A Mathematician's Lament: the book that says we're teaching the wrong subject.

I fell upon a book that kept me glued, and this book forms our story #37: A Mathematician's Lament by Paul Lockhart. It laments the sad state of the US school system's way of teaching and thinking about math, and proposes a solution. It is one of the best critiques of K-12 mathematics education.

The book is built on the assumption that mathematics is art. But unlike the arts we traditionally recognise, where the patterns depend on properties of the physical world, mathematics is about making patterns of ideas.

This strongly worded opinion piece is organised in two parts. The first, "Lamentation", criticises the way mathematics is typically taught in American schools and argues for an aesthetic, intuitive and problem-oriented approach. The second, "Exultation", gives specific examples of how to teach mathematics as an art.

Some of his writing

• "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."
• "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."
• "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."
• "The first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognise it as such."
• "Other math courses may hide the beautiful bird, or put it in a cage, but in geometry class it is openly and cruelly tortured."

The book leaves me with two distinctly different reactions — the lament is both realistic and unrealistic — but it surely caught my eye and kept me glued. Do give it a read if you are an educator or a math lover.