Summary ✓ A Mathematician's Lament How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form ë PDF eBook or Kindle ePUB free

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Summary ✓ A Mathematician's Lament How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form ë PDF, eBook or Kindle ePUB free À “One of the best critiues of current mathematics education I have ever seen”—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. Slightly expanded from the essay online pdf in that it has a Part II Exultation where Lockhart wants to tell you about what math really is and why I love it so much p92Seriously this is a great essaybook Worth reading probably once a semester if not And before structuring a class curriculum The faux dialog at the end of every section is awesome and indicates good ways to respond to nay sayers are there any even if not all of the uestionsconcerns are fully addressedWhen in doubt remember that math is an art Argue for it as you might for music or painting Of course to a Platoist math is discovered instead of created like I think of for music or painting But there's some famous sculptor who said something about freeing a form from the marble instead of making it rightPart I Lamentationp23 there is nothing as dreamy and poetic nothing as radical subversive and psychedelic as mathematics It is every bit as mind blowing as cosmology or physics and allows freedom of expression than poetry art or music Mathematics is the purest of the arts as well as the most misunderstoodchokengtitiktitikchokeng24 If there is anything like a unifying aesthetic principle in mathematics it is this simple is beautiful Mathematicians enjoy thinking about the simplest possible things and the simplest possible things are imaginaryp25 major theme in mathematics things are what you want them to be and later This is the amazing thing about making imaginary patterns they talk backp27 Somehow I was able to create a profound simple beauty out of nothing and change myself in the process Isn't that what art is all aboutp29 Mathematics is the art of explanationp32 33 gross misconception that mathematics is somehow useful to society later Music can lead armies into battle but that's not why people write symphoniesp37 The mathematics curriculum needs to be scrapped later Mathematics is the music of reason later still you gave it sense and you still don't understand what your creation is up to within To do mathematics is to be alive damn itp39 We don't need to bend over backwards to give mathematics relevance It has relevance in the same way that any art does that of being a meaningful human experiencep43 emphasis mineSo how do we teach our students to do mathematics By choosing engaging and natural problems suitable to their tastes personalities and levels of experience By giving them time to make discoveries and formulate conjectures By helping them to refine their arguments and creating an atmosphere of healthy and vibrant mathematical criticism By being flexible and open to sudden changes in direction to which their curiosity may lead In short by having an honest intellectual relationship with our students and our subjectchokengtitiktitikchokeng44 The trouble is that math like painting or poetry is hard creative workp46 Teaching is not about information It's about having an honest intellectual relationship with your studentsp47 your lesson will be planned and therefore false later Teaching means openness and honesty an ability to share excitement and a love of learningp48 We teach them to read for the higher purpose of allowing them access to beautiful and meaningful ideasp51 get curious about a uestionp52 part of one of the dialoguesSimplicioYes but before you can write your own poems you need to learn the alphabet The process has to begin somewhere You have to walk before you can runSalviati No you have to have something you want to run toward Children can write poems and stories as they learn to read and write A piece of writing by a six year old is a wonderful thing and the spelling and punctuation errors don't make it less so Even very young children can invent songs and they haven't a clue what key it is in or what type of meter they are usingchokengtitiktitikchokeng53 Mathematics is not a language; it's an adventurep54 We teach to enlighten everyone not to train only the future professionals think creatively and independentlyp55 56 the exact same things are being said and done in the exact same way and in the exact same order next two which I wrote internet Make the process efficient Of course this isn't what Lockhart wants and thinking about it likely not what I wantchokengtitiktitikchokeng56 Art is not a race seeing mathematics as an organic wholep58 Of course it is far easier to test someone's knowledge of a pointless definition than to inspire them to create something beautiful and to find their own meaningp59 60 Mathematics is about problems Painful and creatively frustrating as it may be Later on p60 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 Why does mathematics education remain stuck in the nineteenth centuryp62 Teaching is a messy human relationsihp if you need a method you're probably not a very good teacherp63 I'm sure most of them love their students and hate what they are being forced to put them through They know in their hearts that it is meaningless and degrading They can sense that they have been made cogs in a great soul crushing machine but they lack the perspective needed to understand it or to fight against itp64 done right according to Lockhart there would obviously be a range of student interest and ability but at least students would like or dislike mathematics for what it really isp66 Doing mathematics should always mean discovering patterns and crafting beautiful and meaningful explanationsp72 ranting on geometry the two column proof The effect of such a production being made over something so simple is to make people doubt their own intuition I'd argue that making people doubt their intuition is actually a good thing Later Rigorous formal proof only becomes important when there is a crisisp75 This is what comes from a misplaced sense of logical rigor uglinessp76 Mathematics is about removing obstacles to our intuition and keeping simple things simplep78 private personal experience of being a struggling artistp79 definitions matter And they are problem generatedp80 I don't want students saying the definition the theorem the proof I want them saying my definition my theorem my proof Later Efficiency and economy simply do not make good pedagogyp81 It's hard to completely ruin something so beautiful LaterSimplicio So we're supposed to just set off on some free form mathematical excursion and the students will learn whatever they happen to learnSalviati Precisely Problems will lead to other problems techniue will be developed as it becomes necessary and new topics will arise naturally And if some issue never happens to come up in thirteen years of schooling how interesting or important could it bePlus in all that time students will have learned how to think and learn and so picking something up later will be easierchokengtitiktitikchokeng82 a good teacher can guide the discussion and the flow of problems so as to allow the students to discover and invent mathematics for themselves individuals doing what they think best for their studentsp87 88 How ironic that people dismiss mathematics as the anitthesis of creativity They are missing out on an art form older than any book profound than any poem and abstract than any abstractPart II Exultationp91 School has never been about thinking creating School is about training children to perform so that they can be sortedp92 mathematics is an art Math is something you do And what you are doing is exploring a very special and peculiar place a place known as Mathematical Reality elegant fanciful wonderful imaginary fascinating curious Later In this way being a mathematician is a lot like being a field biologist a nice analogy that he expands onchokengtitiktitikchokeng94 the difference between the thing itself and the representation of the thing The only thing that matters in mathematics is what things are and important how they actp100 Mathematical objects are still nothing than figments of our imagination they are what we ask them to bep101 we mathematicians do not like being told what we can and cannot dop103 we play and create and try to get closer to ideal beautyp104 Being a mathematician is not so much about being clever it's about being aesthetically sensitive and having refined and exuisite tastep106 The only thing I am interest in using mathematics for is to have a good time and to help others do the same And for the life of me I can't imagine a worthwhile goal We are all born into this world and at some point we will die and that will be that In the meantime let's enjoy our minds and the wonderful and ridiculous things we can do with them I don't know about you but I'm here to have funp108 This is the Frankenstein aspect of mathematics we have the authority to define our creations to instill in them whatever features or properties we choose but we have no say in what behaviors may then ensue as a conseuence of our choices Later I am drawn in by the possibility of a connectionp109 Nothing I have ever seen or done comes close to having the transformative power of math Later Mostly I love the abstraction of it all the sheer simplicityp110 on checking the first umpteen cases We could then say that it's true for all practical purposes and be done with it But that's not what mathematics is about Math is about reasoning and understanding Later That is the goal of the mathematician to explain in the simplest most elegant and logically satisfying way possiblep111 112 This is a uniue art form within the world of rational science Later imagine a Two Headed Monster of mathematical criticism The first head demands a logically airtight explanation The second head wants to see simple beauty and elegance to be charmed and delightedp113 a lot of pain and frustration and crumpled up paperp114 115 mathematics is our most uintessentially human art form We are biomechanical pattern recognition machines and mathematics is nothing less than the distilled essence of who we arep117 118 what it's like to do mathematics Playing with patterns noticing things making conjectures searching for examples and counterexamples being inspired to invent and explore crafting arguments and analyzing them and raising new uestionsp118 That's really what it means for something to have a pattern if we can capture it with languagep119 For a brief shining moment we lifted the veil and glimpsed a timeless simple beauty Is this not something of valuep120 121 We're talking about a perfectly innocent and delightful activity of the human mind a dialogue with one's own mentality Math reuires no pathetic industrial or technological excuses LaterTo say that math is important because it is useful is like saying that children are important because we can train them to do spiritually meaningless labor in order to increase corporate profitschokengtitiktitikchokeng126 Mathematics is fundamentally an act of communicationp128 problems can be classified The point of this sort of framework to help us understand helps us make predictions and to know what to look for Classifications are a guide for our intuitionp131 132 The historical development of mathematics first come the problems connections are made structures are then devised New uestions then arise And then the process continuesp133 as modern mathematicians we are always on the lookout for structure and structure preserving transformationsp135 math problems come from playingp137 How bizarre that something so simple should turn out to be so hardp138 Does math ever come to an end No Later learning and playing are the same thingp139 if you are a math teacher throw the stupid curriculum and textbooks out the windowp140 final paragraphAnd if you are neither a students nor teacher but simply a person living in this world and searching as we all are for love and meaning I hope I have managed to give you a glimpse of something beautiful and pure a harmless and joyful activity that has brought untold delight to many people for thousands of years

Paul Lockhart ✓ 5 review

Math 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 is brilliant After reading this I finally remember what fascinated me about maths before I was trained to sit maths examsThe author's stunningly poethic approach to math as a study of world and its transcendent nature that is so elouently explained in this work can make even the most antimathematically thinking person to fall in love with mathsA sure must reread

Summary ç PDF, eBook or Kindle ePUB free ✓ Paul Lockhart

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