# Sloppy Fractions

Allison, your local procrastinator who hasn’t posted in almost a month.

Five kids sit around a table staring down at their math textbooks, their expressions ranging from utter confusion to contented understanding. One kid hurriedly fills out his answers, ripping small holes with his erasable pen into the thin paper. His fractions are sloppy and he never writes down his work but his answers are almost entirely correct. The boy next to him hasn’t written anything underneath the problems I wrote up for him, even though he was able to answer the same questions just a few moments ago. One boy is trying his hardest to solve for x, but he keeps forgetting how to cancel out addition with subtraction and the intricacies of adding positive and negative numbers are lost on him. The only girl in the room is staring at a test marked with a red 67, tasked with the responsibility of fixing every mistake she made on the exam.

My job is to make sure each of these students are retuned to their parents in exactly sixty minutes with their homework finished and a new topic in math mastered. Parents expectations are always unrealistic and the hour always passes away faster than any normal 3600 second period of time. All I can do is work with what I have.

I breeze past the first boy and ask him to explain to me how he got his answers. He cannot. I stop and slowly repeat his work with him, making sure he understands what he’s doing. I reiterate how to solve negative exponents with the second boy, who slowly answers the first question and stares at the second one in new and utter confusion. The second question is the same as the previous one with a single number replaced by a different one, but he doesn’t see that yet. He’ll understand the concept in a week, and he’ll be able to answer hundreds of these questions in his sleep. But today isn’t next week, so we work through the second problem as well. The third looks foreign to him as well. I encourage him to try working on his own as I move to the third boy. I have him repeat the rules of adding a positive and negative number to me, which we’ve gone over three times this session. He says them verbally. (“If the signs of the numbers are different, subtract, and keep the sign of the bigger number.”) He smiles when he says it to me and suddenly finds the confidence to answer the rest of his sheet. I sit next to the girl and work through her test. She forgot to write units on each of her answer and the teacher didn’t give partial credit. We talk about the importance of units. (“Sixty five inches isn’t the same as sixty five centimeters and sixty five inches definitely isn’t the same as sixty five elephants. Remember to write the unit of measurement. Always.”)

Suddenly 20 minutes have passed and only a quarter of everyone’s homework is done. I dig in and focus harder. I move through the room, picking up pencils, crossing out mistakes, and circling incorrect multiplication. Ten more minutes have passed, three more problems have been answered.

And so the hour passes, jumping from student to student, trying to instill each student with an understanding of math, with an appreciation for numbers, and hardest of all, with the confidence to work on their own. They’re all bright students. In all my tutoring I’ve never encountered someone who can’t learn to solve for x or divide three digit numbers, but I have worked with students who just don’t understand things the same way most students do. So I think of new ways to explain a problem and I learn better methods of teaching with each student I encounter. Sometimes drawing small pictures of Jedi’s after each math problem really does help a student stay engaged.

“Every student is different.” We’ve all heard the mantra. Everyone learns differently and likes different things. It’s practically the motto for home schooling, which allows for virtually any teaching style. But I’ve also heard terrible reasons for learning. Children love to ask the question why? Questioning education is an inevitable stage in childhood; what’s not inevitable are the poor answers teachers give in response to students’ queries.

“But Mrs. Smith, when am I ever going to need synthetic division in my real life?”

“Well, maybe you’ll be a mathematician,” Mrs. Smith shoots back, “or a teacher, like me.”

But the response is lackluster. If the only reason for mathematics was to teach it to a new generation of helpless, frustrated students, then math simply shouldn’t be taught.

But this doesn’t mean mathematics should be forsaken along with the dodo bird and Pluto. Math is important, and yes, it is useful. But any high school student studying higher level calculus will eventually begin to question it. That’s when teachers need new answers.

“But Mrs. Smith, why do I need to learn how to differentiate the equation?”

Because it’s beautiful. It’s artistic. It’s mesmerizing. Let’s stop saving these words for the English class and the drama club.  Maybe students won’t be spending their adult career graphing y=mx+b, but grasping the difference between linear and exponential growth is an enriching experience. A student shouldn’t learn math solely to answer math questions on their future tests. A future employer is unlikely to ask them them to multiply a complex fraction with its conjugate. But understanding imaginary numbers brings a certain depth and beauty into anyone’s life, the same way the Iliad is enriching even if one is unlikely to ever attempt to write an epic poem themselves.

When you find yourself questioning math, wondering about the necessity of knowing how to derive an equation, remember that learning will broaden your worldview more than its immediate application. Remember that math is a beautiful thing, and if you dig deep enough, it will bring you joy. Spend five minutes thinking about the concept of infinity. Stare at a flower, something ubiquitously considered beautiful, and know that without math, you would not see that beauty.

Go forth and learn math. If you need help, its likely I’ll be tutoring five students simultaneously. You’re welcome to join the table.