Re: Ask the Mineshaft: Heebie's Shoes edition

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Explain to the editor how the baby is stealing all of the blood that should otherwise go to your brain. It really couldn't be helped.



Posted by: Tassled Loafered Leech | Link to this comment | 01-29-09 12:17 PM
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I think for me the average difference between "time I'm reasonably sure I will complete a paper" and "time paper is completed" is at least three months -- maybe more -- so, if you are anything like me, postponing everything to finish the paper is a bad idea.


Posted by: essear | Link to this comment | 01-29-09 12:17 PM
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My inclination would be to just send it to him as-is just to be done with it.

That's probably really bad advice.


Posted by: Di Kotimy | Link to this comment | 01-29-09 12:19 PM
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(I say, while commenting on Unfogged instead of finishing the paper that was a week away from completion in mid-November.)


Posted by: essear | Link to this comment | 01-29-09 12:19 PM
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is at least three months -- maybe more

Oh dear god. I have a sinking feeling now.


Posted by: heebie-geebie | Link to this comment | 01-29-09 12:20 PM
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3: At least in terms of the math, perfection matters. In terms of the prose, readability has a fairly high importance, although it's okay if it's a little choppy still.


Posted by: heebie-geebie | Link to this comment | 01-29-09 12:22 PM
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If you were a software firm, you might plot the occurrences of these realizations and time-to-resolution for each one; you would, in your corporate personhood, hope to see these marks getting smaller and farther apart, like drips of blood from a barely-scratched bicyclist.

Limit and convergence theorems are left to --- huh, I asked the compiler team how they knew the compiler would converge, and I don't believe anyone told me.


Posted by: clew | Link to this comment | 01-29-09 12:26 PM
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Lower your standards.

This is the hardest thing to do, but the only way to get rid of papers that won't let you complete them. Don't rewrite the whole section to fix the mistake. Gloss over it with a sentence. Practice writing sentences like "This is an important issue, but it falls outside the scope of this study." "The validity of this inference can be easily seen with a moments thought." "Strictly speaking, this inference isn't valid, but it can be easily replaced with a valid one." (I believe the philosopher John Searle actually used that last line.)


Posted by: rob helpy-chalk | Link to this comment | 01-29-09 12:27 PM
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Heebie's academic style is just like her livejournal style.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 12:28 PM
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5: Well, I wouldn't generalize from my experience. For one, I'm not a mathematician. Anyway, my problem is that by the time I understand something well enough to write a paper about it I'm bored by it and thinking about the next two or three things I can work on.


Posted by: essear | Link to this comment | 01-29-09 12:29 PM
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"Strictly speaking, this inference isn't valid, but it can be easily replaced with a valid one."

Oh, I hate it when people do that.


Posted by: essear | Link to this comment | 01-29-09 12:30 PM
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Maybe the editor would let you make a diorama instead.


Posted by: jms | Link to this comment | 01-29-09 12:31 PM
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Here's a video to inspire you


Posted by: rob helpy-chalk | Link to this comment | 01-29-09 12:33 PM
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I've been postponing all social activities in preference of this paper. Which is unsustainable

Not at all unsustainable, heebie. In fact, it's preparing you quite well for parenthood. Consider it practice for the next five years of your life.


Posted by: apostropher | Link to this comment | 01-29-09 12:33 PM
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12 FTW.


Posted by: JRoth | Link to this comment | 01-29-09 12:33 PM
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Maybe the editor would let you make a diorama instead.

Yeah, maybe.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 12:33 PM
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Not at all unsustainable, heebie. In fact, it's preparing you quite well for parenthood. Consider it practice for the next five years of your life.

When you make the finishing touches on a paper, your body releases oxytocin that triggers your bonding instinct and makes you protective of the paper forever.


Posted by: essear | Link to this comment | 01-29-09 12:35 PM
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12 made me laugh out loud. And I think I will take 8 to heart. This is helping.


Posted by: heebie-geebie | Link to this comment | 01-29-09 12:37 PM
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Heebie's academic style is just like her livejournal style.

Are you saying my livejournal is full of mistakes and incohent? Or that the paper is suffering from verbal diarrhea?


Posted by: heebie-geebie | Link to this comment | 01-29-09 12:38 PM
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It took me a few seconds to arrive at what I believe to be the correct interpretation of the post title.


Posted by: Stanley | Link to this comment | 01-29-09 12:44 PM
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No post about this story yet? I'm disappointed in you, Unfogged. It's even better than Modern Love.


Posted by: Ginger Yellow | Link to this comment | 01-29-09 12:46 PM
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20 Um .... yeah, me too. But since you said first, maybe go ahead and post your interpretation.


Posted by: JP Stormcrow | Link to this comment | 01-29-09 12:47 PM
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20: It was kind of half-assed, I admit. All ask the mineshaft questions inherently ask you to step inside the person's shoes.


Posted by: heebie-geebie | Link to this comment | 01-29-09 12:47 PM
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22 & 23: Oh. I thought it was a shoegazing reference.


Posted by: Stanley | Link to this comment | 01-29-09 12:48 PM
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21: A story like that, you'd think it'd have been linked five or six times in the comments by now.


Posted by: essear | Link to this comment | 01-29-09 12:48 PM
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21: Not to mention litotes John Updike's death, for God's sake!


Posted by: JP Stormcrow | Link to this comment | 01-29-09 12:49 PM
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24: Oh. I thought it was a shoegazing reference.

Oh, I thought it was *exactly* what heebie said.


Posted by: JP Stormcrow | Link to this comment | 01-29-09 12:51 PM
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Applying the sound principles of structured procrastination, the solution seems pretty straightforward: find another long-term project that's even more important, but less urgent than the math paper. Then you will finish the math paper as a means of avoiding work on the other project.

As far as selecting the long-term project, teaching your baby to walk and/or talk might just fit the bill.


Posted by: Knecht Ruprecht | Link to this comment | 01-29-09 12:54 PM
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I thought it was a shoegazing reference.

Isn't anything?


Posted by: essear | Link to this comment | 01-29-09 12:54 PM
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5: Well, I wouldn't generalize from my experience. For one, I'm not a mathematician. Anyway, my problem is that by the time I understand something well enough to write a paper about it I'm bored by it and thinking about the next two or three things I can work on.

Boy, do I know this feeling.


Posted by: redfoxtailshrub | Link to this comment | 01-29-09 12:56 PM
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See, I don't realize how poorly I understand the topic until I actually sit down to write the paper.


Posted by: heebie-geebie | Link to this comment | 01-29-09 12:57 PM
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See, I don't realize how poorly I understand the topic until I actually sit down to write the paper.

Oh, believe me, I know this feeling too.


Posted by: redfoxtailshrub | Link to this comment | 01-29-09 12:58 PM
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I get bored by things well before I understand them.


Posted by: Eggplant | Link to this comment | 01-29-09 1:00 PM
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I find the very process of coming to understand things boring.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:01 PM
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I don't get it. No, no, don't explain.


Posted by: Eggplant | Link to this comment | 01-29-09 1:03 PM
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I'm bored.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:07 PM
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Anyway, my problem is that by the time I understand something well enough to write a paper about it I'm bored by it and thinking about the next two or three things I can work on.

Yes. And the related feeling that, once I get something, it seems so hugely obvious and hence not paper-worthy.


Posted by: oudemia | Link to this comment | 01-29-09 1:11 PM
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Tied up with this, of course, is the fact that you can easily think you understand something so long as you don't attempt to manifest your understanding in something publicly disputable, such as, for example, a paper, and so, having never been put through the refinements of dialectic, your cod-understanding never attains the truth!


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:13 PM
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Not to threadjack too brazenly, but the joke in 12 reminded me that I'm curious about the opinions of heebie et al. on elementary school math pedagogy.

One of the little Ruprechts attends a public school that is basically Ground Zero for standards-based mathematics, a pedagogical philosophy that rejects drilling young children in algorithms in favor of teaching them to develop an intuitive sense of mathematical concepts. For example, instead of learning to "carry" and "borrow" from the 10's column to solve addition and subtraction problems, they have to work out their own procedures, then discuss with the group how they propose to solve the problem.

Sometimes derided as "the new New Math" or "Rainforest Math", standards-based mathematics occupies a place in the demonology of "back-to-basics" education reformers akin to that of Whole Language in the debate over reading instruction. In some ways, the reform pedagogy is easy to demagogue: it doesn't teach children long division or even standard notation; it values creativity in solution paths more than getting the right answer; it uses a lot of examples from ecology; and mjuch of the homework involves thing like gluing objects onto paper. Indeed, the specific curriculum that my child's school employs (Investigations in Numbers, Data and Space; see here for a highly tendentious Wikipedia entry) is pretty much the antithesis of back-to-basics.

My tentative opinion is that the curriculum is a Good Thing; the school is in a well-regarded, reasonably well-financed school district with dedicated teachers and engaged parents. I wonder, though, if this is another one of those good-in-theory educational reforms that tends to raise the ceiling and lower the floor on student achievement; that is, that it might "leave behind" children who never make the conceptual leaps, and who therefore lack the rote algorithms to fall back on. (If true, this would be ironic, because equity in mathematics education is supposed to be one of the shibboleths of the reform math movement.)


Posted by: Knecht Ruprecht | Link to this comment | 01-29-09 1:15 PM
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And the related feeling that, once I get something, it seems so hugely obvious and hence not paper-worthy.

Oh boy do I know that feeling.


Posted by: NickS | Link to this comment | 01-29-09 1:18 PM
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it values creativity in solution paths more than getting the right answer

More than merely getting the right answer makes sense (and who doesn't esteem Gauss more highly than the sods who would actually have totted up every number from one to a hundred?); more than getting the right answer, sans phrase, doesn't: it's not a solution path if it doesn't get the right answer.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:18 PM
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Also, I note that the engaged, well-off parents' presence is likely to confound estimations of the curriculum's efficacy: these are people who are, I assume, able to explain the "default" algorithms, should the need arise.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:19 PM
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And the related feeling that, once I get something, it seems so hugely obvious and hence not paper-worthy.

Oh, that too.

And then there's the one where half the people in the field think something is totally obvious and you shouldn't bother writing a paper on it, and the other half think that's not only not obvious but it's wrong, and why would they bother reading the paper when they already know it's wrong?


Posted by: essear | Link to this comment | 01-29-09 1:21 PM
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In conclusion, poop.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:22 PM
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I toiled at Ground Zero for the Phonics v Whole Language debate in the 90s, so, thanks, KR, for giving me hives by mentioning it.


Posted by: oudemia | Link to this comment | 01-29-09 1:22 PM
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I had one of those "hookt on foniks werkt four me" or however it went shirts as a lad.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:23 PM
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39: I think the big problem, in any pedagogy, with the kids that get left behind, is that they never master the basics to the point where the material is on quick-retrieval. I don't know what goes wrong - in the cases where it goes right, kids usually learn to work an example for themselves, and thus spot the pattern and re-teach themselves until they get it at the level of quick-retrieval. So is the breakdown for the other kids that they can't derive an example for themselves? Or do they need more supervised reviewing of the procedure, because they aren't going to be able to solve the example without help?

So I don't know. But sure, if the kids enjoy it more, go for it.


Posted by: heebie-geebie | Link to this comment | 01-29-09 1:26 PM
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these are people who are, I assume, able to explain the "default" algorithms, should the need arise.

This is apparently one of the criticisms of the curriculum: parents who have learned the standard computational algorithms don't know how to productively help their children, and get frustrated.

Also, I understand that the latest revision of Investigations is not quite so dogmatic about teaching algorithms, and makes provision for teaching them in the later elementary school years. But it you learned the simple formula for finding the volume of a rectangular solid in third or fourth grade, you're going to wonder why your fifth grader has never heard of "length X width X height".


Posted by: Knecht Ruprecht | Link to this comment | 01-29-09 1:26 PM
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I agree with "Lower your standards". It takes a while to realize that it'll never be perfect and there's always something else. It also takes a while to realize that what seems like a glaring error to you in the midst of composition will not even be noticed by 95% of your readers.


Posted by: F | Link to this comment | 01-29-09 1:28 PM
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But it you learned the simple formula for finding the volume of a rectangular solid in third or fourth grade, you're going to wonder why your fifth grader has never heard of "length X width X height".

How is it possible to explain what volume is without, at some point, giving a formula like that? I mean, at some point there must be a definition; the kid isn't going to get the meaning of "volume" just from the sound of the word.


Posted by: essear | Link to this comment | 01-29-09 1:28 PM
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Also, I understand that the latest revision of Investigations is not quite so dogmatic about teaching algorithms,

Indeed, I have the third edition, and there's a whole long section about simply grasping equations in a flash—and you should hear what the author has to say about following rules!

There's even a section on teaching reading, which you may have overlooked.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:29 PM
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How is it possible to explain what volume is without, at some point, giving a formula like that?

Volume is how much space something occupies, or how much could be held in it, were it hollow. This sphere (ostends) and this cube (ostends) have the same volume, as can be seen thus: when we submerge them in this water-filled tank, the amount of water forced out by the one into this receptacle is the same as, after the tank is refilled, is forced out by the other. Blah blah blah.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:31 PM
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39: My first rule of education is to never, ever lean to hard on one approach, philosophy or technique. Pedagogy is a field where little is known and less can be measured. It is a classic high uncertainty situation. When uncertainty is high, you want to maintain diversity and don't make changes very rapidly. Its like the stock market.

The annoying thing about the whole language/phonics debate was how extreme everything got. The phonics people won't let children even look at the length of the word as a way to recognize it. The whole language people won't force a child to do anything. This is just stupid.

In the name of maintaining a diverse portfolio, I think it is a huge mistake to chuck algorithms and memorization altogether. It is also a mistake to go "back to basics" and only use them. Also, the very fact that the back to basics people propose radical changes shows the problem with their approach, a problem which real conservatives would be wary of.


Posted by: rob helpy-chalk | Link to this comment | 01-29-09 1:34 PM
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It's not so clear to me that that works; you're assuming they know that water is incompressible, for instance. Which means that the volume doesn't change when you force it occupy a space of a different shape. But what is the volume? Etc....


Posted by: essear | Link to this comment | 01-29-09 1:34 PM
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54 to 52, of course.


Posted by: essear | Link to this comment | 01-29-09 1:35 PM
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It's not so clear to me that that works; you're assuming they know that water is incompressible, for instance

Somehow, I don't think the incompressibility or otherwise of water will be a major stumbling block for fourth graders. As a way of getting a handle on what length x width x height measures, or why it's interesting, I think things along 52's lines more than suffice.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:36 PM
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54: So, Archimedes was wrong?


Posted by: peep | Link to this comment | 01-29-09 1:37 PM
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As a way of getting a handle on what length x width x height measures, or why it's interesting, I think things along 52's lines more than suffice.

No, I completely agree with that, but I still don't see how you avoid telling them it's length x width x height.

And if any fourth grader can figure out the formula for the volume of a sphere on their own, they don't really need a math teacher.


Posted by: essear | Link to this comment | 01-29-09 1:37 PM
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doesn't teach children long division or even standard notation; it values creativity in solution paths more than getting the right answer

Math is one area where there really is a no-shit no-argument right answer. Creativity is all well and good in painting or writing, but if you don't focus on getting the right answer and knowing why that's the right answer and not just somebody's opinion, you are not teaching math.

Not teaching standard notation is simply negligent. Standards are good because they enable us to put our effort into doing the important stuff rather than reinventing the wheel all the time.

Different kids have different learning styles, but appropriate teaching styles vary by subject, too. Kids develop favorite subjects in part because of a match between learning style and appropriate teaching style. This sounds to me like grafting a language or art appropriate teaching style onto math.

As always, YMMV, worth what you paid, etc.


Posted by: togolosh | Link to this comment | 01-29-09 1:37 PM
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Wouldn't you explain volume by saying "It's how much milk there is in the glass"?


Posted by: heebie-geebie | Link to this comment | 01-29-09 1:38 PM
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How is it possible to explain what volume is without, at some point, giving a formula like that?

52 gets it about right. The whole pedagogical philosophy is built around teaching the abstract concepts in a variety of ways, so that (in the best case) all the children come to have an intuitive understanding of numbers and space. For example, when they learn measurement, they use made-up units like "squares" or "kid jumps" instead of cm or inches, so as to impart the abstract concept of units and scales. Supposedly this will make them all able to learn algebra, geometry and calculus when the time comes.


Posted by: Knecht Ruprecht | Link to this comment | 01-29-09 1:40 PM
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61: So they don't actually calculate things, just build up a touchy-feely intuitive sense of things? I mean, I'm all about touchy-feely intuitions about things, but at some point you have to get your hands dirty and use numbers.


Posted by: essear | Link to this comment | 01-29-09 1:43 PM
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No, Knecht. 52 gets it exactly right.

For most of these kids centimeters are probably as good as made-up units anyway.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:43 PM
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Maybe the editor would let you make a diorama instead.

Apparently Rory had a model due this week for her book report that she totally blew off. Upon informing me of this event, she wept that such an assignment was so unfair to kids like her who don't have supplies in their after-school and whose working parents pick them up so late at night that they barely have time for anything.


Posted by: Di Kotimy | Link to this comment | 01-29-09 1:45 PM
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Eh, I guess I can kind of see how it can work. Give them some little block and call it a unit of volume. Then tell them the volume of something is how many of those little blocks fit inside it. You never explicitly have to say "the volume of this little block is the side length cubed". OK, fair enough. Then they just figure out how to invent integral calculus and they're set.


Posted by: essear | Link to this comment | 01-29-09 1:45 PM
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64: Rory's been reading Unfogged!


Posted by: essear | Link to this comment | 01-29-09 1:46 PM
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Centimeters are made-up units.


Posted by: Brock Landers | Link to this comment | 01-29-09 1:47 PM
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Someday when I have to teach a class I'm going to be so godawfully terrible at it.


Posted by: essear | Link to this comment | 01-29-09 1:47 PM
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The only genuine, non-made-up unit is the hogshead, and even that takes work.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 1:48 PM
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Math is one area where there really is a no-shit no-argument right answer. Creativity is all well and good in painting or writing, but if you don't focus on getting the right answer and knowing why that's the right answer and not just somebody's opinion, you are not teaching math.

There's a difference between emphasizing creativity in strategy versus creativity of result.


Posted by: heebie-geebie | Link to this comment | 01-29-09 1:50 PM
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67: What part of "the distanced traveled by light in free space in 9192631770/29979245800 periods of the transition between the two hyperfine levels of the ground state of cesium 133" doesn't look natural to you?


Posted by: essear | Link to this comment | 01-29-09 1:51 PM
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66: Yeah, actually I foolishly let her read LB's diorama post. Which one might have thought would have triggered, "Oh, hey, by the way Mom, I have to do one of those things." Instead, it apparently triggered, "Oh, hey, that sounds like a great built-in excuse when I blow off my assignment. This internet thing really is useful!"


Posted by: Di Kotimy | Link to this comment | 01-29-09 1:53 PM
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Anyway, my problem is that by the time I understand something well enough to write a paper about it I'm bored by it and thinking about the next two or three things I can work on. splashing my boredom all over the internet.


Posted by: essear | Link to this comment | 01-29-09 1:53 PM
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Using arbitrary units (like "the length of this block here in my hand") seems fine, altough I'm not sure that's any less conceptually difficult to grasp than simply saying "there are arbitrary units of measure known as centimeters, which are this long" (demonstrating). But using something like "kid jumps" seems like it could easily badly muddle the whole idea of a "unit", the primary point of which is to provide a uniform measure.

In other words, Knecht, your child is doomed. Go ahead and cross the maths and the sciences off her future. I hope she likes art.


Posted by: Brock Landers | Link to this comment | 01-29-09 1:54 PM
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There's a difference between emphasizing creativity in strategy versus creativity of result.

Which are you using in your paper, heebie?


Posted by: rob helpy-chalk | Link to this comment | 01-29-09 1:55 PM
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Knecht's threadjack inspired me to listen to Tom Lehrer's "New Math", and in looking it up I discovered this gem, featuring Lehrer at the height of his powers with an adaptation of "New Math" for a British audience. Bonus au courant points for the introduction by David Frost.


Posted by: Jesus McQueen | Link to this comment | 01-29-09 1:56 PM
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But using something like "kid jumps" seems like it could easily badly muddle the whole idea of a "unit", the primary point of which is to provide a uniform measure.

I would think it would actually reinforce the point that unless you're using uniform units, you're not going to get very usable results.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 1:56 PM
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75: creativity of procrastination?


Posted by: heebie-geebie | Link to this comment | 01-29-09 1:57 PM
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77: okay, in a lesson on "what is a unit?", I could see that. "Kid jumps don't make good ones, as we've just demonstrated". But that doesn't sound like the way they were being used.


Posted by: Brock Landers | Link to this comment | 01-29-09 1:58 PM
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I suspect that I would have done better in mathematics had my mathematics education focused more on drilling methods to use to solve problems. I could usually see in a flash what was supposed to happen but have no idea how to get there (because apparently knowing how to complete the square is a BIG DEAL.)

heebie, what's the next step after this revision? If it's just the editor bouncing it back to you for more revisions, might as well make it her problem for a few days.


Posted by: Cala | Link to this comment | 01-29-09 1:59 PM
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I hope she likes art stitching tennis shoes.


Posted by: apostropher | Link to this comment | 01-29-09 2:02 PM
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"what is a unit?"

I can show you, but you'll have to stand back.


Posted by: apostropher | Link to this comment | 01-29-09 2:03 PM
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maths masters are wet and weedy
http://www.stcustards.free-online.co.uk/masters/pic4.htm


Posted by: nigel molesworth, esq | Link to this comment | 01-29-09 2:05 PM
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Completing the square is fantastic.


Posted by: ben w-lfs-n | Link to this comment | 01-29-09 2:05 PM
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58
I still don't see how you avoid telling them it's length x width x height.

Well, that's not volume. For example, the volume of a pyramid is a lot less than the length x width [of the base] x height. Your formula only works for the volume of a cube.

You apparently prefer to think of volume by approximating everything as cubes, and that's fine, but just because cubes aren't touchy-feely doesn't mean your way is intuitively superior to water-displacement.


Posted by: Cyrus | Link to this comment | 01-29-09 2:08 PM
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It is. I should have encountered it as a technique sooner.


Posted by: Cala | Link to this comment | 01-29-09 2:08 PM
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heebie, what's the next step after this revision? If it's just the editor bouncing it back to you for more revisions, might as well make it her problem for a few days.

This is actually the a paper I submitted before I began my dissertation, and I graduated almost three years ago. Basically for the first few rounds of revisions, I was a half-immature-writer and half-plain-half-assing-it, and then the referee would sit on it for 6 months to a year.

The paper was kind of getting Frankensteiny and worse and worse with each revision. So this past time I've really, really overhauled it and would really like to hear back that it needs minimal revisions after this.


Posted by: heebie-geebie | Link to this comment | 01-29-09 2:11 PM
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Similar to Heebie's situation (vaguely...), I'm sitting here wondering whether I should write a paper on a topic I've been batting around. But I'm not in academia, and it's definitely an "academic" paper, not a "practioner" paper, so the professional benefit would likely be slim to none. (I've got vague interests in possibly thinking about potentially wondering if I should try to think about becoming an academic one day, but I think the chances of that ever happening are realistically near zero.) And I've written enough papers to know that I'm not going to think it's fun or interesting AT ALL once I'm about 20% into it. And I'd say it also likely that, with no deadline and no appreciable benefit, there's roughly a 70%? 85%? chance I'd get bogged down at some point and never actually get around to publishing the damn thing. But! I do think it's an interesting topic, and I'm very slow at work right now. The alternative might be just wasting day after day on the internet. (That's also the expected result of my trying to write the paper, to be sure, but at least in that case I'd be usefully procrastinating, whereas now I'm just wasting time.)


Posted by: Brock Landers | Link to this comment | 01-29-09 2:12 PM
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Well, that's not volume. For example, the volume of a pyramid is a lot less than the length x width [of the base] x height. Your formula only works for the volume of a cube.

No shit, really!?

My point was that at some point, if you are actually asking them to calculate (rather than explore by playing with water) volumes of some shapes (because that is what KR's comment seemed to imply they were being asked to do without knowing length x width x height), you have to give them some sort of formula. On further thought, I realized that maybe you don't have to, if you e.g. tell them the volume of some cube is 1 and ask them to extrapolate from there.


Posted by: essear | Link to this comment | 01-29-09 2:12 PM
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I suppose one could do pretty well by asking them to calculate the volumes of various rectangular solids by trying to figure out how many unit cubes fill them, hoping to lead them to length x width x height on their own, and then having them dunk the things in water in e.g. a graduated cylinder and read off what changes and see if the results match. So, sure, the more I think about the more this seems like a plausible way to build up intuition. Still, at some point they're just going to have to be told what some formulas are.


Posted by: essear | Link to this comment | 01-29-09 2:16 PM
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90: That seems more like science class than math class. On the other hand, "volume" is a pretty sciencey concept, I guess.


Posted by: heebie-geebie | Link to this comment | 01-29-09 2:22 PM
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On further thought, I realized that maybe you don't have to, if you e.g. tell them the volume of some cube is 1 and ask them to extrapolate from there.

Sometimes there's value in re-inventing the wheel, of course. This just seems like one of those things where, you know, give them the damned wheel so they can get the car rolling.


Posted by: Di Kotimy | Link to this comment | 01-29-09 2:23 PM
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I agree with "Lower your standards". It takes a while to realize that it'll never be perfect and there's always something else.

My boss's formulation of this, which sunk in after many years, is, "It doesn't have to be perfect. It has to be good enough."

Query: Is staying in bed with my cats snuggled down beside me instead of going to my therapy appointment, my gym session with a partner, and a drawing class which meets for only 4 sessions good enough? Or do I strive for perfection and get up in the next 10 minutes?


Posted by: Sir Kraab | Link to this comment | 01-29-09 2:25 PM
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This just seems like one of those things where, you know, give them the damned wheel so they can get the car rolling.

Not till they're 16, Di, and have undergone rigorous training and licensing requirements.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:26 PM
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85, 89: Your formula only works for the volume of a cube.

Well actually, rectangular parallelepiped (or right cuboid, or right rectangular prism, or whatever the hell they are calling them these days). But thenwe'd never get pedantic about it.


Posted by: JP Stormcrow | Link to this comment | 01-29-09 2:26 PM
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Is staying in bed with my cats snuggled down beside me instead of going to my therapy appointment, my gym session with a partner, and a drawing class which meets for only 4 sessions good enough?

Does your gym have a steam room or a sauna? If so, you should get up and go sit in the steam room or sauna. Otherwise, those cats need you.


Posted by: Di Kotimy | Link to this comment | 01-29-09 2:28 PM
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93: Oh I think you know the answer to that question, slugabed.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:28 PM
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87: If you've fixed the major technical problems, I wouldn't waste time on the cosmetic stuff since chances are the editor will have her own idea of what cosmetic-y stuff needs to be done. Only because I've found the fix when I get the Frankenstein paper problem is to let someone else's eyeballs deal with it.


Posted by: Cala | Link to this comment | 01-29-09 2:29 PM
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95: Well actually, rectangular parallelepiped (or right cuboid, or right rectangular prism, or whatever the hell they are calling them these days).

And then you can apply Cavalieri's principle and use it to calculate the volume of all sorts of funny-shaped regions!

91: That seems more like science class than math class. On the other hand, "volume" is a pretty sciencey concept, I guess.

Down with artificial disciplinary boundaries!


Posted by: essear | Link to this comment | 01-29-09 2:29 PM
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@39

My big problem with that kind of pedagogy can be summed up as "well, that's what college is for". Less flippantly, people learn and then they learn how to learn. And I just don't think my students that age are capable of the meta-mastery that's required.


Posted by: F | Link to this comment | 01-29-09 2:30 PM
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Only because I've found the fix when I get the Frankenstein paper problem is to let someone else's eyeballs deal with it.

Someone else's eyeballs, stolen from a morgue, that is.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:31 PM
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Reanimated with LIGHTNING.


Posted by: Cala | Link to this comment | 01-29-09 2:32 PM
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Down with artificial disciplinary boundaries!

That's right. We've got to help these kids learn to intuitively feel where the boundaries between disciplines are.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:32 PM
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Maybe this explains the effect I've heard about from physics professors where students are completely unable to apply linear algebra to solve problems because after all, they learned it in a class in the math department and this is a physics class.


Posted by: essear | Link to this comment | 01-29-09 2:34 PM
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||

Google Earth reveals two-acre field of weed to Swiss police

Uh oh.

|>


Posted by: Sir Kraab | Link to this comment | 01-29-09 2:34 PM
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93: But those things kind of sound like fun. Would you like to work on a paper?


Posted by: heebie-geebie | Link to this comment | 01-29-09 2:36 PM
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105: Is there something you haven't told me, Sir K? Are these "trips to DC" you've been taking really trips to Switzerland??


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:36 PM
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Or to think of it another way: You do realize that the Archimedes principle was discovered by a grown man? After decades of work on basic science and math had already been done. Ditto, calculus, except substitute centuries.

In other words, discovering these things yourself requires brilliance, not competence. And, yes, I realize that that's where the teacher is supposed to come in, but realistically expecting any but the most brilliant of students to figure this out for themselves seems unlikely.


Posted by: F | Link to this comment | 01-29-09 2:37 PM
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106: A paper about snuggling with cats? No, but I'd be happy to conduct lots of field studies about it for you.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:37 PM
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107: You didn't expect me to keep my money in the stock market, did you?


Posted by: Sir Kraab | Link to this comment | 01-29-09 2:39 PM
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109: I've got a feline subject who could give you some really interesting results.


Posted by: heebie-geebie | Link to this comment | 01-29-09 2:40 PM
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discovering these things yourself requires brilliance, not competence.

Discovering these things from scratch requires brilliance. Discovering these things in a rigged context, designed to expose you to cause and effect until you understand the mechanism is accessible to most kids.


Posted by: heebie-geebie | Link to this comment | 01-29-09 2:41 PM
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111: Just out of curiousity, how does this feline subject feel about baby humans?


Posted by: M/tch M/lls | Link to this comment | 01-29-09 2:42 PM
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108 makes good points. But, for the record, I think what was discussed here was that the volume of an object that sinks in water equals the volume of water it displaces; Archimedes' principle is that the buoyant force on an object is equal to the weight of the water it displaces. Different things, one much simpler than the other. (Though, as I was trying to say somewhere above, the simple fact does rely on incompressibility of water, which is a nontrivial material property not shared by all substances [cf. air]).


Posted by: essear | Link to this comment | 01-29-09 2:42 PM
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Just out of curiousity, how does this feline subject feel about baby humans?

Judging by the video that I have seen, it probably thinks that they are much easier to catch and kill than the full grown variety.


Posted by: CJB | Link to this comment | 01-29-09 2:44 PM
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113: We think he'll be fine. He's always been immediately fine with my mom and my grandma, (but not other friends and family members who he's seen a bunch), and he's generally okay with people I've dated. So there's something about being closely related to me, or being physical with me, or something, that makes people acceptable. So basically we have no idea and we'll keep a close eye on Krazy Kat.


Posted by: heebie-geebie | Link to this comment | 01-29-09 2:47 PM
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In my experience, cats are fine with babies. It's toddlers that get bloodied up.


Posted by: apostropher | Link to this comment | 01-29-09 2:57 PM
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In my experience, cats are fine with babies. It's toddlers that get bloodied up.

In my experience, this is closely related to the propensity of toddlers to pull tails.


Posted by: Di Kotimy | Link to this comment | 01-29-09 3:00 PM
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116: In my experience this can be rather unpredicatble. We had a great cat that had found us a few years before our first was born. However, he was completely unnerved by children, going so far as to break out a screen in our house once to get away when a friend's children came over. But turned out to be an absolute, um ... pussycat with our own children (and their friends).


Posted by: JP Stormcrow | Link to this comment | 01-29-09 3:06 PM
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118: Oh fine, Di, take the cats' side.


Posted by: M/tch M/lls | Link to this comment | 01-29-09 3:06 PM
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One of our cats puts up with unbelievable amounts of abuse (well-intentioned, but still) from little ones, while the other doesn't at all. Noah calls her "scratchy kitty".


Posted by: apostropher | Link to this comment | 01-29-09 3:13 PM
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I call Noah "pully twolegs".


Posted by: scratchy kitty | Link to this comment | 01-29-09 3:17 PM
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The problem with emphasizing memorizing formulas and doing calculation is that paper is much better at remembering things than people and computers are much better at, well, computing. No matter how much drilling you do, integrals.com is going to beat you at second semester calculus every time. It'd be much better for people's general education if in math classes they actually learned how to think about abstract concepts creatively.

If students actually learned how to think about place value by thinking about multiplication differently that'd be great. (Full disclosure: I used a nonstandard algorithm for multiplication from around 4th-8th grade.) On the other hand, if you don't know your multiplication tables you're in trouble no matter how you think about multiplication.

I've always been pretty resigned to the idea that elementary math education is going to have major issues no matter what the curriculum because people who understand and enjoy mathematics rarely teach elementary school.


Posted by: Unfoggetarian: "Pause endlessly, then go in." (9) | Link to this comment | 01-29-09 3:19 PM
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Also, heebie, the upside of being a mathematician is that you can embrace absentmindedness. I'm not sure why you're so scared of the editor, I'm sure this editor gets mathematicians flaking on deadlines all the time. Sure you should feel a little bad about not having it done yet, but you shouldn't feel really bad until you're at least 2 months past when you would have liked to have gotten it done.


Posted by: Unfoggetarian: "Pause endlessly, then go in." (9) | Link to this comment | 01-29-09 3:21 PM
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you shouldn't feel really bad until you're at least 2 months past when you would have liked to have gotten it done.

Now with birth, on the other hand . . .


Posted by: M/tch M/lls | Link to this comment | 01-29-09 3:25 PM
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Why is no one taking seriously my plight?


Posted by: Brock Landers | Link to this comment | 01-29-09 3:31 PM
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integrals.com

Holy wow is that cool. I'd never seen it before.


Posted by: Brock Landers | Link to this comment | 01-29-09 3:33 PM
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I've been pushing my kids forward a bit in math because they've both got a knack for it and being a couple of years ahead should be helpful when competitive high school admissions roll around. (And because I remember how dreadfully, dreadfully dull grade school math was.) The process is a little insane, though --I'm not really on top of exactly what they've learned already, so mostly what I've done is get them some reasonable looking workbooks for a couple of grades ahead, and told them both "You know how to do some of this, but not all of it. If you run into a page where you don't know what's going on, come find me and I'll teach it to you."

I'm not sure if it's much use -- they put effort into it off and on, and I don't keep the pressure on to do more. But I enjoy teaching them, and amusing me is the main point of everything I do.


Posted by: LizardBreath | Link to this comment | 01-29-09 3:35 PM
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126: Totally do it. Heck, if you're slow, there's probably some first year who's slow who you can shanghai to do the dull bits and be a co-author.


Posted by: LizardBreath | Link to this comment | 01-29-09 3:36 PM
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@123

That's all true, but again, I think that changes based on the level of education (and intelligence). I shy away from memorization for college classes because they can always look it up in a book if it's just a random fact. The only things you should have to memorize are the basic framework that would be necessary to make any further progress and should be available without having to look up. But grade school math is exactly that kind of stuff - arithmetic, very basic geometry.

Also, I think the emphasis on creativity at early levels is misguided as well, especially in math and science. We all wish that adults were more creative because they already know the inviolable rules. Kids are plenty creative; it's just that they're wrong most of the time.


Posted by: F | Link to this comment | 01-29-09 3:37 PM
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I'm not sure exactly how, but in some manner the part of The Thought Gang (pp 75-80) where after years of missed deadlines, Eddie Coffin's exasperated editor kidnaps him and chains him to a radiator (and ultimately writes the book herself) should come in handy. My choice would be to read the book while procrastinating on the paper. Alternatively, you might send it to the editor so he realizes how reasonable you are in comparison.

"Dr Coffin, you are lazy ...thoughtless ... crapulent ... contemptible." I was biding my time until something came up to which I could object, but nothing surfaced in her disdain that I could really contest. "You're on Barra. You're miles from the nearest off-licence, even if you could decuff yourself. "
...
"No, we can sit down and write. Ten pages a meal. When you've done two hundred you can say goodbye to the radiator."
...
I weighed things up: which fork had "indolents this way" posted on it, fuming and refusing and enduring, or capitulating and scribbling?


Posted by: JP Stormcrow | Link to this comment | 01-29-09 3:39 PM
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Pedagogical theory: people learn differently.


Posted by: Sifu Tweety | Link to this comment | 01-29-09 3:39 PM
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132: How did you learn that?


Posted by: JP Stormcrow | Link to this comment | 01-29-09 3:40 PM
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133: made a diorama.


Posted by: Sifu Tweety | Link to this comment | 01-29-09 3:41 PM
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130: There's also the fact that having a reliable algorithm can help you develop deeper understanding. That's generally how I've learned math: exposure to the concept; learning an algorithm; successfully working problems but without deep understanding; light-bulb moment, after which any reasonable algorithm makes sense. Maybe deep understanding, then algorithm would have worked just as well if I'd been taught that way, but it seems harder.


Posted by: LizardBreath | Link to this comment | 01-29-09 3:42 PM
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Follow-on to 127: how does a computer solve an integral? It's not a raw number-crunching exercise.


Posted by: Brock Landers | Link to this comment | 01-29-09 3:49 PM
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Next thing you know, they'll have computers that play chess.


Posted by: Brock Landers | Link to this comment | 01-29-09 3:50 PM
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how does a computer solve an integral? It's not a raw number-crunching exercise.

They describe it briefly and hand wavingly in the faq for the website. Basically it boils down to it is very complicated.


Posted by: CJB | Link to this comment | 01-29-09 3:51 PM
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I was amused by the stories about how scientists at the University of Alberta have "solved checkers". First Fermat's Last Theorem, then checkers, now on to the next big challenge.


Posted by: Cryptic ned | Link to this comment | 01-29-09 3:53 PM
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Wait, I'm revealing my math rustiness, aren't I? I seem to remember a method of successive approximations. But I thought that only worked for certain types of equations? (And hell, I could be thinking of a method for differentiation. This is all growing very fuzzy in my mind.)


Posted by: Brock Landers | Link to this comment | 01-29-09 3:53 PM
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136: See Macsyma and Wolfram, Really Smart but Arrogant Guy. Also rules/symbolic manipulation.


Posted by: JP Stormcrow | Link to this comment | 01-29-09 3:55 PM
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No matter how much drilling you do, integrals.com is going to beat you at second semester calculus every time. It'd be much better for people's general education if in math classes they actually learned how to think about abstract concepts creatively.

It occurs to me that my main complaint about my undergraduate math education (about which there is really very little to complain about, but I'll try) is that it involved a lot of proving general facts about, say, cohomology or Galois groups or whatever and very few instances of just calculating the damn things. And it's entirely possible to grok the general concept and prove all sorts of general facts and still not have the concrete intuition that comes from knowing lots of good examples. It's not so clear this lesson generalizes to grade school, but to some extent it might. Doing hundreds and hundreds of integrals in high school calculus might have been overkill, but there were more abstract lessons to learn beyond just the definition of an integral (why substitution works, how it changes the measure of the integral, etc.) and it seems like doing lots of examples made that stuff sink in pretty well.


Posted by: essear | Link to this comment | 01-29-09 3:55 PM
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I seem to recall the short answer to most questions of the form "How does Mathematica do X?" is "Grobner bases", and the subsequent response to "but... how?" is "Stephen Wolfram is smart."


Posted by: essear | Link to this comment | 01-29-09 3:57 PM
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You know what always annoyed the crap out of me? Math classes that assumed you would pick up the intuition from endless repetition. Tell me what the intuition is, then let me prove to myself that I believe it.


Posted by: Sifu Tweety | Link to this comment | 01-29-09 3:58 PM
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Grobner s/b Gröbner.


Posted by: essear | Link to this comment | 01-29-09 3:59 PM
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about which there is really very little to complain about this ever-changing world in which we live in.


Posted by: essear | Link to this comment | 01-29-09 4:00 PM
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Posted here before in a different context, but ...

"Can you give us the answer to life?", they asked the computer.
Deep Thought pondered their question.
"Yes," he said. "But it will be tricky. And first I have to write Mathematica."


Posted by: JP Stormcrow | Link to this comment | 01-29-09 4:01 PM
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No matter how much drilling you do, integrals.com is going to beat you at second semester calculus every time.

For myself, I spent years in school being bored by math classes, getting everything conceptually, but being a bit lazy about working out every problem (because it was obvious that they were all variations on the same problem).

It wasn't until I started doing math team in HS that I really cared about the difference between being correct 85-90% of the time and being correct 95-100% of the time. The math team coach had us spend a lot of time drilling, and my general math abilities improved a lot.

Learning that paying attention to the details is a skill, and learning to do it, made my ability to grasp the concepts far more valuable.

So I'm in favor of a certain amount of drills in mathematics.


Posted by: NickS | Link to this comment | 01-29-09 4:02 PM
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In other words, I agree with this:

[I]t's entirely possible to grok the general concept and prove all sorts of general facts and still not have the concrete intuition that comes from knowing lots of good examples.


Posted by: NickS | Link to this comment | 01-29-09 4:03 PM
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The converse of 149 holds as well.


Posted by: Sifu Tweety | Link to this comment | 01-29-09 4:05 PM
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142, 144: Fight, fight!

Actually, I'm on both sides of this one. Most math concepts, I can demonstrate understanding of after fairly little in the way of repetition, which means that classes with no drilling were always very low effort.

On the other hand, there's a kind of fluency you get from doing lots of problems that makes it much easier to comprehend the next concept, which generally relies on easy facility with prior concepts. My mental algebra got very, very good in the two years I was teaching high school math; all the making up problems and solving them on the fly for the kids was great practice. And at the time I remember thinking that if I'd been that fluent when I was taking college math classes, they would have been noticeably easier.


Posted by: LizardBreath | Link to this comment | 01-29-09 4:05 PM
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I did a lot of advanced math at an early age, and I was always amazed to find that my arithmetic really suffered from not doing it on a daily basis. Like, I could do calculus in junior high but forgot my multiplication tables.


Posted by: F | Link to this comment | 01-29-09 4:06 PM
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128 - oh, I remember you asking about that.

The Ruprecht school maths sounds really interesting. But I imagine it's still mostly a case of those who get it will get it, those who don't will flounder about. I dunno, maybe if you catch kids young enough, it helps?

I know with mine that they hate having maths explained to them, but they love being asked questions and having to work out how to do things. E.g. #1 and #3 refused to learn any methods of writing down long multiplication until they had worked out the method in their heads. #3 finally conceded about a year ago that it was quite useful to write stuff down when he was working out how many seconds his dad had been alive for, and I had to do the remembering bits for him. (We were in the car, so he approximated a year to 300 days, and did it more accurately on paper at home.)


Posted by: asilon | Link to this comment | 01-29-09 4:07 PM
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FWIW, I was also that annoying shit who refused to show his work because "I got it right; why should I have to take all the time to write out the stupid little steps just to prove it to you". Now I hate those people.


Posted by: F | Link to this comment | 01-29-09 4:09 PM
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On second thought, I suspect the lesson of 148 may be that drilling is useful if and only if the student has a direct reason to be invested in it.


Posted by: NickS | Link to this comment | 01-29-09 4:10 PM
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Yeah, I hear myself saying "showing you working" to my private tuition students and inwardly groan. I don't bother saying it to my kids - if I need to know, they can tell me.


Posted by: asilon | Link to this comment | 01-29-09 4:11 PM
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FWIW, I was also that annoying shit who refused to show his work because "I got it right; why should I have to take all the time to write out the stupid little steps just to prove it to you". Now I hate those people.

I don't know about you, but at some point I discovered that showing (some of) my work did help me get it right a higher percentage of the time. It just took me a while to figure it out.


Posted by: NickS | Link to this comment | 01-29-09 4:11 PM
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wtf? If I heard myself saying "showing you working" to anyone, I'd assume I'd been drinking.


Posted by: asilon | Link to this comment | 01-29-09 4:11 PM
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I say it because it will help them get more marks in exams.


Posted by: asilon | Link to this comment | 01-29-09 4:12 PM
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I know with mine that they hate having maths explained to them, but they love being asked questions and having to work out how to do things.

As a kid, my parents would read me puzzles from Raymond Smullyan books on car trips. Frustratingly, I suspect I would do worse on those sorts of puzzles now than I did as an eight year old.


Posted by: NickS | Link to this comment | 01-29-09 4:13 PM
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Try showinging you working, NickS.


Posted by: Cryptic ned | Link to this comment | 01-29-09 4:15 PM
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I say it because it will help them get more marks in exams.

This hasn't been much of a problem yet, but I'm trying to figure out how to sell "showing your work" intelligibly to my kids if it turns into a problem for them. I always hated it ("I got the right answer, get off my back"), and then found in college that I had a hell of a time writing out a problem set anyone could understand; I'd end up with these horrible scrawled lumps of paper.

Come to think of it, I remember not really understanding what a sane way to lay out a solution to a math problem would be (although that sounds ridiculous in retrospect. Write out a step, write the next step below it, and so on.)


Posted by: LizardBreath | Link to this comment | 01-29-09 4:20 PM
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Ah, Raymond Smullyan ... I was in love with the beard as much as anything else.

#3 is quite into chess, and has been looking at the RS retrograde analysis books. My chess is not great, to say the least, and it has been a real pedagogical effort to go through those puzzles with him. I have to read the answer, and then ask him leading questions until he gets it. After about 3 of them my head literally hurts.


Posted by: asilon | Link to this comment | 01-29-09 4:20 PM
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but I'm trying to figure out how to sell "showing your work" intelligibly to my kids if it turns into a problem for them.

I don't know if this sells it or not, but I tell my students that they're being graded on how well they've communicated their procedure to their answer; that math is a language, and they're learning to communicate in that language.


Posted by: heebie-geebie | Link to this comment | 01-29-09 4:23 PM
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164: Yeah, that's the sort of thing I was thinking about.


Posted by: LizardBreath | Link to this comment | 01-29-09 4:25 PM
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139: Hungry Hungry Hippos remains tantalizingly out of reach.


Posted by: feldspar | Link to this comment | 01-29-09 4:25 PM
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I remember hating "show your work" up until sometime in high school when problems sometimes took multiple steps to write out. But that intermediate 7th-grade-ish phase when one would be asked to solve, say, 3x + 2 = 4x + 5 by writing out like 7 lines instead of just writing down x = -3 drove me insane. Then there were the "proofs" in high school geometry when one had to laboriously write out lots of lines, each in ridiculous symbols, and support each one by appealing to some trivial "theorem". Did everyone have to do those? I remember the teacher earnestly telling us that this is exactly how real mathematicians write proofs. I knew better.


Posted by: essear | Link to this comment | 01-29-09 4:26 PM
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This water-based volume-finding system totally fails when it comes to sponges. I've been trying for like an hour now, and I got nothing.


Posted by: Stanley | Link to this comment | 01-29-09 4:26 PM
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I remember the teacher earnestly telling us that this is exactly how real mathematicians write proofs. I knew better.

Did I not mention this? My paper is divided into two columns. On the left, I number the steps. On the right, I put the page number and theorem number where you can find the theorem I used to prove each claim. I think I showed that opposite external angles of a traversal through a pair of parallel lines are equal!


Posted by: heebie-geebie | Link to this comment | 01-29-09 4:28 PM
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Hee.


Posted by: essear | Link to this comment | 01-29-09 4:29 PM
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167

You mean things like SAS (side-angle-side)? To be fair, that is actually most people's first introduction to a real proof.


Posted by: F | Link to this comment | 01-29-09 4:30 PM
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To be fair, that is actually most people's first introduction to a real proof.

Not anymore it's not! The high school graduation test in Texas does not require proofs; guess what gets scrapped in high school geometry classes. (At least in schools with poor passing rates.)


Posted by: heebie-geebie | Link to this comment | 01-29-09 4:33 PM
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I think I showed that opposite external angles of a traversal through a pair of parallel lines are equal!

Lobachevsky would like a word with you (and, thus, we are back to Tom Leher).


Posted by: NickS | Link to this comment | 01-29-09 4:35 PM
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"Leher" s/b "Lehrer"


Posted by: NickS | Link to this comment | 01-29-09 4:36 PM
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I like this idea as a way to teach non-Euclidean geometry.


Posted by: essear | Link to this comment | 01-29-09 4:40 PM
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I became a deep believer in showing your work in between my two years of engineering school at CalPoly. They were superstrict at CalPoly ag engineering. The whole department had a standardized header, specific things for each box in the header of the green lined paper. If you didn't fill out the header right on every page you got a zero on the assignment (department-wide -they weren't fucking around). They were equally strict about the equation/substitution/solve steps of doing problems. I was fine with it, because I didn't have a social life there to compete with homework, and I'm an obediant student anyways.

But I wasn't a believer until that summer, when I was working at Reclamation. They had hand-written old water rights calculations in notebooks that I had to refer to. They were amazing. I could pull out any one of them and follow them instantly. Was I missing a page? Nope, here's 1/3, 2/3 and 3/3. It was so amazingly useful, and I went back to school very appreciative of that system.


Posted by: Megan | Link to this comment | 01-29-09 4:42 PM
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Silence on Unfogged for over an hour in the middle of the day....I'm suddenly worried about whether or not the East Coast is still extant.

My favorite line when it comes to rewriting and rewriting is that "A done paper is a good paper." I imagine this fits right along with the idea of lowering your standards. Then again, I've not been published, so perhaps I'm not the right person to comment on it....


Posted by: DL | Link to this comment | 01-29-09 5:45 PM
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Posted by: | Link to this comment | 01-29-09 5:51 PM
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OT: Kottke needs to read the archives.


Posted by: mrh | Link to this comment | 01-29-09 5:53 PM
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Posted by: | Link to this comment | 01-29-09 5:54 PM
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179: Wow, that's still in there? Upon further investigation, indeed it is.


Posted by: teofilo | Link to this comment | 01-29-09 6:04 PM
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179: That's got to be a joke -- Unfogged pops right up if you google "The Ogged".


Posted by: LizardBreath | Link to this comment | 01-29-09 6:08 PM
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Dammit, Kottke's gonna queer the Ogged.


Posted by: Cryptic ned | Link to this comment | 01-29-09 6:23 PM
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queer the Ogged

Title of a dissertation in Gender Studies on the social dynamics of blogging.


Posted by: LizardBreath | Link to this comment | 01-29-09 6:27 PM
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I have to call bullshit on this Wolfram crap. There's a whole research field called "computer algebra". They figured it out. It's like giving the Matlab people credit for figuring out how to solve a 100-by-100 linear equation. (And it's not like Wolfram writes the code, either.)

Easy integrals are solved by a set of heuristics. They first try to look it up. Then they try to guess a variable transformation. They they see if it can be simplified by integration-by-parts. If none of that works, then they use the Risch algorithm, which can compute any integral that has a solution in terms of elementary functions.


Posted by: Walt Someguy | Link to this comment | 01-29-09 6:41 PM
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Heebie, to quote Steve Jobs, "Great artists ship." Just send the damn paper out, secure in the knowledge that no one else will ever scrutinize it as carefully as you.


Posted by: Gaijin Biker | Link to this comment | 01-29-09 6:45 PM
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||
I am obliged to use Word to write papers with my PI (possibly if I had finished perfect first drafts he would have accepted PDFs from LaTeX, but not in the real world). I have been embarrassingly ept with Word in the past, so I didn't expect this to be *this* painful, but after one day of work and one Track Comments round trip:

It can't edit its own equation,
it can't save the AutoBackup file, and
it can't display Normal characters nearly as fast as I can type. I'm getting a crick in my neck looking away from the screen as I type so the delay doesn't flummox me.

WTF??

|>


Posted by: clew | Link to this comment | 01-29-09 6:49 PM
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187: Time for your PI to learn LaTeX!


Posted by: essear | Link to this comment | 01-29-09 7:18 PM
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He thinks Word is good, even though he also complains that it crashes a lot. I am perplexed.

So's he; I used to work for the 'soft and he wasn't expecting a wild-eyed emacs user, and not just because I don't think he's ever had to learn that emacs exists.

Perhaps OpenOffice will save us, or at least me.


Posted by: clew | Link to this comment | 01-29-09 7:27 PM
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Always find it odd to hear folks refer to "their PI."

Because to me, that's the shady dude you hire to dig up dirt (which sounds a lot more like a grad student or at most a post doc).

Also, Walt: he may have gone 'round the bend, but he's a freakin' genius.


Posted by: TJ | Link to this comment | 01-29-09 7:33 PM
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190: We have more dirt than most people have ever thought of.

I thought the annoyance with Wolfram was that he was unwilling to recognize anybody else's genius. Remember the bit in Kind-Of Science thanking his early advisors only for having the skill to recognize his genius.


Posted by: clew | Link to this comment | 01-29-09 7:45 PM
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We've had a Wolfram discussion here before, but I don't this tidbit came up. From a letter from Feynman to Wolfram:

You don't understand "ordinary people." To you they are "stupid fools"--so you will not tolerate them or treat their foibles with tolerance or patience--but will drive yourself wild (or they will drive you wild) trying to deal with them in an effective way.

Posted by: essear | Link to this comment | 01-29-09 7:49 PM
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I don't think this tidbit came up, that is.


Posted by: essear | Link to this comment | 01-29-09 7:49 PM
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Oh, I came up with a great use for ANKOS: it is boosting my monitor that crucial 2.4 inches.


Posted by: TJ | Link to this comment | 01-29-09 7:58 PM
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179: It's just a version of the classic "Shi'a-in-a-Poke" con.

And Stephen Wolfram didn't invent symbolic integration any more than he did cellular automata. Look up Joel Moses's review article, "Symbolic Integration: the stormy decade," or google the phrase "risch algorithm".


Posted by: arthegall | Link to this comment | 01-29-09 9:22 PM
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Next you'll be telling me Wolfram didn't prove Rule 110 was universal!


Posted by: essear | Link to this comment | 01-29-09 9:28 PM
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||

Sprouted whole wheat bread smells fermented. Also, combining the aforementioned with strawberry jam and peanut butter tastes like mint.

I'm no expert, but this doesn't seem correct. I guess I'll be dying soon.

|>


Posted by: feldspar | Link to this comment | 01-29-09 9:32 PM
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197: Maillard reaction byproducts, maybe, or you could be going crazy. Keep us posted.


Posted by: Jesus McQueen | Link to this comment | 01-29-09 9:37 PM
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I have to call bullshit on this Wolfram crap. There's a whole research field called "computer algebra". They figured it out. It's like giving the Matlab people credit for figuring out how to solve a 100-by-100 linear equation.

Wait...Wolfram figured out computer algebra? And this is something that should not be considered impressive?


Posted by: Cryptic ned | Link to this comment | 01-29-09 9:38 PM
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176: My chemistry teacher in high school held us to similar standards. No missing notes for us!


Posted by: Cala | Link to this comment | 01-29-09 9:49 PM
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Ergotism. Many enjoy the experience if they survive.


Posted by: John Emerson | Link to this comment | 01-29-09 9:54 PM
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Word is great. If you don't need to actually use equations.

I love to tell my students that browning ground beef and fake tans are both due to the Maillard reaction. Except the new drug, which is a different mode of action.

And as far as Wolfram is concerned, I'm torn. There is nothing new under the sun, and yet it's really fucking annoying when scientists don't acknowledge their immediate predecessors.


Posted by: F | Link to this comment | 01-29-09 10:53 PM
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Math is one area where there really is a no-shit no-argument right answer. Creativity is all well and good in painting or writing, but if you don't focus on getting the right answer and knowing why that's the right answer and not just somebody's opinion, you are not teaching math.

This kind of reaction is why I say that Standards-Based Math is prone to being demagogued. In reality, the reform pedagogy is equally concerned with equipping children to find "the right answer"; it just encourages a lot more variety in how the children get there, so as to promote a deeper abstract understanding of arithmetic operations.

I visited my child's school yesterday and saw some of the exhibits from the math instruction, and I have to say I was impressed. There was a display memorializing (with photos) an exercise where they took a number line from 1 to 100 (made on a continuous role of paper about 30 feet long), converted it into a number table (10X10 matrix, revealing the place notation), then taped it together again into a number line. I know from playing Chutes & Ladders with my daughter that she coneptualizes addition and subtraction with reference to a number line, so this seemed cognitively appropriate to me.

Also, I saw that they were engaged in gathering and categorizing data. Each day, they survey one another to count up the number of pupils who will eat school lunch versus brownbag lunch, and record the results on a binomial plot. There was also a frequency distribution diagram in which they recorded how many baby teeth members of the class had lost by taping little cutouts of teeth to the chart.

I don't hold any particular brief for Investigations. AFAICS the research around it (both for and against) seems kind of sketchy. Anecdotally, the school my child attends has the highest scores in the statewide standardized math test, but that could be due to other factors, and it's not inconsistent with the hypothesis that the reform pedagogy works well when delivered under ideal circumstances, but fails elsewhere.

One memory I have from childhood makes me sympathetic to the philosophy of Investigations. I was in a county-wide grade school math competition, and I saw a problem with two terms separated by a long horizontal bar. I asked the exam procter whether that was meant to be a fraction bar or the notation for division. He told me he couldn't give me the answer, as that would be unfair assistance. Obviously a fraction bar and the division operator are the same damned thing, but I had no conceptual grasp of that, even though I was highly proficient in computing both fractions and division problems.

MAYBE the sequence "learn algorithms by rote, then wait for the conceptual A-HA moment" is superior to the inverse, but I don't think you can automatically assume so just because it has always been done that way.


Posted by: Knecht Ruprecht | Link to this comment | 01-30-09 5:39 AM
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185, 195: As the person who introduced Wolfram into the conversation above, I certainly was not trying to imply any invention or precedence for him in computer fucking algebra. Was trying to simply point Brock to Macsyma and Mathematica as prominent examples of programs that do symbolic integration and could not help myself from slipping in the Wolfram joke. Given Wolfram's well-known assholosity on the subject it might not be surprising that people's thoughts went there, but no one was claiming it. When we defend what is not under attack we reveal ourselves.

The "first I have to write Mathematica" crack, in fact, is from a page of blasts at A New Kind of Shit Science.


Posted by: JP Stormcrow | Link to this comment | 01-30-09 5:51 AM
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and knowing why that's the right answer and not just somebody's opinion

Yeah, it seems to me that this is actually the point of the reform pedagogy approach, whereas with rote memorization the focus is only on getting the correct answer without necessarily needing to understand how and why it is right.


Posted by: M/tch M/lls | Link to this comment | 01-30-09 5:54 AM
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Dammit, JP Stormcrow, for the last time: Wofram did NOT invent computer algebra!


Posted by: M/tch M/lls | Link to this comment | 01-30-09 5:55 AM
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Ugh - this is the depressing bit of tutoring maths - getting a kid about 6 weeks before their exam and just having to drill the method into them. Trying to explain WHY can be counterproductive when they've already had 10 years of teaching that hasn't worked and don't understand anything.


Posted by: asilon | Link to this comment | 01-30-09 6:02 AM
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Ugh - this is the depressing bit of tutoring maths - getting a kid about 6 weeks before their exam and just having to drill the method into them. Trying to explain WHY can be counterproductive when they've already had 10 years of teaching that hasn't worked and don't understand anything.

I once taught an SAT-prep course for a somewhat unsavoury, but very successful outfit that took this approach to the extreme. Their basic insight was this: The SAT is multiple choice. The grading system is designed to avoid rewarding random guessing (there are five choices, you get 1 point for a correct answer, -0.2 points for an incorrect answer, and 0 points for no answer). So if you can eliminate one or two wrong answers and guess from among the remainder, the odds are in your favor, and your score will go up. About 90% of the preparatory program was geared toward teaching the kids to spot the wrong answers, which, it's true, had a certain systemic predictability to them.

For example, for the reading comprehension section, we taught the kids to rule out any answer that could be construed as disparaging toward women or minorities, because obviously the test-designers would never include a reading passage that contained any such content.


Posted by: Knecht Ruprecht | Link to this comment | 01-30-09 6:29 AM
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So if you can eliminate one or two wrong answers and guess from among the remainder, the odds are in your favor, and your score will go up.

Just knowing that strategy makes test-taking a lot easier. A lot of 16 year olds fret over every answer, as if they needed a perfect score, and refuse to guess, and sometimes they'll get stuck on the hard questions and not finish.

It would be interesting if the deduction for error were 0.5.


Posted by: John Emerson | Link to this comment | 01-30-09 6:50 AM
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It would be interesting if the deduction for error were 0.5.

Nah, to make it interesting, you'd have to make the deduction at least $1.00 per error.


Posted by: M/tch M/lls | Link to this comment | 01-30-09 6:55 AM
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Nah, to make it interesting, you'd have to make the deduction at least $1.00 per error.

...thus restoring the class bias of the SAT of yore.


Posted by: Knecht Ruprecht | Link to this comment | 01-30-09 7:03 AM
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I think they'll always be a class bias. Even a practice test can be worth 50-100 points; maybe more, for a smart kid with a sketchy background. the best guessing strategy must be worth 100 points over the worst guessing strategy. Coaching really helps.


Posted by: John Emerson | Link to this comment | 01-30-09 7:13 AM
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For example, for the reading comprehension section, we taught the kids to rule out any answer that could be construed as disparaging toward women or minorities, because obviously the test-designers would never include a reading passage that contained any such content.

I figured this out as a elementary schooler. Not kidding; stupid standardized tests.

I never took an SAT prep course, but being able to take the test twice and sneak* a look at a prep course book meant my score took a healthy jump.

*My dad thought that preparing for the exam was immoral or bad advice along the lines of Teaching to the Test; apparently everyone who gets into the Ivies just does so by being smart, not coached. Or something. My mother, being more practical, borrowed the book from the local library. I hid it under my bed.


Posted by: Cala | Link to this comment | 01-30-09 7:20 AM
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213: Test pron!


Posted by: M/tch M/lls | Link to this comment | 01-30-09 7:32 AM
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My first week back here I had fresh corn, fresh tomatoes and fresh fish all in the same meal. It only happened once, though.


Posted by: John Emerson | Link to this comment | 01-30-09 7:39 AM
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Woops.


Posted by: John Emerson | Link to this comment | 01-30-09 7:45 AM
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