This week I've been doing some reading about different ideas in how to teach math, including The Mathematicians Lament by Paul Lockhart and a piece by Jo Boaler, a Stanford Professor of Mathematics Education (called the "goddess of math education" by some). Both of these authors points out flaws they see in the current mainstream form of math education and encourage others to make changes to how they think about teaching math.
Both authors talk about how misguided it is to think of some people as having "math brains" and others as not having "math brains". As Boaler sees it, the attitude with which on approaches a problem has an effect on how much you will learn - begin with the belief that you can succeed and you will always learn more that beginning with the belief that you can't do it. Such divisions only propagate the misnomer that math ability is inherent and unattainable without genetic predisposition, according to Lockhart, and in fact every one has the ability to learn and perform and enjoy high levels of math. To these authors, math education should be much more about creative problem solving and slow contemplation than solving lists of numerical problems.
In Lockharts' work I really like his discussion about honesty, which I think applies to all of what I do. He says, "Teaching is not about information. It's about having an honest intellectual relationship with your students." While likely was true in the past, it is especially true now. Students have access to all the information typically delivered by teachers available to them at all times. There are thousands of lectures online far more engaging and informative than anything I could perform. If motivated or passionate about a subject a person can learning anything about everything with available information. What I can uniquely share with students is that passion and motivation. After establishing a relationship I'm able to help students find problems worth solving and give them the reason to seek out paths to solutions.
I don't agree with Lockhart on all points. He asserts "...there is no actual mathematics being done in our mathematics classes..." While it's easy to dispute such an absolute statement I think it's worthwhile because this author would keep nothing of our current math experience. I'm reminded of the tension that I felt when becoming critical of traditional schooling - I am it's product. I am creative, curious and have a passion for learning which if you believe critics of traditional education like Lockhart should be almost impossible. Relating to math I left school a confident math user feeling that with practice I could learn as much math as I cared to. To revise the above absolutist view I might say "the mathematics being done in our mathematics might be made much richer if only..."
After reading these works I will make changes to my class and practice, though maybe not to the degree the authors would wish. Emphasizing creativity and making an attempt should take precedence over explanation of "the right way", and rather than show someone why they are wrong I want to ask them to show me why they're right. Ultimately I want students to leave my class with a passion for learning, solving problems and the confidence to try and I think that by following the advice of these authors I'll do that a little better.
Philip Estrada is a teacher at High Tech High Media Arts in San Diego California. He teaches Physics by having kids build things in a woodshop.