Math education has fascinated me for a very long time. I was always good at arithmetic and despite having a pretty bleak elementary school experience, I could do what they called, “math.” Test scores in the 6th grade indicted that I was mathematically gifted and earned me a place in something called Unified Math. “Unified” was an accelerated course intended to rocket me to mathematical superiority between grades 7 and 12. Rather than take discrete algebra, geometry, trigonometry, etc., Unified Math was promised as a high-speed roller-coaster ride through various branches of mathematics.
Then through the miracle of mathematics instruction I was back in a low Algebra track by 9th grade and limped along through terrible math classes until my senior year in high school. In 12th grade, I enrolled in a course called, “Math for Liberal Arts.” Today this course might be called, “Math for Dummies Who Still Intend to Go to College.” I remember my teacher welcoming us and saying, “Now, let’s see if I can teach you all the stuff my colleagues were supposed to have taught you.”
This led to two observations:
- Mr. O’Connor knew there was something terribly wrong with math education in his school.
- I looked around the room and realized that most of my classmates had been in Unified Math with me in 7th grade. These lifeless souls identified as mathematically gifted six years ago were now in the “Math for Dummies Who Still Intend to Go to College” class. If this occurred to me, I wondered why none of the smart adults in the school or district had observed this destructive pattern?
Two things I learned in school between 7th and 12th grade kept me sane. I learned to program computers and compose music. I was actually quite good at both and felt confident thinking symbolically. However, majoring in computer science was a path closed to me since I wasn’t good at (school) math – or so I was told.
I began teaching children in 1982 and teachers in 1983. I was 18-19 years old at the time. While teaching others to program, I saw them engage with powerful mathematical ideas in ways they had never experienced before. Often, within a few minutes of working on a personally meaningful programming project, kids and teachers alike would experience mathematical epiphanies in which they learned “more math” than during their entire schooling.
In the words of Seymour Papert, “They were being mathematicians rather than being taught math.”
Teaching kids to program in Logo exposed me to Papert’s “Mathland,” a place inside of computing where one could learn to be a mathematician as casually as one would learn French by living in France, as opposed to being taught French in a New Jersey high school class for forty-three minutes per day.
I met Seymour Papert in 1985 and had the great privilege of working with him for the next 20+ years.
Papert was a great mathematician with a couple of doctorates in the subject. He was the expert Jean Piaget called upon to help him understand how children construct mathematical knowledge. Papert then went on to be a pioneer in artificial intelligence and that work returned him to thinking about thinking. This time, Papert thought that if young children could teach a computer to think (via programming), they would become better thinkers themselves. With Cynthia Solomon and Wally Feurzig, Papert invented the first programming language for children, called Logo. That was in 1968.
What makes Papert so extraordinary is that despite being a gifted mathematician he possesses the awareness and empathy required to notice that not everyone feels the same way about mathematics or their mathematical ability as he does. His life’s work was dedicated to a notion he first expressed in the 1960s. Instead of teaching children a math they hate, why not offer them a mathematics they can love?
As an active member of what was known as the Logo community, I met mathematicians who loved messing about with mathematics in a way completely foreign to my secondary math teachers. I also met gifted educators who made all sorts of mathematics accessible to children in new and exciting ways. I fell in love with branches of mathematics I would never have been taught in school and I understood them.Computer programming was an onramp to intellectual empowerment; math class was a life sentence.
It became clear to me that there is no discipline where there exists a wider gap than the crevasse between the subject and the teaching of that subject than between the beauty, power, wonder, and utility of mathematics and what kids get in school – math.
Papert has accused school math of “killing something I love.”
Marvin Minsky said that what’s taught in school doesn’t even deserve to be called mathematics, perhaps it should just be called “Ma.”
One of our speakers, Conrad Wolfram, says that every discipline is faced with the choice between teaching the mechanics of today and the essence of the subject. Wolfram estimates that schools spend 80% of their time and effort teaching hand calculations at the expense of mathematics. That may be a generous evaluation.
Over the years, I’ve gotten to know gifted mathematicians like Brian Silverman, David Thornburg, Seymour Papert, Marvin Minsky, and Alan Kay. I’ve even spent a few hours chatting with two of the world’s most preeminent mathematicians, John Conway and Stephen Wolfram. In each instance, I found (real) mathematicians to embody the same soul, wit, passion, creativity, and kindness found in the jazz musicians I adore. More significantly, math teachers often made me feel stupid; mathematicians never did.
You can read the remainder of this post at the Reinventing Mathematics Education blog, which originally published this piece. Gary Stager is the founder of the Constructing Modern Knowledge summer institute for educators. He will lead a day-long symposium in Los Angeles on January 4th to explore Reinventing Mathematics Education. Dr. Stager’s latest book, Invent To Learn – Making, Tinkering, and Engineering in the Classroom was published in May 2013 by Constructing Modern Knowledge Press.