Mathematician's Lament

"It is not the job of mathematicians... to do correct arithmetical operations.  It is the job of bank accountants." ~Samuil Shchatunovski

Came across Paul Lockhart's excellent Mathematician's Lament today.

Excerpt: "Music class is where we take out our staff paper, our teacher puts some notes on the board, and we copy them or transpose them into a different key. We have to make sure to get the clefs and key signatures right, and our teacher is very picky about making sure we fill in our quarter-notes completely. One time we had a chromatic scale problems and I did it right, but the teacher gave me no credit because I had the stems pointing the wrong way.”

Lockhart doesn't mince words: 

"Sadly, our present system of mathematics education is precisely this kind of nightmare. In fact, if I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done— I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

Read the article for its full effect, but here are some pearls:

* play at math and mathematical relationships, look for patterns and ask questions
* math should not be about following's about making new directions
* students should hear about great problems in math, and also the stories about how they were solved
* a good problem is something you don't know how to solve
* let students struggle a bit, experiment, respond to criticism, and refine arguments
* math should be taught by math thinkers
* play games like Go and Hex and work on puzzles in math class

If you need a little inspiration for mathematical play and beauty, check out Erik Demaine's Transformation of a Cube:


  1. Thanks for reminding me about the Mathematician's Lament. I will go back and read it. My 4 year old and I watched metamorphosis of the cube together. She loved it. Are there any parallel's in math instruction and reading? I'm thinking about each student reading the same collections of stories with questions that are too often bland written at the end for discussion.

  2. Great question. Anyone know of a similar paper for reading? If so please send or send a link.

    Difference #1 is that there are no career 'readers' as opposed to career mathematicians. Maybe that should tell us something there. We like the idea of history being taught by historians or art classes being taught by artists, but is reading really just a tool or something different? Should reading be taught by linguists? How about professional writers, verbal pundits, or rhetoricians? Or is reading really a different subject from oral language?

    There ways we think to make the teaching of reading (or recognition of written ciphers) more interesting, beautiful, and like a puzzle.