The Man Who Taught Me Fractions

Alicia Berenyi

Thirty minutes out of my daily 45 minute treadmill run are completed. Sweat is pouring down my face, my Nalgene water bottle is almost empty and I can feel a strain in my calf. Fifteen more minutes seems like eternity. However, my rational problem solving voice jumps into my head. Two and half minutes goes into 45 minutes 18 times. That means 12/18ths of my run in completed, simplified to 2/3.  Though increments of five minutes seem more practical in gauging one’s progress in a run, I prefer to use a fraction of five because doing the extra math in my head distracts me from my physical exertion. With only one third of the run left, I decide that if I am already more than half way done, I can surely muster up the endurance to finish strong. My good physical condition is due to my persistence in daily workouts, which comes from my dexterity at manipulating fractions in my head. Fractions save me every day in my routine of running.

I see the world in fractions. There are 32 marking periods in a four year high school education. As of now, 23/32 of high school is over for me. I have come to love fractions. It is easier to finish a task, overcome an obstacle or rationalize any situation with the use of simple fractions.

The significance of my daily use of the division bar is much more complex than a quirky eccentricity I have. My use of ratios in my daily habits stems from the man who taught me fractions, my middle school math teacher, Mr. Israel. He instructed me in both 7^th and 8^th grade. The word ‘instruct’ is important. Mr. Israel certainly did not teach, he instructed us on how to best do math, how to appreciate history, how to evaluate good cinematography. He made sure we knew the rules of chess, that we read at least one article from the New York Times every week, and that we were aware of our own capabilities. Throughout his two years as my teacher, Mr. Israel did not just teach my how to manipulate complex fractions, he instructed me on how to live life.

A graying man in his 50s, Mr. Israel arrived to teach us in late August of my 7^th grade year. A retired lawyer and a math enthusiast, Mr. Israel took one look at my class and ordered us to put away our calculators.

“Math,” he declared, “teaches you how to think. How can you think when a calculator is thinking for you? We will never be using calculators in my class.” An inexperienced teacher, he looked at the white dry-erase board quizzically, uncapped a marker and wrote our first homework assignment in the top corner: write a paragraph on why not to use calculators in math.

I was furious. Mr. Israel was a new teacher, and I was missing out on the typical 7^th grade math experience. Mr. Israel was not about to let us down though. We started plowing through pre-algebra, learning one variable equations and the many functions of exponents. What I did not realize at the time was that I was not about to just get an introductory course on Algebra; I was embarking on a two year course in learning valuable life skills that no other teacher has bothered to teach me.

Our very first lesson began with a review of simplifying fractions. He wrote two thirds divided by three fourths on the board and turned to the class asking, “Who knows already how to divide fractions?” Most people timidly raised their hand half way, but without thinking, I shot my hand up, vaguely remembering the few pages of accelerated worksheets I had done the year before.

Smiling at my zeal, Mr. Israel looked at me and said, “Perfect. Alicia, right? Why don’t you come to the board and show the class how to divide two thirds by three fourths.” I approached the board, my confidence draining.

“Wait, I don’t think I remember anymore,” I quietly said, shaking my head at the marker outstretched in his hand.

“That’s ok,” he responded. “Why don’t we do this problem together? Ok? Good. Now Alicia, what’s funny about dividing fractions?”

Trying to recall the faded memories of 6^th grade math I shrugged my shoulders saying, “all I remember is that you don’t divide at all.”

“Alicia is on to something!” he exclaimed excitedly, winking at me. Handing me the marker, he told me to write down in big letters what he said. “Ours is not to reason why, just invert and multiply!” Pausing for me to finish writing, he took the marker from my hand and motioned me back to me seat. “Those ingenuous words come from my interpretation of a great war poem.” As the bell rung and we began to pack up our binders he called out, “For homework I will give extra credit to the people who discover which poem those lines originally came from.” Exchanging skeptical looks with my friends as I left the classroom, it crossed my mind that we hadn’t completed a single problem all period.

One morning class in October, Mr. Israel handed out a copy of an op-ed piece from the previous day’s New York Times. “Read this,” he mandated, “and try to look up any words you don’t know. Most of you are already 13-years-old. Its time you started reading the newspaper.” Most of his students stuffed the paper into their already messy notebooks, and then shuffled out the door never bothering to fish the article out of the clutter when they got home; however, I was intrigued. I went home, began to struggle through my first New York Times article. Sitting at my kitchen table, I read for an hour trying to make sense of everything the columnist was saying while flipping through the Merriam-Webster dictionary that was at my side. I read the entire thing, maybe understood half of it, but was probably the only student in the class that had done the assignment. Some students were not ready for lessons on life.

Mr. Israel’s greatest endeavor his first year teaching was to set up a chess club at school. He encouraged us all to come.

“Chess is just like math,” he preached.  “It teaches you how to think and how to live your life. In chess you must always be aware of where every piece is on the board. Same in life. You wouldn’t want to be check-mated by a pawn because you had overlooked its presence.” So he called in some friends and every Thursday after school about 20 of his students would first observe his skill at moving the hand carved pieces on his antique chess board as if it was all part of a choreographed dance and then attempt to learn and practice intricate, incomprehensible chess strategies he had just perfectly executed. That’s the way Mr. Israel was with us. He expected so much from all of us, especially me, no matter what the task was. He observed my motivation, my true desire to learn and held me to the very highest standard that any person has ever held me to.

This became apparent in my second year as his student in my 8^th grade algebra class. He assigned us a paper to write on the importance of Euclid and Galileo in mathematics. I wrote the paper, handed it in and got a B-. “Mr. Israel,” I whined to him after class, “I probably did more work than anyone else. You knew Zak copied his paper off a website on the internet and you gave him a C. I actually wrote my paper!”

“Alicia, you know very well that you could write so much better than this. I don’t care what trash your English teacher lets you get away with. Write me another paper and hand it in to me. Go to Barnes and Noble and buy The History of Pi and Galileo’s Daugher. They are two books you should have anyway. You are almost in high school, and now is the time to start building your own library of important books to have.”

I went home, bought the books and struggled through them, reading a few pages every night of complex calculus derivations and the origins of mathematical constants. I never rewrote the paper, but I would occasionally ask him to explain a concept one of the books. He knew I was getting more out of his paper assignment than anyone else in the class, and that was all he had wanted.

Mr. Israel did so much more than just hope for me to succeed. He pushed me to focus on a math concept, a famous director, a chess play and really understand the role it played in my life. He made me look the world around me, and really try to look hard, addressing complex issues like human nature. His instruction and guidance throughout all of 7^th and 8^th grade forced me to realize what an education is—not memorization of dates in United States history, or breaking down grammatical sentence structure, or conjugating Spanish verbs—but the deepening of one’s intellect, the broadening of one’s horizon, the process of maturing.

As the clock on my treadmill ticks from 44:59 to 45:00 and then beeps signaling the conclusion of my timed run, I immediately think, “18/18 completed. 100%.” Ah, fractions. One more thing that Mr. Israel taught me.