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:
- thinking rather than following directions
- math need not relate to real life, sometimes it's beauty is in it's complete irrelevance to real life
- give them a problem and let them struggle with it, don't show them how to solve it
- give them some technique to solve the problem, 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 notation and technique.
- help them to become active and creative mathematical thinkers
- don't get caught up in the vocabulary (ie. quadrilateral)
- 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.