Several weeks ago I was asked by a principal to read an article,
"The Mathematician's Lament". The school was considering me as a potential addition to their math department and they claimed the article explained their philosophy on math.
The Author, Paul Lockhart makes a beautiful point, math is an art. The exact point I spent an entire hour debating with a physics major at a Mexican Restaurant last night. He claimed that math was too rigorous to be an artistic pursuit. Which lead me to believe that he was taught math the same way most of us were. Spoonful upon spoonful of ipecac like formulas shoved down the throat without explanation.
Lockhart went wrong in two critical areas. His overwhelming negativity and his naive belief that the stronger your math skills the better teacher you are. He puts down the art of teaching by acting like teacher education is a waste of time.
This is not to say that some people are not naturally gifted educators. Born teachers are similar to my gifted 6th grade math students who independently learn the skills required to solve a math problem. Some inexperienced teachers intuitively create exciting and meaningful lessons.
Perhaps I have misunderstood the point this writer intended to make because the root of his philosophy is quite beautiful, "math as art." My first experience with exploratory math was like an adventure. I could choose any path that interested me, as long as it got me to a fruitful destination.
Even before reading the "lament" I was indebted to the founders of this style of math education. During my time as a MIT student at Seattle University I attended a math conference with a friend from my cohort. It shattered my previous ideas about math (math was painfully dictated and repetitively uncreative). I used to hate math but now I love teaching it as a fun and creative pursuit.