I was imagining a branch of algebra so complicated and mind-boggling that teachers would have the hardest time teaching it. This imaginary branch of algebra deals with eccentric functions, that random mix of formulas and confusing methods needed to solve them. To make eccentric functions easier to teach, I imagined one of the teachers producing an e-mail newsletter with tips and tricks on solving them. I even imagined each newsletter opening with an anecdote from the teacher to lighten the mood. A sampling:
I came up with a rather novel way to explain eccentric functions this morning but it backfired in the worst way possible.
“Suppose there’s a car filled with pong-ping balls,” I started, “and whoever comes the closest to guessing the actual number wins the car. However, someone in the mathematics department tipped us off that the eccentric function for calculating the number of pong-ping balls is p(y/x)=x(y(p²)). How many pong-ping balls are in the car?”
I turned to the board and started calculating the function, occasionally turning to face the class to see if everyone understood what I was doing. Several students were covering their snickers while others were shaking their heads and smiling.
“Is there a problem?” I asked.
“I believe you’re referring to ping-pong balls,” one student piped up.
“Yes, isn’t that what I’ve been saying?” I replied.
“No, you’ve been saying ‘pong-ping’ balls.”
Without even thinking I shot back, “Pong-ping balls, ping-pong balls, it’s all balls to me.”
Immediately the entire classroom erupted into uproarious laughter, and I was so embarrassed that I fled to the restroom, where I hid for the rest of the hour.
I was sitting in the teacher’s lounge on break from a very rough morning. I gave out tests in both of my morning classes and everyone in both classes failed the test, despite my very best efforts to make them understand the material.
Tol Tureki, a fellow teacher, came in for his cup of coffee and saw me looking depressed.
“What’s wrong?” he asked.
“My career,” I replied, in no mood whatsoever to elaborate.
“Oh,” he said. “Congratulations.”
This afternoon I had to go to the classroom next door and fetch George Sherman, the one teacher who could explain eccentric functions the best. His classes always got the highest grades in the mathematics department and thought it would be best if he lent his expertise to my class. My students were in for a treat!
George entered my classroom grumbling, “I don’t know how many times I have to explain this.” He walked up to the blackboard and wrote:
x² = y³
“This,” he told my class, “is the most famous eccentric function in the world. How can a square equal a cube? Take it one step down. x² = y², right? So where does the cube come from? The cube is equal to x base x, which is x². Therefore, x² = y³.”
“OHH!” my students yelled in unison as they finally understood. They rose to their feet and gave George a round of thunderous applause.
“DOES EVERYONE UNDERSTAND THIS!” George yelled.
“YES!” my students yelled back, still applauding.
“What do I need to do, go on a tour?” he said as he left the room.