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Bellevue Literary Press (2009), Paperback, 140 pages
Description
A brilliant research mathematician reveals math to be a creative art form on par with painting, poetry, and sculpture, and rejects the standard anxiety-producing teaching methods used in most schools today. Witty and accessible, Paul Lockhart's controversial approach will provoke spirited debate among educators and parents alike, altering the way we think about math forever.
User reviews
LibraryThing member dmcolon
Paul Lockhart seems like he'd be an amazing math teacher. His book The A Mathematician's Lament shows him to be an incredibly motivated teacher of the subject. The book is a prolonged critique of contemporary mathematics education and as such, Lockhart lands a number of serious blows.
Math
On the whole, I found the book convincing. One point that stuck out especially for me was his call to include the history of math in math courses. He'd also like to see the philosophy of the subject discussed so that students can see the passion that mathematicians have. Doing so would certainly have given someone like me more to work with rather than the memorization and pattern recognition that dominates so much of math education today.
Where he loses me is in his dismissal of all attempts to develop curriculum. He dismisses it and every attempt to do so as "bunk". Education schools are absurd. The only thing that matters to Lockhart is the individual teacher and his efforts to do what's best for students. One part of me wants to believe that this is in fact the case, but this seems misguided at best. This Randian view of the heroic individual standing up against all the world's fools sounds good (I guess), but does not conform to the reality I've encountered in my years of teaching and as an administrator.
Can teachers learn from others? I don't have a sense that Lockhart feels he's learned much from anyone but himself. How is a teacher to ensure that students have some consistent and meaningful expeience over the years? Are they to wander from master to master with no direction? Is there really no responsibility to give students some semblance of a coherent experience?
The heart of the problem seems, to me, at least, to be Lockhart's overweening self-confidence. From his text, Lockhart apparently has all the answers and those who don't agree with him are fools. So while I am sure he's a great teacher, I do wonder if his students come to possess what appears to be his elitist dismissal of "lesser intellects". That has nothing to do, I guess, with math, but it does have everything to do with character.
Math
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education, he argues, is currently designed to kill students' love of the subject. It is devoid of the aesthetic beauty that is the essence of math and is instead a pointless series tasks to be memorized. His goal is to elevate mathematical pursuits to the level of an art. Rid the topic of all its pseudo "usefulness" and teach as something to be appreciated on its own terms.On the whole, I found the book convincing. One point that stuck out especially for me was his call to include the history of math in math courses. He'd also like to see the philosophy of the subject discussed so that students can see the passion that mathematicians have. Doing so would certainly have given someone like me more to work with rather than the memorization and pattern recognition that dominates so much of math education today.
Where he loses me is in his dismissal of all attempts to develop curriculum. He dismisses it and every attempt to do so as "bunk". Education schools are absurd. The only thing that matters to Lockhart is the individual teacher and his efforts to do what's best for students. One part of me wants to believe that this is in fact the case, but this seems misguided at best. This Randian view of the heroic individual standing up against all the world's fools sounds good (I guess), but does not conform to the reality I've encountered in my years of teaching and as an administrator.
Can teachers learn from others? I don't have a sense that Lockhart feels he's learned much from anyone but himself. How is a teacher to ensure that students have some consistent and meaningful expeience over the years? Are they to wander from master to master with no direction? Is there really no responsibility to give students some semblance of a coherent experience?
The heart of the problem seems, to me, at least, to be Lockhart's overweening self-confidence. From his text, Lockhart apparently has all the answers and those who don't agree with him are fools. So while I am sure he's a great teacher, I do wonder if his students come to possess what appears to be his elitist dismissal of "lesser intellects". That has nothing to do, I guess, with math, but it does have everything to do with character.
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LibraryThing member sruszala
Easy, fun, devastatingly on target in terms of the math curriculum. My only criticism: what to do next if you're a parent and want to know how to engage your child in the art of math?
LibraryThing member _Zoe_
This is an interesting indictment of our current system of mathematics education, a subject that I almost always enjoy reading about (I very nearly became a mathematics teacher myself not long ago). Lockhart makes his point clearly, eloquently, and succintly--this is a very quick read at only 140
I agree with much of what he says, though I do think that his claims sometimes go a bit too far: he doesn't seem to see much point in learning to add in an age of calculators, for example.
The main problem I had with this book is that, as far as I'm concerned, Lockhart doesn't offer up a viable alternative to the status quo. It's always easy to criticize, but it's a lot harder to come up with a better way of doing things. Lockhart does offer some ideas about how the ideal mathematics education should function: a mathematics teacher should be a practicing mathematician himself, and should be so engaged in the subject that he has no need for lesson plans or curricula, but can rely solely on his passion for mathematics. Teacher training should be abolished, since someone either is a good teacher or isn't, and nothing can change that. While this sounds nice in theory, it just doesn't seem feasible. I'm not convinced that all these perfect mathematics teachers will suddenly appear, and if they don't, we're left with nothing (which I suppose Lockhart would say is better than the current state of affairs). To me, this doesn't seem like a solution. After reading about how terrible the current system is, I'd like to have seen some real suggestions for how it could be reformed.
Still, this is a worthwhile read, and one that should generate a lot of interesting discussion; despite the fact that I wasn't entirely satisfied with it, I plan to encourage my family to read it so that I can see what they think. And there were parts of it that I loved, particularly the initial description of a musician's nightmare that provided a powerful insight into how ridiculous mathematics education can be. So, even with its shortcomings, this is a book that I would recommend.
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pages of fairly large type.I agree with much of what he says, though I do think that his claims sometimes go a bit too far: he doesn't seem to see much point in learning to add in an age of calculators, for example.
The main problem I had with this book is that, as far as I'm concerned, Lockhart doesn't offer up a viable alternative to the status quo. It's always easy to criticize, but it's a lot harder to come up with a better way of doing things. Lockhart does offer some ideas about how the ideal mathematics education should function: a mathematics teacher should be a practicing mathematician himself, and should be so engaged in the subject that he has no need for lesson plans or curricula, but can rely solely on his passion for mathematics. Teacher training should be abolished, since someone either is a good teacher or isn't, and nothing can change that. While this sounds nice in theory, it just doesn't seem feasible. I'm not convinced that all these perfect mathematics teachers will suddenly appear, and if they don't, we're left with nothing (which I suppose Lockhart would say is better than the current state of affairs). To me, this doesn't seem like a solution. After reading about how terrible the current system is, I'd like to have seen some real suggestions for how it could be reformed.
Still, this is a worthwhile read, and one that should generate a lot of interesting discussion; despite the fact that I wasn't entirely satisfied with it, I plan to encourage my family to read it so that I can see what they think. And there were parts of it that I loved, particularly the initial description of a musician's nightmare that provided a powerful insight into how ridiculous mathematics education can be. So, even with its shortcomings, this is a book that I would recommend.
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LibraryThing member aarrott
I teach statistics for decision-making to business students. Paul Lockhart's brilliant little book, "A Mathematcians's Lament", has had a profound effect on my whole approach to teaching. But the travesty of modern mathematics education is just the tip of the iceberg of Lockhart's indictment of
After more than a half-century of observation, this little book finally showed me why educated people tend to be liberals - and, more importantly, why liberals prefer to remember the thoughts of others instead of thinking for themselves.
It's as simple as this: Learning the thoughts of others - however wise and important these thoughts may be - is not the same as learning to think.
Goethe said: "That which thy fathers have bequeathed to thee, earn it anew if thou wouldst truly possess it." (Faust)
Bravo, Mr. Lockhart - schoolteacher and practicing mathematician. Thank you.
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intellectual modernity.After more than a half-century of observation, this little book finally showed me why educated people tend to be liberals - and, more importantly, why liberals prefer to remember the thoughts of others instead of thinking for themselves.
It's as simple as this: Learning the thoughts of others - however wise and important these thoughts may be - is not the same as learning to think.
Goethe said: "That which thy fathers have bequeathed to thee, earn it anew if thou wouldst truly possess it." (Faust)
Bravo, Mr. Lockhart - schoolteacher and practicing mathematician. Thank you.
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LibraryThing member Georg.Miggel
If you like Mathematics and if you like a Polemic Opinion this wll be your book. Lockhart's criticism is certainly exaggerated, but I knew from the beginning that in his heart he was right. The best parts of his book were not dedicated to the educational system but to his love for Mathematics. And
(n – 1)(n + 1) + 1 = n²
Das ist die Formel, mit der sich beweisen lässt, dass die Summe aller ungeraden Zahlen immer eine Quadratzahl ergibt. Der geometrische Beweis besteht aus Quadraten, deren oberstes linkes Feld ein einzelnes Quadrat ist. Darum jeweils L-förmige Gebilde, die die ungeraden Zahlen repräsentieren (aus Lockhart, aber die arithmetische Formel habe ich selbst rausgekriegt)
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though he only gave some examples I knew what he meant. I was sitting on the shore of the Maltese Meditaranian ocean and I needed four beers to understand his (geometrical) "proof for the fact, that the sum of all uneven numbers always give a square numer". With his L-shaped examples he convinced me, but I could not rest before I had the "arithmetical approach as well". That took some other bottels of CISK (Maltese Beer). Sorry that I am not able to convey it in English, but everyone who likes numbers will understand me anyway. (n – 1)(n + 1) + 1 = n²
Das ist die Formel, mit der sich beweisen lässt, dass die Summe aller ungeraden Zahlen immer eine Quadratzahl ergibt. Der geometrische Beweis besteht aus Quadraten, deren oberstes linkes Feld ein einzelnes Quadrat ist. Darum jeweils L-förmige Gebilde, die die ungeraden Zahlen repräsentieren (aus Lockhart, aber die arithmetische Formel habe ich selbst rausgekriegt)
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LibraryThing member otterlake
Someone has said it out loud...mathematics is creative. It is not a mind numbing, rote exercise in memorization. I don't know how many times I've tried to explain this to colleagues and friends who simply don't understand and who think I've lost my mind. Now I have backup. Hallelujah!
LibraryThing member bobbrussack
Mathematician Paul Lockhart gave up university teaching a decade ago to become an antidote to conventional math education for the K-12 students at St. Ann's School in Brooklyn.
Lockhart's book, "Mathematician's Lament" -- easily readable in a sitting or two or three -- makes short work of the math
Lockhart's critique is merciless, but not mean-spirited. His ambition is to rescue both students and teachers from the arid, rote manipulation of symbols that dominates contemporary math education.
Teachers should encourage their students "to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs ...." When you deny students these experiences, "you deny them mathematics itself."
Throughout the volume, and especially in Part II, entitled "Exultation," Lockhart uses simple, elegant examples to allow us a taste of the feast of imaginative delights that draws him daily to his art.
I'll continue to do my best to help my son navigate safely through the math curriculum we have, but I'll try harder to encourage him to explore the math curriculum we ought to have, a journey through a "landscape of elegant, fanciful structures, inhabited by wonderful, imaginary creatures who engage in all sorts of fascinating and curious behaviors."
Lockhart's book, "Mathematician's Lament" -- easily readable in a sitting or two or three -- makes short work of the math
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curriculum that you and I endured and that my son must survive over the next few years. What goes on in math classes, Lockhart argues with the deadly precision of an épée master, is not mathematics. It is a regime of "senseless, soul-crushing" exercises at the other end of the universe from the magical, inspiring, creative art that mathematicians actually practice.Lockhart's critique is merciless, but not mean-spirited. His ambition is to rescue both students and teachers from the arid, rote manipulation of symbols that dominates contemporary math education.
Teachers should encourage their students "to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs ...." When you deny students these experiences, "you deny them mathematics itself."
Throughout the volume, and especially in Part II, entitled "Exultation," Lockhart uses simple, elegant examples to allow us a taste of the feast of imaginative delights that draws him daily to his art.
I'll continue to do my best to help my son navigate safely through the math curriculum we have, but I'll try harder to encourage him to explore the math curriculum we ought to have, a journey through a "landscape of elegant, fanciful structures, inhabited by wonderful, imaginary creatures who engage in all sorts of fascinating and curious behaviors."
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LibraryThing member KateLowry
Wonderful; adapted from the essay of the same title that had previously been circulated unpublished in mathmatical circles for years. This is Paul Lockhart's brilliant 140 page arguement that maths is 'the purest of the arts, as well as the most misunderstood.' And his arguement is very persuasive,
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writing that the 'maths' we are presented with in school is not the real thing at all, but a frighteningly dummed down version. That which is done to maths in school is the equivalent of painting-by-numbers being presented as art's true essence. Lockhart states 'Mathematics is fundamentally an act of communication', and, as if to prove his point, it is clear that the author has communication down to an art form. As a non-mathematician I was fully able to follow and appreciate the arguements and mathematical problems presented in this book. Perhaps best summed up in Lockhart's own phrase; 'If tears aren't streaming down your face, maybe you should read it again.' Not that that would be a chore. Five stars are not enough. Show Less
LibraryThing member macsbrains
This is an opinion piece; an extended essay that is part rant about the inadequacies of mathematical education in the United States, part lament over the current state of affairs, and part impassioned plea to reinvent approaches to the subject.
I have to be careful I don't segue into a rant of my
Anyone involved in any aspect of education should give this a read.
Disclaimer: This book was provided to me for free by the publisher. No review was explicitly requested, but I have obviously written one anyway.
I have to be careful I don't segue into a rant of my
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own here because Lockhart is definitely preaching to the choir with me. As someone who has tutored math of all levels on and off since my high school days, I see the same issues in my students (and in myself when I was a student). There is nothing like the school curriculum to kill any interest you might have in any subject, math most especially.Anyone involved in any aspect of education should give this a read.
Disclaimer: This book was provided to me for free by the publisher. No review was explicitly requested, but I have obviously written one anyway.
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LibraryThing member ifisher
Outstanding! As a father trying to help his 15 year-old daughter, I find much that he says on target. I wish there were more teachers like him in the schools.
LibraryThing member jen.e.moore
This is the kind of math I love, and would have done a lot more of if I had been exposed to it at an earlier age. (I have far too many things I like to do to spend time getting up to speed on mathematical logic at this point.)
Original publication date
2009
Physical description
140 p.; 4.88 inches
ISBN
1934137170 / 9781934137178