So, ultimately, not all that different from staying home and changing diapers?
Hey, this is a good place to continue the math-teaching conversation from the end of the "Nobel Laureates" thread.
To sort of restate what I was saying there, while mostly I resist blaming poor educational outcomes on a belief that teachers suck, I do kind of lean that way for elementary school math. It's sort of socially okay to "suck at math" in a way that people would be ashamed of if they were that bad at, say, knowing how to read. And I can't help wondering if you don't get a fair number of grade school teachers like this, who systematically fuck up all of their students who aren't capable of effortlessly self-teaching the material.
The only solution I can think of is going to heavily scripted standardized lessons for math specifically, but when I call that a solution I don't mean to say I think it's a good one.
I thought "New Math" was teaching everything through set theory, or something. Now, of course, I have a Tom Lehrer earworm. ("You can't take three from two, two is less than three, so you go to the four in the tens place. Now that's really four tens, so you make it three tens, regroup and you change the ten to ten ones...")
I do kind of lean that way for elementary school math. It's sort of socially okay to "suck at math" in a way that people would be ashamed of if they were that bad at, say, knowing how to read. And I can't help wondering if you don't get a fair number of grade school teachers like this, who systematically fuck up all of their students who aren't capable of effortlessly self-teaching the material.
Yep. There's a lot of research supporting this. Anti-math attitudes in teachers, particularly elementary ed, really poisons student performance, and is really common.
It's really screwy how okay it is. Newt's teacher for next year knows he's coming, and we've been told that she's got a plan for him to do some kind of math thing that will be over her head. And that's lovely, and Sally had her before and she's generally a good teacher and we like her. But Newt's not a prodigy - he's a mouthy kid who's competent with arithmetic and fractions, and is ready to start fooling around with something slightly more interesting: that catering to this sort of thing is intimidating her is a real mess.
My kids haven't taken any damage, because they've got me and Buck. But geez, that's not good.
so you go to the four in the tens place
My brain imprinted on this record while very, very young and immediately stumbled on "go to" and corrected to "look at."
4: Yes, my "joke" was even stupider than that. Just great nits in math pedagogy.* And Tom Lehrer.
*I think I was taught "New Math" for a couple of years but ignored it along with most everything else I was being taught.
Why is it so hard for me to remember if the % symbol goes before or after the number? It goes the way you read it aloud; there's nothing to remember. And yet I always fumble with it.
It goes the way you read it aloud; there's nothing to remember.
Just remember it's the opposite of the way you place the dollars sign.
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Anyone else on the east coast just feel an earthquake?
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Pretty sure just felt a noticeable earthquake here in P'burgh. Twitter is confirming. Not that big but still not that common. Apparently felt in a lot of the mid-Atlantic.
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We felt it in NYC. I am on the 25th floor, so we probably felt some extra swaying up here.
There have been jackhammers outside all day, vibrating me, so for a while I thought they just had turned them up more or something. Then I thought they accidentally damaged the foundation. Then I looked at facebook and found "5.8 earthquake".
Well, that was interesting. Totally took me by surprise - I thought the house was going to collapse what with crap falling.
USGS says the epicenter was about 20 miles west of Charlottesville.
max
['You ok, Stan?']
My first earthquake. How exciting. Also, office evacuated twice in one day, apparently by coincidence. Bizarre.
Felt it *quite* clearly here in my government building in DC. p- and s-waves nicely distinct.
I'm in Raleigh; my office-mates felt the earthquake, but I didn't. But the geologist I work with is very popular right now.
Hey, the earthquake is in this thread too.
Less exciting and more annoying now that we're allowed to go home, but I need to go back for keys and more, but they're not letting us back into building just yet. Also, hate to complain about time off, but this won't be good for a deadline.
I'm fine. Thanks for asking. I'm in Richmond for the day.
|| EMess, you seen any pix of that fire near EMo? Went from 5 to 1000 acres in two hours yesterday; it's hot, windy and dry today. I don't think it'll come to Jumbo, but who can be sure. |>
Four full bookcases fell over. Two of them are 7' high, 42" wide. The floor is a sea of books.
Yow! That could have hurt somebody.
Anyone else on the east coast just feel an earthquake?
Will this be on the exam?
25: ugh. One of my bookshelves at home is wobbly. Im going to be worried about that until I get there.
26: Both cats gt themselves out of the way very quickly and are still hiding. We've figured out where they are, but they can't be coaxed out.
29: Cats aren't stupid about earthquakes (on the other hand, some dogs seem to think that the meagrest thunder is an announcement of the Last Judgment, which they expect to go badly for them). Isn't one of Mary Renault's notes in The King Must Die the suggestion that Theseus, like a cat or other domestic animal, was sensitive to little pre-quake tremors?
limited reports of damage reported near the quake's epicenter in Virginia, where a nearby nuclear power plant was taken offline.
Only one solution: we must immediately nuke this power plant in order to save it.
And now I can't find that thread. Truly one of the all time top 6 Bob moments.
At first I thought this was quick work by someone ("Shaken! Earthquake Rocks Central Virginia"), but it is write-up of a December 2003 quake in the same general vicinity and has good info on the local geology and faults.
Allow me to be the first to report that there was an earthquake here today.
5: So has anyone done any research on the best way for a math-phobic teacher to teach math to children without scarring them?
36: Doesn't it suggest we should have specialized math teachers in elementary school?
That does make a certain amount of sense. I wonder if it'd be a serious cost difference, or a no-change-in-spending reorganizational thing.
36: I'm really not up on the literature, but I'm pretty familiar with the standard math-for-elementary ed teachers course, which when taught well, is really really good, and supposed to address things like that.
It's supposed to accomplish two things:
1. showing the underlying math beneath elementary ed level ideas
2. placing the future-teacher in situations where things like addition and place-value are confusing, to get them to observe what it's like when these things are new. For this one, it's typical to have a unit on math in base 7, for example.
When done poorly, the courses look like you're jerking a bunch of future-teachers through an assortment of really random topics.
6
It's really screwy how okay it is. Newt's teacher for next year knows he's coming, and we've been told that she's got a plan for him to do some kind of math thing that will be over her head. And that's lovely, and Sally had her before and she's generally a good teacher and we like her. But Newt's not a prodigy - he's a mouthy kid who's competent with arithmetic and fractions, and is ready to start fooling around with something slightly more interesting: that catering to this sort of thing is intimidating her is a real mess.
Sounds like he is a prodigy at least compared to the other kids if his reputation has preceded him to this extent. Or is it your reputation?
It's a small school, and he had a bad habit of straightening out last-year's teacher's arithmetic errors. We're working on his manners. (Also, the next-year teacher remembers Sally.)
I want to respond further to JBS's comment from the other thread, about algebra traditionally separating the smart students from the dumb ones. I don't think this is a particularly useful view of the situation as I've seen it. There's nothing particularly intellectually impaired about the vast majority of the struggling students in the algebra classes I've substituted in, particularly if you talk with them about something else they are interested in. Sure, some of them are struggling with language barriers, and quite a few of them have holes in their arithmetic background that make algebra harder for them, e.g., struggling with negative numbers, multiplication, or fractions in some way. But those things are fixable given sufficient time and resources. I've met a lot of students who were not learning, but hardly any who I was convinced could not learn the material, given the right circumstances.
I've also had some remarkable turnarounds with students I've worked with in individual tutoring. One high school kid was having trouble working with rational functions, which I diagnosed as based on a weakness doing fraction arithmetic. So we went over the rules for fraction arithmetic, and I gave him some 5th-grade worksheets to practice with. When we came back to rational functions a couple of weeks later, he did just fine. That's the kind of thing you can do when you are working one-on-one, and have the schedule flexibility to move topics around as needed. It's much harder when you are working with a classroom of 25-35 kids at a time and have a schedule to meet come hell or high water.
42
... But those things are fixable given sufficient time and resources. I've met a lot of students who were not learning, but hardly any who I was convinced could not learn the material, given the right circumstances.
I am not sure how this contradicts what I said. Perhaps with sufficient effort most students could be taught high school algebra but what would be the point? For the most part it won't benefit them in later life. Why not spend the effort teaching them something useful?
As I said before the push to make learning algebra a requirement stems from a misunderstanding of why success in high school algebra predicts success in later life. It is because (under current conditions) success in high school algebra is a strong indication that you are smart (and in particular good at a certain type of abstract thinking) and being smart is helpful in the modern economy. It is not because knowing high school algebra is essential to function in the modern world. So if at great expense you teach nearly everyone high school algebra, learning high school algebra will no longer predict later success (perhaps passing high school calculus then would) but the students who are now passing won't do any better in life.
Perhaps at one time success in high school latin predicted success in life. But this doesn't mean it is a good idea to make everybody learn latin.
43: If you're still reading this...
I don't know if you view this as useful, but, when I was a EE TA for a weedout class, I taught basic algebra to a group of kids who would have otherwise failed. No one took the time to explain it to them in high school, they weren't the sort of kids who could figure out themselves, and the professor thought it was a waste of time to cover remedial material.
In one sense, it was useless. None of those kids took a job that used the skills required by that class (Laplace transforms, Fourier analysis, etc.). But, the median starting salary for an EE degree from my alma mater was something like 55k or 65k, and there are plenty of EE jobs you can get that never do any fourier analysis, as long as you have the little piece of paper that says you have a BS EE.
If you don't think that was useful, I'm curious why not. Did I devalue the EE degree, reducing the income of all other EEs by epsilon, canceling out any benefit?
44: WTF? How could one function *in any way* as an EE without algebra?
Now you know why all that work is done in Asia.
44 actually sounds heroic to me. Congratulations and that's awesome.
I just did a fourier analysis today, but then my boss told me to stop.
45/46: I meant that most EEs don't need Laplace and Fourier, but I think you could get by without algebra. Ironically, the high value work in my little subfield (microprocessor design) is done in the U.S., and probably requires a lot less math than the things that have successfully been outsourced.
There have been a few papers that mathematically model performance, but they're not practically useful. Since mathematical modeling is intractable, it comes down to intuition* and detailed simulations. The latter is just a lot of programming (and not math-y programming). Then you need to actually make the thing, but, at a high level, that's just more programming. In one sense, it's even easier than programming software, because of how limited hardware and HDLs are.
When I did lower level stuff in classes (which is much of the work that's now been outsourced), like circuit design, we often worked through mathematical models by hand. But, if I were doing it for real, I imagine I'd run SPICE rather than model it by hand. It would be 100x faster and much more accurate.
* this is why so much of the high-value work is still in the U.S. It started here, so there are lots of old geezers who have good intuition; youngsters who work nearby seem to pick it up osmosis, and the cycle continues. It's purely historical accident, and I don't expect it to last, but I'll take advantage of my good luck while I can.
The latter is just a lot of programming (and not math-y programming).
Programming without some grasp of algebra seems implausible at best.
Programming without some grasp of algebra seems implausible at best.
Meet some more COBOL 74 monkeys. Or not, if you value your time. You can usually tell old commercial code that was written by people with no grasp of algebra: it tends to read like a rather circuitous narrative, and there's far too much of it about.
Meet some more COBOL 74 monkeys.
Sure, or Forth. You can't convince me they're plausible.
50: I think it's only implausible because algebra is so basic that almost everyone who didn't go to a poor inner city or rural school knows algebra. If you're just writing if X then Y else Z, what do you need algebra for?
Maybe it's a bit more complicated than that, because directly interpreting the model is way too slow, so you do dynamic translation or what have you. But, if that's done correctly, it's nearly transparent to the person writing the model, who just has to know that if these four conditions are met, you do this, otherwise, you do this other thing. For this kind of thing, it's just a bunch of state machines (when it's even stateful at all), and state machines are simple.
In other words, an eighth grader could do my job. Probably better than me, because they wouldn't waste time commenting here.
Perhaps even more implausible, but also true: we had a Forth processor inside our processor at one point. Stack processors are tiny, so it was free, since we could drop it in a hole in the floorplan. Writing an LLVM backend for it was painful, though, since the closest thing it had in terms of support for a stack processor was the x87 FPU.
or rural school knows algebra
I went to a rural school and everybody had to have at least some algebra.
55: Sure, there's assignment, but how is algebra a pre-requisite for understanding assignment? Considering how the meaning of = is overloaded, I think it actually makes it harder. I remember the exasperation of CS TAs, who couldn't understand why their students were confused by statements like a = a + 1. That's something that's only going to be confusing if you've had algebra: how can something be equal to itself plus one?
I don't know anything about the programming implications or the math pedagogy, for that matter, but it seems worth distinguishing understanding variables and the idea of solving for x and that sort of stuff from knowing whatever it is that algebra is these days.* The former seems quite useful for lots of people, the latter, if you're getting into quadratics and then all the stuff beyond that, is useful if you're going to build on it, but fades quickly if it doesn't come up in the course of everyday life.
*I remember an algebra-geometry-algebra sequence.
Without quadratic equations, you don't have any simple, rigorous way to describe breasts.
In junior high, that would involve typing 80085 on a calculator.
62: Oh, right. I knew that looked wrong.
44
If you don't think that was useful, I'm curious why not. Did I devalue the EE degree, reducing the income of all other EEs by epsilon, canceling out any benefit?
This is a little different, you are teaching students who want a credential that legitimately requires being able to learn algebra. Obviously your efforts were helpful to your students. (Or at least some of them, were they all able to pass?) Not so much for society as you are helping one marginal job candidate move ahead of another. But to the extent you are just compensating for a below average prior education you are making the evaluation process slightly more accurate.
60,61: The iPhone's calculator has inadequate boob visualization technology.
Not so much for society as you are helping one marginal job candidate move ahead of another.
James, you're a fucking idiot. And I mean that all friendly-like.
65: Each person who supplies or demands from a market affects that market in real ways, but teachers just stand at a chalkboard so you don't need to worry at all about anybody's individual effort.
62: No, you were right too.
I was just thinking of other words-with-numbers that required an inverted calculator, such as 71077345
63: Pass the class? Yes, with one exception. Pass all their classes and get a degree? I don't know, since I graduated and didn't keep in touch. But the curve made it nearly impossible to fail once you made it past the weedout classes, so I suspect most of those kids did fine.
I don't think it's zero sum in that way. I was only half kidding, above, when I said an eight grader could do my job. It's really not very hard, but hiring managers only want people with the right credentials, even though you could train most anyone to get up to speed in a month or two (and you need to train people with the right degree anyway because, for any particular job, school is overly broad and theoretical). Here in Aus/tin, this subfield has been hot for the past decade. Companies have been killing each other over warm bodies; they'd love a "marginal" candidate. The marginal candidate, of course, is better off with a job than without, so it's win-win. As with the Laffer curve, you can say that, at some point, increasing the number of credentialed people will be a net loss, but I don't think we're even close to that point.
56: Sorry! Over-generalization. I should have said something like, kids who didn't have the proper math background at my school were more likely to come from schools in poor urban and rural school districts because we were a state school with a policy of admitting the top N% of students from any in state high school. Poor, small, schools have all the problems of poor schools, plus higher variance because they're small, and rural districts are more likely have schools that are both poor and small.
68
... you could train most anyone to get up to speed in a month or two ...
I doubt this and am curious what the real numbers are.
... at some point, increasing the number of credentialed people will be a net loss, but I don't think we're even close to that point.
By your account the credential is useless and you could benefit society by handing them out at random (which would be a lot less trouble than teaching marginal students algebra). But is that really the case?
69: With a sufficiently long piece of scratch paper and sufficiently explicit instructions, anyone can do advanced math:
http://en.wikipedia.org/wiki/Turing_machine
Of course "up to speed" implies that they can do it quickly, which may not be the case...
69.1 and 69.2: I'm aware that I have an extreme minority position, which is good meta-evidence that I'm wrong. Moreover, there's no way I can provide empirical evidence for my claims, so there's no hope that I'll convince you. I still don't see why everyone else believes what they believe, though.
When I was doing optics, back before telecom crashed, I could see why you'd want someone with a degree for that. You couldn't even understand the basic operation of a new device unless you had a strong background in solid state, mathematical physics, waveguides, and so on, let alone develop intuition and creativity. What I'm doing now seems completely different, though. Skill at the job comes down to pure intuition, which you get by doing the job. There's not much else to it.
I haven't heard of anyone who's been able to figure out which new grads can develop good intuition, so picking people at random seems like a good a scheme as any. I think it would certainly be better than what we do now, which is to interview all the people from top schools with a 3.9x or 4.0 GPA, and then give half of them job offers. Those folks get sweet offers from all our competitors, too, as well as companies who don't play in our niche, so we spend a huge chunk of time interviewing people who go elsewhere.
Do you believe that candidates who are on the margin in terms of ability to get a degree are also only marginally productive? If you buy that, I don't think it's a big leap to the idea that people without a degree at all may be fine. We declined to hire the most creative and fastest engineer I know because he failed a weedout class a couple of times and switched to a related degree where he didn't have to take that class. He was underemployed for a few years, but someone at N/vidia managed to sneak him past HR and he now works on a product that promises eat our lunch.
Yesterday's NYT op-ed on How to Fix Our Math Education offers a different perspective. I'm not sure I agree with their whole article, but it's an interesting idea. I do think that often HS math is taught as an isolated bunch of skills, without really tying it all together.
71
I haven't heard of anyone who's been able to figure out which new grads can develop good intuition, so picking people at random seems like a good a scheme as any. I think it would certainly be better than what we do now, which is to interview all the people from top schools with a 3.9x or 4.0 GPA, and then give half of them job offers. Those folks get sweet offers from all our competitors, too, as well as companies who don't play in our niche, so we spend a huge chunk of time interviewing people who go elsewhere.
If all you are saying is that you could skip the interview and flip a coin instead this is plausible as long as your pool remains people with 3.9+ GPA's from top schools. If picking people at random means expanding the pool to include people who dropped out the LA schools because they flunked algebra six times I don't think it is plausible.
71
... What I'm doing now seems completely different, though. Skill at the job comes down to pure intuition, which you get by doing the job. There's not much else to it.
It seems to me that microprossessor design requires a capacity for abstract thinking which is likely strongly correlated with the ability to pass high school algebra even if high school algebra is not used directly. And I think the capacity to solve "word problems" (which is part of high school algebra and which many students have trouble with) is needed. For example if you are breaking cycles per instruction down into cache misses, branch mispredicts, instruction stalls etc. this is basically a word problem.
43: You're arguing that algebra is just an arbitrary shibboleth that identifies the smart kids, like latin used to be. I agree that there are some individual skills there that are mostly taught because they are useful when learning more math. But I think there are some bigger issues with *not* teaching kids algebra:
1. It's part of an entrance requirement for most four-year colleges. Admittedly, not all these kids are going to want to go to college, and most of them aren't thinking about college now. But life is a long time. Some of these kids may discover, after they've been out in the world for a while, that maybe they do want something that requires a college degree. While it's possible to make up some high school requirements in adult school or community college, the more they have to make up, the less likely it is that they will actually complete the program. If you want to apply somewhere that requires three years of high school math, it's a lot easier to catch up if you already have one or two years under your belt, than if you have to start from scratch. Even if you have to review what you studied in high school, its easier to do that than learn it from scratch. I think it's awfully early to be writing these kids off as "never going to go to college."
2. It's a prerequisite for learning other subjects - particularly the lab sciences that are also part of most college entrance requirements. I can't imagine trying to do chemistry or physics without algebra, and even biology/geology/physiology are going to be easier if you can use and manipulate equations.
3. It seems to be easier to learn this stuff when you are young. Yes, there are people who come back to math midlife and manage to master it, and I deeply admire those who do. But it seems to be harder for many people. I've had a couple of midlife clients who really struggled with learning algebra in a way that my younger clients rarely did - and these were people who were strongly motivated to learn algebra, to the extent of voluntarily signing up for a class in the subject, and hiring a tutor when they got stuck. There was an aspect of Just Not Getting It there that I didn't usually see with the younger kids when I explained stuff.
4. In many cases, the troubles these kids are having with algebra are based on troubles they are having with some aspect of arithmetic. In arguing that they don't need to learn algebra, you are implicitly also arguing that they don't need arithmetic either - because I'm convinced that in many cases they can learn algebra if you can address their problems with arithmetic.
5. In a few years, these kids are going to be voting and serving on juries. I think it's helpful for society if they can at least follow the general outlines of a quantitative argument, and algebra is helpful there. I don't want these kids to become Fox News voters by default, going "Tax Cuts gooood. Obamacare baaaaad," just because they tune out every time someone starts looking at the math.
75
4. In many cases, the troubles these kids are having with algebra are based on troubles they are having with some aspect of arithmetic. In arguing that they don't need to learn algebra, you are implicitly also arguing that they don't need arithmetic either - because I'm convinced that in many cases they can learn algebra if you can address their problems with arithmetic.
Can we agree it's stupid to try to get everybody to learn algebra when you haven't been able to get everybody to learn arithmetic? Nobody should be in an algebra (or any other class) who doesn't have the prerequisites (and can't be reasonably expected to catch up on their own).