Saturday, December 4, 2010

Mathematician's Lament

Yesterday Will Richardson tweeted the Mathematician's Lament by Paul Lockhart. It is, hands down, the best read I have ever had pertaining to mathematics education. Where was this kind of direction when I was being trained as a teacher? How long has this been available to me and why have I not been exposed to it?

If you can't read the whole thing (25 pages) I would suggest you move to his conclusion where he gives a scathing description of math education as it is in most schools.

His main idea is that math education is broken and not worth fixing. The patient is dead. Math needs to be recreated, not revived. He says students claim "..math class is stupid and boring...they are right...". Math is taught as a paint by number method void of imagination, creativity and discovery. Students are never allowed to create or think. Traditional math is about following directions, not creating directions. His main claim is that none of us recognize math as an art.

Math reformers claim for testing and/or higher standards will fix the problem. Lockhart says they are all wrong. He gives solutions:

  1. thinking rather than following directions
  2. math need not relate to real life, sometimes it's beauty is in it's complete irrelevance to real life
  3. give them a problem and let them struggle with it, don't show them how to solve it
  4. give them some technique to solve the problem, but not too much
  5. play games, teach them chess and go, hex and backgammon, sprouts and nim, whatever, make up a game. Do puzzles.
  6. expose them to situations where deductive reasoning is necessary.
  7. don't worry about notation and technique.
  8. help them to become active and creative mathematical thinkers
  9. don't get caught up in the vocabulary (ie. quadrilateral)
  10. story that matters, not the ending

I have been in love with teaching math for my entire career. I feel like I have many things right. Thanks to him I have a more accurate road map for the learning of math in my class. I can hardly wait to get back into the classroom and to share this with my colleagues.


  1. The first concern I could see people having (as I had it myself while reading the article, and the author addresses it to some extent himself)is that kids may not learn basic skills like addition, multiplication, and division which are used on a daily basis in most jobs (such as working at a gas station). However, having discovered that many people in todays society somehow failed to develop those skills anyway, I am inclined to say that we have nothing to lose approaching math as he suggests it. If you teach math by looking at the story behind the procedure, people will be far more likely to remember to procedure (and understand why), or even be able to recreate the procedure should they forget it. And perhaps more people would find they are "good" at math if it was presented to them in such a helpful manner that we might start having an explosion of mathematical breakthroughs, which could benefit society as a whole greatly.

    The way so much math has been taught as "Mathemagic" (as an author of an ebook on logarithms calls it) where you either plug numbers into a formula (as is the case of the quadratic equation, or the manipulation of a sine wave) or just "use your calculator", there is a complete lack of understanding in what a person is doing with the numbers. Even though I was taught math in the traditional way up to Grade 9, we were at least given enough time and rigor to master the procedures that we were able to "get it" (in the sense that we could do it reliably) and remember it. But from grade 10-12, the procedures and equations came too fast and without enough meaning or story to remember (twice the material, half the time). Consequently, I can perform up to about grade 9 "math" with reasonable proficiency, but beyond that it is all pretty fuzzy.

    As a result of the lack of real explanation of the hows and whys of math, I pretty much completely lost interest by the end of Grade 12, and it took me probably a good 5 or 6 years to start to regain an interest in it again. If I EVER take a math course again, I would like it to be something like what this fellow proposes. I don't just want to be told that the square root function works by pushing a button on my calculator. I want to understand how it works, how it came to be (Seriously, I asked my grade 8/9 math teacher how square roots are calculated, and she told me something about tables that you look things up on). I don't want to just push "sin" on my calculator. I want to know how that came to be, and how that can be done without a calculator. Apparently the ancients could do it, so is it too much to ask that I be taught how?

    Anyway, I'm probably rambling now. Thanks for the link to the article. I felt it to be most enlightening. Maybe on Monday for your "read aloud", you should read some of the poignant parts to your class (definitely give them the comparison to painting and music). I think you'd have a lot of students in agreement with this guy.

  2. thanks for your insight Calvin. I happen to know how smart a person you are and I am convinced that people like you would have flourished with the knd of math (or other) instruction that is in the mathematician's lament. Remember, this guy is no slouch academically. You might say he sees the world differently.
    I appreciate your helping me to sort out my thoughts as well as the tremdendous work you do for our youth.