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Thread: Lamentation on Mathematics

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    International 12th Man Shaggy Alfresco's Avatar
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    Lamentation on Mathematics

    http://www.maa.org/devlin/LockhartsLament.pdf

    Personally I found it quite an interesting read, and it might be why I never really liked maths at school even though I was alright at it. What does our mighty forum make of it?

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    International Captain luffy's Avatar
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    I can count and can use a calculator.

    All I need maths-wise.

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    International 12th Man Shaggy Alfresco's Avatar
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    Quote Originally Posted by luffy View Post
    I can count and can use a calculator.

    All I need maths-wise.
    Good for you.

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    State Captain krkode's Avatar
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    I haven't read much of the article as I'm studying for big exams coming up, but with respect to Math, I myself experienced a transition some time during high-school. I remember, really disliking Math when I was doing school in India (grades 1 through 9). I was average at it, and truth be told, I never really "got it." I had to memorize proofs, regurgitate them on paper, got my passing grade and moved on. Then I moved to the US and somehow found the method of teaching in Math (and other subjects too) a lot more enjoyable at my new school. I got better at it and ended up doing some pretty advanced math before I decided I couldn't really wrap my head around Linear Algebra sometime in college.

    I can't put my finger on why it got more interesting or why I got better at it. But I'm glad I did because Math really is beautiful and I'm glad I can appreciate that even if my ultimate understanding of the subject matter is limited.

    There’s no ulterior practical purpose here. I’m just playing. That’s what math is— wondering, playing, amusing yourself with your imagination.
    I love how he puts Math along with music and painting rather than with the Physics/Biology, etc. Spoken like a true Mathematician. Man, those guys are the real nerds! But much respect.

    That said, teaching Math this way to kids in school seems like a fruitless objective, IMO. In school, kids are at an age where they are questioning their teacher's every motive... Why do I have to read about this war that happened a hundred years ago? Why do I have to read this sonnet? Why do I have to be able to calculate how far a ball will go if I shoot it at a 30 degree angle at a speed of 45 mph? etc. Fact is, finding someone who is truly passionate about a subject the way the author is, especially one as "dull" as math is quite rare. You can always give a kid a canvas and paints and allow him to express himself, or you can give him pen and paper and he will take joy in writing short stories, or you can give him a computer and he will try to program his first game, but rare is the kid who will start to think about abstract and imaginary mathematical ideas. Now that I've long since finished high school and college too recently, I would say that Math is one of the hardest subjects to make interesting for kids. The teacher who can do it is truly a genius.
    Last edited by krkode; 03-12-2008 at 06:46 PM.


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    Cricket Web: All-Time Legend Uppercut's Avatar
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    School just is ****, tbh. Maths being taught in a boring manner is just a symptom of a particularly soul-crushing establishment.
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    Cricket Web: All-Time Legend Top_Cat's Avatar
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    Most sciences are having the fun crushed out of them, though. So many experiments which are the most interesting, happen to be even a little bit dangerous.

    Personally I think the sheer weight of knowledge required to get to know some concepts gets in the way. It's a difficult balance to strike. For example, in chem, to understand molecular orbital theory, you have to have an understanding of physics, calculus and know that electrons can behave in all sorts of crazy ways, make new orbitals, be de-localised over multiple centres in a molecule, be arranged at different energy levels to totally change the properties of a transition metal. And then on top of all that, you have nanochem which is a whole new branch of MO theory. It's just easier to teach VSEPR theory, pretend that ozone makes sense under it and ignore all the maths and physics in it.

    Science, especially biology, has moved on more in the past 50 years than it did in 200 before it so insisting that kids have to know all the basics (Newton's Laws, atomic theory, etc.) on top of all the new stuff, well, something has to give.

    Must be tough for teachers. Have to strike that balance between keeping students interested and technical detail for the nerds so they have to be a bit more macro about the topics. And, on top of that, people are expected these days to be more socially aware about topics. It's not enough to know about fission products of uranium, you also have to understand how nuclear winter is caused by a series of plutonium bombs exploding. You can't just know the technicalities of DNA replication, you have to understand all of the controversial applications of it like cloning, gene-splicing, embryonic stem-cell research, etc. You can't just understand chaos theory, you have to also be taught it's application to weather patterns, El Nino, etc..

    That's a LOT of stuff to teach people in 5 years of high school. Stands to reason that with so many topics to teach which educators and politicians insist are all essential, the first thing to be sacrficed is detail.
    Last edited by Top_Cat; 03-12-2008 at 07:54 PM.
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    The Wheel is Forever silentstriker's Avatar
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    Dire. Teach them everything. Beat it into them.

    But seriously, people who know me will attest that I’m pretty much an uber science nerd when it comes to any type of hard science, or mathematics. But I never really understood or got into science until college – and the primary reason for that was experimentation. The experiments were dull, unimaginative, tedious and we did them just to get credit. They didn’t teach me anything. They didn’t inspire awe. If it is to stick, it must absolutely evoke that emotion in students. How can you?

    In college, I had three or four moments where I started to ‘wake’ up to science. The first was in multivariable calculus, when I finally ‘got’ something. I used the calculus to come to a simple law of physics. That just hit me – I had used an imaginary system created by a bunch of overgrown monkeys to describe something that goes on in the natural world. Math is imaginary, why should it so perfectly describe nature? The second experience was when I first understood, with all its implications, general relativity. And final was when I began to understand (no one fully does ) all the implication of quantum mechanics. Of course, I didn’t get laid my freshman year, so at least my one hand was free to explore things like this.

    The question is how do you get students to have these moments with science at an earlier age? Many young children are fascinated by images from the Hubble telescopes, stars, planets, dinosaurs and all manner of things without having it proven to them by experimentation. It’s heresy to imply that experimentation shouldn’t be an integral part of science, but it shouldn’t come along until much further along. I think most kids would buy basic principles taught in middle and high school without a pretty stupid experiment proving it for them. The people who want more practical science taught are absolutely wrong. Practical science has too many limitations; it is too bound by details that must be perfected for it to work. It is too mired in the process rather than the idea. With all due respect to the monumental achievements by experimentalists like Faraday, the scientists that have revolutionized and inspired people have dealt in big ideas. Again, experiments are the foundation of science, but one must learn to appreciate the building first. The foundation can always be examined later when sufficient interest had been cultivated, and knowledge has been imparted.

    For kids to be inspired, they need big ideas, and they need them early. The practical sciences are absolutely essential, but can come later. What happens when you try to teach practical sciences too early is you have a Newtonian mechanics class without calculus, and it is sort of like learning to read without knowing the alphabet. I don’t blame the kids for hating it – there was nothing to like. It was simply formulas pulled from thin air and you just had to modify them and plug them in. Tedious and boring. The best way to go is to teach them the ideas first, the big ones, the ones that’ll make them think. The ones that’ll amaze them. F=ma, as valuable as it is, does not do it for most people – especially if its just given and not derived.

    I’m doing a mini experiment on my cousin. Ever since he was four, I gave him videos on stars and galaxies, on DNA and atoms. Simple stuff, but still mostly removed from every day life. I showed him pictures of the Hubble. I started doing basic math with him. But I kept at it, and I made sure I gave him stuff that didn’t get mired in too much technical detail. He is nine now, and I am happy to say he can do pretty advanced algebra and some trig, and I’m going to try calculus next year. I gave him videos about time dilation, the event horizons of black holes, the way a virus infects a cell, and a hundred things that he is very far from in the every day world, but which make him wonder. We’ve moved up to videos like this , which are still completely outside the realm of his reality, but which make him go ‘that’s so amazing. How can a particle know someone is watching it?’ That’s the reaction I want. That’s the reaction you should aim for. If he doubts it, I can’t prove it using math, as that’s beyond him, but frequently I can explain things to him conceptually, which in the end is much more important. The details can come later. Inspire them, they'll want to learn the details if you do.

    Wow, when I get on a rant, I type way more than I should. But it was like that post on the LHC, nothing gets me more fired up than science discussions (yes, I know that says a lot about my social life).
    Last edited by silentstriker; 03-12-2008 at 09:54 PM.
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    International Captain thierry henry's Avatar
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    The writer of the article is very wrong to assume that people will want to engage with mathematics, even if it is taught in his way.

    Personally, I could never get excited about figuring out *why* the triangle takes up exactly half the square or rectangle or whatever. It's just not interesting imo.

    I guess I'm not necessarily saying he's wrong, just that no matter how you conceive of it, mathematics will always be a minority interest to say the least.

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    The Wheel is Forever silentstriker's Avatar
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    Quote Originally Posted by thierry henry View Post

    Personally, I could never get excited about figuring out *why* the triangle takes up exactly half the square or rectangle or whatever. It's just not interesting imo.
    But maybe you might be more interested in why pi, which is the ratio of a cricle's circumference and its diameter finds itself into equations of probability and statistics, which have nothing to do with circles, at least superficially. Or maybe you aren't. But I think there is a way to get people more interested, that doesn't mean everyone will be.

    In the end, math, like most science, does require sustained effort before you see results. It's not like doing assignments and readings in most of your crap (e.g, non-math/science) classes. There is, I think, a way to engage people to be much more interested than they are. But it's obviously not going to be a universal appeal, nothing is.

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    Cricket Web: All-Time Legend Top_Cat's Avatar
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    Quote Originally Posted by thierry henry View Post
    The writer of the article is very wrong to assume that people will want to engage with mathematics, even if it is taught in his way.

    Personally, I could never get excited about figuring out *why* the triangle takes up exactly half the square or rectangle or whatever. It's just not interesting imo.

    I guess I'm not necessarily saying he's wrong, just that no matter how you conceive of it, mathematics will always be a minority interest to say the least.
    That whole example, I gathered he was speaking metaphorically. There's less joy actually doing the problem then there is finding the way to be able to do it. Largely what we get taught at school is to follow instructions, like every mathematical problem there ever was has been solved.

    Agree with SS entirely, though. I always liked science but when I got to the end of 1st year at Uni, I had done physics, chem, biol and maths and none of them really grabbed me. Figured I'd finish what I started and picked the one I hated least, chem.

    Fell in love with chem again during 2nd year and realised the lack of inspiration was largely due to how I was taught to that point. From then on, I 'got' science but particularly chem. Physics 1 was incredibly uninspiring; two weeks of relativity, the rest was largely electronics. Oye, how dull. And I hated maths at school but enjoyed it much more at Uni, especially after 1st year.

    But yeah agree that maths ans science will never have universal appeal so I wonder whether we should stop trying? Short-changing the students actually interested in the material seems unfair but, like I said, it's a hugely difficult balance to strike.

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    I love math. The only subject other than physics I used to score regularly above 95.

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    Cricket Web: All-Time Legend Samuel_Vimes's Avatar
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    Well. Certainly explains why I'm not a good mathematician.
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    Global Moderator Matt79's Avatar
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    Don't think he's saying that everyone will love maths and become mathematicians, no more than everyone becomes painters or musicians. But how many people end up hating drawing or singing or looking/listening to others doing so as a result of being encouraged to have a go at doing so as a kid? I thought what he was saying he was keen to do was avoid making the vast majority of people HATE maths - presumably including some that might otherwise enjoy the field.

    Makes sense to me. I did humanities, and for example in history the idea that you need to memorise 'answers' or 'proofs' to explain things has been done away with (much to some conservatives horror). Rather than making people learn answers by rote, the aim is generally to encourage the development of skills to enable people to research well, and to distil research into an account - ie. look at a question and be able to find their own answer. You wonder why the same approach couldn't be tried in maths at a junior level: here's a question - how do you think you could work out the answer? Remember your answer must satisfy these points, etc etc. Don't teach them a formula and then ask them to apply it 20 times to variations of the same issue.
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    International Captain cover drive man's Avatar
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    Sounds good in theory but when you actually do try to make Maths or even Science and English more "Fun" The kids throw it back in your face as an excuse to just be kids and piss about, have saw this in action never works and I ended up thinking "**** it, I dont see how drawing a poster is going to make my mind flourish" Sorry to say but it doesnt work because lets face it people are idiots.
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    International Captain cover drive man's Avatar
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    The way my school works this stuff involves getting the whole year group in the hall and make them do something like get in a group of about 5-6 and make a bridge out of paper or something (Which to me is just another excuse of the pathetic laziness put into the actual teaching). To me why should you mix grade A* students and Grade D-E students? But back on Maths, personally I quite like maths probably second favourite lesson to music although the two are very similar.
    Last edited by cover drive man; 04-12-2008 at 11:17 AM.

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