1) It forced you to review the material as you picked which formulas to write down. (2) It let you concentrate on problem solving as opposed to brute memorization.
I attended a major Land-Grant university Engineering school, and we used Thomas's book for Calculus, which had tables of differentials and integrals on the inside covers.
We had to memorize those tables to do well on the closed-book exams, and I'm pretty sure it stifled my progress in the course, although I did ok.
I spoke with a high-school friend who attended MIT, and took Calculus with Thomas himself, and used the same book. According to my friend, Thomas said something like "When you do real engineering work, you have the book in front of you. It won't help you if you don't know what you're doing, so why not have it now?"
I'd forgotten until this thread came up.
I spoke with a high-school friend who attended MIT, and took Calculus with Thomas himself, and used the same book. According to my friend, Thomas said something like "When you do real engineering work, you have the book in front of you. It won't help you if you don't know what you're doing, so why not have it now?"
In grad school, I came across a counterintuitive phenomenon. Closed book exams were a piece of cake. Open book tests were very tough. Take home tests were grueling, with our 9 day take-home final for Mechanics being an act of pure sadism.
I remember with fondness one of my EE engineering classes where, during each test, you could bring in a 3x5 card with whatever formulas you wanted written on it (front and back). For the first test, I had a lot of formulas written down. By the last test, not so many, because I had managed to learn the ones I used the most.
This was pretty much standard (or sometimes a half-sheet of paper was permitted instead) for most of my engineering classes. By the end of the third year, I was pretty much qualified to inscribe microfische slides.
I graduated in good standing, but the consequent GPA hurt my odds in the interview pool for several years, until the recession finally lifted its icy hands off the Colorado Front Range region.
Football has laceless balls? Then what is that white lacey thing Tom Brady grips when he throws touchdowns?
I believe that the author is British, and that the "football" he refers to is the type kicked by Wayne Rooney.
I'd propose the same explanation for the enraging superciliousness of the whole piece, except that everything I've ever read on Crooked Timber is written in the same tone.
If the Flynn Effect is true, then at the same time that most of us old timers think standards are much lower, IQ scores are much higher. So, at least one standardized test is going the other way. Personally, I think the science standards are more important, but I'm just sayin'
I'm with Rex and anony-mouse, but with a spin. The act of making those "cheat sheets" is an important way to study, and I think it's worth doing even in classes where you can't bring them to the exam.
I've had exams where I agonized over what went on the card or paper I would bring. I'd have to think through every formula and decide whether to include it or derive it on the fly. If the latter, I'd practice deriving it to make sure I could. After going through the course content this way, copying the resulting "essentials" into the proper form (possibly through several drafts), and making sure I could reproduce the rest of the class material from the stuff on the paper...
Well, let's just say I didn't need to look at the paper all that much!
Here's some evidence from the University of Washington I find fairly compelling: "Interestingly, the university gave virtually the same mathematics placement test to all freshmen from the mid-1980s until 2000; students' scores declined during this period, objectively confirming our subjective impressions." (http://seattletimes.nwsource.com/html/opinion/2002083521_satrdr06.html)
I think a large part of the problem comes from our attempt to college-educagte a much larger fraction of the population. Given rising IQs and better pre-K and elementary education, it may be possible to slowly increase the fraction of the population that attends college without lowering standards, but not at anywhere near the rate we have attempted.
Those of us who still double-clutch usually drive race cars (with racing transmissions) or some old car without a synchronized transmission. We actually are better drivers due to the track work but on the street the need to think while shifting often precludes the usual annoyances. For instance, I never listen to talk radio while driving, it's just too distracting and shifting while trying to talk on the phone is downright dangerous. Btw, I learned to double-clutch in a modern Porsche so that I could comfortably drive those old cars, that ability once freaked out a family friend, he informed me that some synchro gears had gone bad in his MGTC so I started to effortlessly double-clutch. His response was that I was way too young to know how to double-clutch, the car however is only seven years older than me.