Monday, July 30, 2012

The Mathematician's Lament

"There is surely no more reliable way to kill enthusiasm and interest in a subject than to make it a mandatory part of the school curriculum. Include it as a major component of standardized testing and you virtually guarantee that the education establishment will suck the life out of it."

Paul Lockhart

Ha! Isn't that the truth!

Here are a few more excerpts from mathematician Paul Lockhart's essay, The Mathematician's Lament.

"The mathematics curriculum doesn't need to be reformed, it needs to be scrapped."

Love this guy. 

"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. That's why its so fun!"

"Operate all you want, doctors: your patient is already dead."

Lockhart is an absolute hoot! 

Reading this piece by Lockhart is continually confirming my instinct that Living Math is an excellent approach to a real math education. He states that no other subject is routinely taught without mentioning its history, philosophy, thematic development, etc.  He believes math is really an art, not a science, with aesthetic value and inherent beauty.  This book will change how you think about math!

"The main problem with school mathematics is that there are no problems. Oh, I know what passes for problems in math classes, these insipid "exercises." "Here is a type of problem. Here is how to solve it. Yes it will be on the test.  Do exercises 1-35 odd for homework." What a sad way to learn mathematics: to be a trained chimpanzee."

"I can understand the idea of training students to master certain techniques - I do that too. But not as an end in itself. Technique in mathematics, as in any art, should be learned in context. The great problems, their history, the creative process - that is the proper setting. 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."

"Play games! Teach them chess and Go, Hex and backgammon, Sprouts and nim, whatever. Make up a game. Do puzzles. Expose them to situations where deductive reasoning is necessary. Don't worry about the notation and technique; help them to become active and creative mathematical thinkers."

Hey, have you ever heard of Go, Hex, or Sprouts? Me neither ... but I'm going to find out.

I've given you a little taste of what Paul Lockhart has to say about math education.  Something that has given me pause is his defence of math as an art form done by human beings for pleasure. He likens math to music - musicians may abbreviate their language with little black dots on staff paper, but that does not define the language of music. Nor does it stop even little ones from being able to sing, right? And, becoming proficient at music theory (on paper) in no way makes you a musician.  Its funny, I have a music background in piano, and along the way I often heard how music and math are related.  The idea was that music is made of rhythms and beats which correspond to numbers/math.  Um, big whoop, I always thought.  Kind of a boring connection in my mind.  Well, now I know there is a link between music and math but its not really about numbers! The real connection has more to do with art and creativity and patterns and expression rather than the boring tallying up how many beats in a measure of music! Music is a language that delights, and so should be math.  It makes sense. I don't think God gave us mathematics so we can figure out what happens if train A is coming down the track at 150 km/hr and train B leaves the station 5 min later but is travelling at 110 km/hr and ... you get the idea.  

Read with me.  Download it to your handy dandy kindle.  I'm at the chapter entitled: High School Geometry: Instrument of the Devil. And I'll wait for you to catch up.

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