Wow, this really seems to have struck a chord. I suspect most of us have some childhood war stories about encounters with the tragedy of the way math is taught (or rather, not taught) in secondary schools. In my case, the first hero who came to my rescue was John Schneider, who was at the time a new young teacher at Tappan Zee High School in Rockland County. After the total apathy I had endured on the part of math teachers in middle school, encountering someone like Mr. Schneider was a blast of fresh air for my twelve year old mind as I entered the ninth grade – my first year of high school.
Mr. Schneider truly loved math, and he had none of the “this is just a job” attitude that public schools often beat into their teachers. In addition to a revelatory Geometry class, he also offered, for anyone who cared to take it, an extracurricular course in non-Euclidean Geometry. Five of us signed up, each of us brainy but slightly odd. And all of us were male – I’m sure there were various social forces at work there.
For me, who was still far too young at twelve years old to understand how to fit in socially in high school, our little non-Euclidean group was a dream come true. There were secrets here, mysteries, a sense of power to be had by deliberately breaking the most common sense rules of geometry – such as the rule that says parallel lines exist – and then discovering that things worked anyway. We learned about the spherical world of Reimann, and the beautifully curved hyperbolic world of Lobachevsky. We were amazed to learn that our own universe might be either of these shapes – depending upon how much mass there was out there beyond the stars. But you didn’t even need the physics for it to all make sense – it all stood on its own as pure reason, beautiful and self-consistent. It was my first real encounter with pure thought, the incredible process of building upon a few elegant hypotheses to create an entire world.
And that was the year I first encountered the idea that you can speak truth to infinity without any need to devolve into religious or metaphysical debates. We could all argue in endless circles about whether there is a God, or gods, or whether the world of Edith Hamilton’s “Mythology” was less true than the deity in our prayer books, but five minutes was all it took to understand that there are encounters with the infinite that are indisputable, such as the fact that there are indeed an infinite number of prime numbers – an absolute truth that stands on its own, unassailable, independent of any mere belief system.
Our textbook was a slim dark red hard-cover volume that was blank on the front. The only clue to the treasures within was the phrase “Non-Euclidean Geometry” printed on the binding in plain block letters. Because we felt like rebels, we would pretend it was Mao’s little red book, and we each taped a fake binding onto the edge of our copy that said “Quotations of Chairman Mao John”, in honor of our teacher. I think Mr. Schneider was very bemused by this, but happy nonetheless, because in our quirky adolescent way we had each stumbled upon the beauty of mathematics.
There were so many bad and indifferent teachers in my public school education. I still have one searing memory from when I was eleven years old of bringing a poem I had written – one I was quite proud of – to show an English teacher. He pretended to read it, not bothering to hide his boredom. Never again did I show a poem to a teacher.
But our school was lucky in its math teachers. John Schneider was just the first of a sequence of mostly wonderful math teachers I was to encounter between the ninth and twelfth grades. It was already clear to me, before I graduated high school, that a single good teacher is the most powerful force in the universe for instilling a love of learning in young minds.
That’s how I found my way to math, but it’s also what decided me to end up in a career that involved teaching, and to devote much of my life to turning young minds on to exciting new ideas.