"If you want to build a boat, don't order people to gather wood and assign tasks and work, but instead teach people to long for the boundless immensity of the sea."
A Mathematician's Lament is more of an extended essay than a book - one man's problems with mathematics education without a viable solution. While I agree with him that the current state of mathematics in schools and universities is a travesty, the kind of "solution" he recommends is not the real solution. We all know what most of us thought about the math (and many other fields) in ES and HS, and leaving it all to the student is not an excellent solution.
"Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity - 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 - you deny them mathematics itself."
I think he argues that mathematics education gets tripped up in unnecessary formalism and syntax before conceptually interesting problems are tackled. 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 their students to work on an exciting geometry or abstract algebra problem and wandering around not to give answers but to provide the occasional hint. But, unfortunately, I don't see how this will provide anyone with well-rounded mathematics education.
Don't get me wrong! I liked the premise of his essay. I would love that my professors had just a pinch of Lockhart's teaching spirit; it would make studying math much enjoyable. But, while I can see how it would make learning math so much more fun, it isn't practical. I think it could be accomplished in a small setting, but let's face it, the world doesn't allow for exploration. You have to master what they want you to master, troubling as that may be.
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