## Summary A Mathematician's Lament How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form

A Mathematician's Lament How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form Read ´ 6 ↠ “One of the best critiues of current mathematics education I have ever seen”—Keith Devlin math columnist on NPR’s Morning EditionA brilliant research mathemMath to be creative and beautiful and rejects standard anxiety producing teaching methods Witty and accessible Paul Lockhart’s controversial approach will provoke spirited debate among educators and parents alike and i. This was TERRIBLE The first chapter began so well and had me so psyched about the book Lockhart made an analogy between mathematics and music where a musician wakes from a terrible dream in which public schools teach only the mechanics of music but students are not allowed to compose or listen to music until college level I thought it was a brilliant analogy But it was downhill from there His solution to the problem of math not being fun seemed to be to no longer teach the mechanics of math but to just emphasize over and over that math is art I drug myself a uarter of the way through the book before giving up I love math but I have no clue what the hell he meant by art And I'm not sure how anyone who doesn't know the mechanics of math could ever make it to the fun part which is solving puzzles A good analogy for his method would be a French teacher who doesn't reuire that her students know any actual words in French but instead tells her students over and over what a beautiful language it is Can't be boring them with the mechanics ya know

### Paul Lockhart Ê 6 Characters

T will alter the way we think about math foreverPaul Lockhart has taught mathematics at Brown University and UC Santa Cruz Since 2000 he has dedicated himself to K 12 level students at St Ann’s School in Brooklyn New Yo. Disclaimer 1 This is only a review of the 25 page essay which can be found here Why am I reviewing the essay instead of the book Well I don’t have the book but I did read the essay and thought that posting a review of even part of it would be of worth to some poor sad math challenged but don’t know why soulDisclaimer2 I know next to nothing about mathematics but am endeavoring to want to learn it God bless you Sally B for sending me the link to this paper before I went out and bought a set of Saxon math Okay I admit it I’m math o phobic Always have been What are you going to do Bad teachers Boring subject No natural tendency nor talent Can’t see the relevancy what are calculators for anyway I just plain don’t get it I’m just not a math person I guess Does that sound familiar Do you suffer too Well I think that some relief may lie herein But seriously this essay turned me on my head concerning all things mathematical I have a 12 yo whom I have been feeling needs to “begin” learning math he’s getting on in years it’s time I suppose I truly was all set to get down to the dirty business of it and buy him the Saxon books this year and then give him the “some things are just plain boring hard and hateful and we have to do them anyway so we can someday get into college” lecture It could work Lucky for my kid Lockhart saves the day well Sally saved the day really You must know that Lockhart’s essay is a treatise on great inspirational and inspired teaching than mathematics It also happens to be very well written and laugh out loud hilarious which really helps as the subject matter that millions of souls have been damaged or destroyed by being “taught” the all time worst of subjects math can get a little downheartening Truly it is so You don’t believe it Give this little essay a try Lockhart’s premise is this if I can adeuately sum up Mathematics is the world’s oldest and most beautiful form of art It is inspiring It is gorgeous It is simple It is fun Oh except to everyone who has ever been taught it I uote “There is surely no reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum” The way we are taught math is as if we were mandatorily taught art by first learning theory and how to properly identify colors mediums utensils Then if we’re lucky we can move on to “pre paint by numbers” and then further on to real “paint by numbers” And this is all without ever seeing a real work of art or hear a story of the life of a famous artist If they are really good at that and somehow still retain interest maybe in college we’ll let them actually paint on a blank canvas and look at some art Lockhart’s analogyLockhart says this is exactly how we teach mathematics We’ve extracted all the miserably boring parts and shunted off all the beautiful parts because well because it’s only the boring parts that can be adeuately tested HOLY BUCKETS You mean all the hell we all went through “learning” “math” was only a devilish device for testing To see if we can follow directions That is itThere were only two things I disagreed with in this essay at this reading anyway One was Lockhart’s assumption that math is beautiful because it is so totally irrelevant just flights of fancy and such I’m not sure I read it right and I’m not sure that’s even what he meant Assuming that he meant what I think he said I disagree in that I think it is very probable that as there are mathematical patterns in every living thing God knows pretty advanced mathematics and He used them for a purpose I think it is highly applicable to have fun discovering that relevancy Second I disagree with this statement “English teachers know that spelling and pronunciation are best learned in a context of reading and writing History teachers know that names and dates are uninteresting when removed from the unfolding backstory of events” So if you get what I disagree with sue me or wink too whichever suits you bestReally there’s too much to say about this essay I’d end up regurgitating it all and I really think it would do EVERY SINGLE PERSON ON THE PLANET to give it a read You don’t have to agree but it’s worth a look Sorry for the enthusiasm But hey it’s the first time EVER I’ve been enthusiastic about something mathematical Let’s have a partyI’ll leave you with a little excerpt from one of the little delightful uestion and answer “dialogues” Lockhart intermingles within the essay SIMPLICIO But don’t we need people to learn those useful conseuences of math Don’t we need accountants and carpenters and suchSALVIATI How many people actually use any of this “practical math” they supposedly learn in school Do you think carpenters are out there using trigonometry How many adults remember how to divide fractions or solve a uadratic euation Obviously the current practical training program isn’t working and for good reason it isexcruciatingly boring and nobody ever uses it anyway So why do people think it’s so important I don’t see how it’s doing society any good to have its members walking around with vague memories of algebraic formulas and geometric diagrams and clear memories of hating them It might do some good though to show them something beautiful and give them an opportunity to enjoy being creative flexible open minded thinkers— the kind of thing a real mathematical education might provideSIMPLICIO But people need to be able to balance their checkbooks don’t theySALVIATI I’m sure most people use a calculator for everyday arithmetic And why not It’s certainly easier and reliable But my point is not just that the current system is so terribly bad it’s that what it’s missing is so wonderfully good Mathematics should be taught as art for art’s sake These mundane “useful” aspects would follow naturally as a trivial by product Beethoven could easily write an advertising jingle but his motivation for learning music was to create something beautifulSIMPLICIO But not everyone is cut out to be an artist What about the kids who aren’t “math people” How would they fit into your schemeSALVIATI If everyone were exposed to mathematics in its natural state with all the challenging fun and surprises that that entails I think we would see a dramatic change both in the attitude of students toward mathematics and in our conception of what it means to be “good at math” We are losing so many potentially gifted mathematicians— creative intelligent people who rightly reject what appears to be a meaningless and sterile subject They are simply too smart to waste their time on such piffleSIMPLICIO But don’t you think that if math class were made like art class that a lot of kids just wouldn’t learn anythingSALVIATI They’re not learning anything now Better to not have math classes at all than to do what is currently being done At least some people might have a chance to discover something beautiful on their ownSIMPLICIO So you would remove mathematics from the school curriculumSALVIATI The mathematics has already been removed The only uestion is what to do with the vapid hollow shell that remains Of course I would prefer to replace it with an active and joyful engagement with mathematical ideasSIMPLICIO But how many math teachers know enough about their subjects to teach it that waySALVIATI Very few And that’s just the tip of the iceberg Heck someday if I go about it right I may even end up as math nerdy as Sally But I’m not sure I can ever get to that level of cool PS Per reading some of the unfavorable reviews here on goodreads Sure it is true that Lockhart does not offer many solutions to his problems However we live in an age where we always WANT other people to do the work and give us the solutions I think half the fun of this journey and definitely ALL of the reward will be in finding our own way I am so grateful for the freedom opportunity drive to educate my kids the way I see fit To Sally Perhaps I ought to have found to disagree withbut maybe that will come as I actually learn what math can and should be I’ll have to reread it a year or so from now For now it was like lightning And I can hardly wait to talk to you about the whole subject You are my self chosen mathematic

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A Mathematician's Lament How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form“One of the best critiues of current mathematics education I have ever seen” Keith Devlin math columnist on NPR’s Morning EditionA brilliant research mathematician who has devoted his career to teaching kids reveals. A Mathematician's Lament is of a long essay than a book one man's problems with mathematics education without a viable solution Now I consider myself while no mathematician a mathematicsenthusiast if you will I read the occasional recreational mathematics book I am one of the three people on earth who subscribes to the journal of recreational mathematics I am constantly sneaking new variations on Tangrams and other puzzles into the house And I am definitely not a fan of modern American elementary education; I consider my public school education to have prepared me adeuately enough for the world but it did seem largely like a waste of time Oh those purple dittos with the blocks that had to be colored in based on the results of math problems they were my nemesis and not because I couldn't do arithmetic So partly I think his argument that mathematics education gets tripped up in unnecessary formalism and syntax before conceptually interesting problems are tackled and that the whole thing is defended with the ridiculous you might need this someday pragmatism that children will instantly tune out is a sound one It would be great if every elementary school teacher were the kind of engaged leader capable of putting his or her students to work on an interesting geometry or abstract algebra problem and wandering around not to give answers but to provide the occasional hint Unfortunately I just don't see how this is going to provide anyone with a well rounded mathematics education Lockhart argues that what they get now not learning anything because they're so bored is worse It's tempting to believe all of this And yet I couldn't get a nagging thought out of my mind I managed to get through all that arithmetic algebra geometry and calculus with an ability to apply most of it I didn't go through school memorizing formulas and I never felt forced to do so either; to this day I couldn't tell you most trig identities without starting at the Pythagorean theorem and deriving them Is the state of things really that bad Even accepting that it is Lockhart's book is breezy and uickwhat might have been called a pamphlet perhaps in earlier days And like satirical pamphlets it does an excellent job lampooning the state of things but offers very little in the way of realistic alternatives I am all ears to hear new ways of teaching children math; I imagine classrooms could be greatly improved by incorporating topics from recreational math calculus and abstract algebra at an earlier age and have never understood the obsession with arithmetic that dominates the first years of mathematics education But Lockhart doesn't provide much in the way of real solutions just the clue that he really likes circumscribed triangle problems Spend all of mathematics class playing chess and go That might be fun but I'm unconvinced that the primary purpose of school is to entertain