Monday, October 31, 2016

Book review: A Mathematician's Lament by Paul Lockhart

Summary of review of A Mathematician's Lament by Paul Lockhart

If you teach math, if you like math, if you know a kid who gets  subjected to what the schools call math, if you write books about math,  if you plan math curricula - in short, if you are in ANY way connected  to both kids and math, GO GET THIS BOOK. It is absolutely fantastic.

Summary of A Mathematician's Lament

This is an impassioned plea for the rescue of mathematics education.  More precisely, it is a plea for the creation of math education,  because, at present, we aren't doing any - at least, not in grade school  or high school, in the vast majority of schools in the USA.

The author of A Mathematician's Lament

Paul Lockhart has a PhD in mathematics, and was a professor of  mathematics at Brown University and UC Santa Cruz. In 2000, he gave that  up, to teach math to K-12 students at St. Ann's school in NYC.

Contents of A Mathematician's Lament

This is a short book - only 140 pages, and they aren't very big  pages, or small type. It's in two parts: Lamentation and Exultation.  Lamentation describes what we currently do to kids in what we call math  class. Exultation delights in describing what math really is.
Lamentation has 4 chapters:
1. Mathematics and culture
2. Mathematics in school
3. The mathematics curriculum
4. High school geometry: Instrument of the devil

Exultation is one chapter

Review of A Mathematician's Lament

Let me ask you some questions. They are very easy.

  • If a woman had never read a novel or written anything since college, would she be a good English teacher?
  • If a man had never gone to a concert, played an instrument, or sang, would he be a good music teacher?
  • If a woman had never gone to a museum, painted a picture, played with clay, or drawn, would she be be a good art teacher?

I told you they were easy!

Here are some more:

  • If you were forced to take 12 years of music theory before you were permitted to pick up an instrument, would you do so?
  • If you were not allowed to paint until you could name 100 types of brushes and distinguish 200 pigments, would you paint?
  • If you had to learn all about iambic pentameter before you were permitted to write a poem, would you write one?


But this is precisely what we are doing with math. I've been saying  this for years, but, in a A Mathematician's Lament, Paul Lockhart says  it more eloquently, with greater authority, and at slightly greater  length than I have.

Math is not about rules, it's not about arithmetic, it's not about  notation. Math is about the search for beauty. Here are some quotes from  the book:

Mathematics is an art, and it should be taught by working artists,  or if not, at least by people who appreciate the art form and can  recognize it when they see it
Mathematics is not a language, it's an adventure

A proof should be an epiphany from the gods, not a coded message from the Pentagon

 In A Mathematician's Lament,  Paul Lockhart shows that he actually IS  a mathematician; he's got the chops. We know this not only because of  his formal credentials, but because of the way he talks. Good math is  "elegant", "beautiful", "charming". And he's right. And if you can't see  that he's right, it's because you have never had a mathematics  education - you've been to school, instead.

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