A Mathematician's Lament
by Paul Lockhart
The best recommendation I can make for a book is to say that every one should own it and read it. Paul Lockhart's A Mathematician's Lament is one such book that I unreservedly recommend to teachers, math educators, state and federal senators and congressmen, state governors, parents and children.
The author decries the state of math education, focusing on school mathematics. His point of departure is the idea that mathematics is the purest form of art and should be taught as such. What he proposes is not another reform but a fundamental revamping of the whole of the educational system. Realizing that the system is part and parcel of the cultural atmosphere, he soberly laments the impossibility of achieving his goal.
However, Paul's view is only partially utopian. A professional mathematician, he left a university professorship to devote himself to teaching K-12 level students. He taught at St.Ann's School in Brooklyn, NY since 2000. In the book he not only offers his passionate critique of the state of education but also shares his experience as a teacher and outlines his view of what teaching of mathematics should be.
... I'm not complaining about the presence of facts and formulas in our mathematical classes, I'm complaining about the lack of mathematics in our mathematical classes. (p. 29)
(p. 41-42) I can understand the idea of training students to master certain techniques--I do that too. But not as an end in itself. Techniques in mathematics, as in any art, should be learned in context. ... Give your students a good problem, let them struggle and get frustrated. See what they come up with. Wait until they are dying for an idea, then give them some technique. But not too much. (p. 41-42)
Here's on the fundamentals of math education:
Mathematics is about problems, and problems must be made the focus of a student's mathematical life. Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in this process ... (of problem solving.) (p. 60)
The problem of math education is cultural.
It would be bad enough if the culture were merely ignorant of mathematics, but what is far worse is that people actually think they do know what math is about - and are apparently under the gross misconception that mathematics is somehow useful to society! ... Everyone knows that ... math is 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. (p. 32)
Of math reform he says:
The saddest part of all this "reform" are the attempts to "make math interesting" and "relevant to kids' lives." You don't need to make math interesting--it's already more interesting than we can handle! And the glory of it is its complete irrelevance to our lives. (p. 37)
And of the attempts to make math "relevant":
In any case, do you really think kids even want something that is relevant to their daily lives? You think something practical like compound interest is going to get them excited? People enjoy fantasy ... (p. 39)
It is hard to do justice to Lockhart's passion and eloquence. The book consists of two parts: Lamentation and Exultation. There are examples of good mathematics on both parts as are thoughts on math education. The division into two parts merely reflects the emphasis of author's narrative. The book is small but, if need be, I could quote resonating passages from every page. This would certainly do injustice to the book. For this book must be read!
A Mathematician's Lament, by Paul Lockhart. Bellevue Literary Press, 2009. Softcover, 140 pp, $12.95. ISBN 1-934137-17-0