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.


Overheard at the Dentist


I came across my job by accident. I wasn’t particularly looking for a part-time job, but one day my friend came to me, and being the naïve, capricious person I am, I accepted—completely uninformed of what the job entailed or how long exactly this job would last. One summer turned into two years, and here I still am, as a file clerk at a dental office.

I soon found out that my job did not entail much. I was, essentially, told to take things out of and put things into alphabetical order, 3-4 days a week. I filed patient charts. Pulled patient charts. Prepared patient charts. Labeled patient charts. I sat at my little desk in the corner, click-clacking away on the electronic typewriter, only interrupted whenever someone came over to use the fax machine beside me.

Each day, during the mechanical humdrum of it all, my mind would drift towards other things while my hands typed and scribbled and paperclipped away. College. Homework. Things I needed to do. Dinner. I got my best solutions to my problems while sitting at that desk. I became the most motivated to do homework while sitting at that desk. Ideas of all the great things I could do seemed to come to me when I had the least opportunity to do them, leaving me to jot it down on my phone and hope I rediscover it at the opportune time.

Sometimes, I’d snap out of my daydreaming to listen to the conversations between the patients and the receptionists. Even though it has been such a large amount of time since they last saw each other, the patient and receptionist chat like old friends, picking up exactly where they left off six months ago, and catching up each other up on their respective lives. And then, forty-five minutes later, they part with a cheery “see you in 6 months!” and the patient goes his way. I don’t think you’d even be able to tell they only talk twice a year simply by the nature of their conversation.

But it’s a beautiful cycle. The patient comes in, on the same day of the week, at his usual time, greets the usual receptionist, and sees his usual hygienist and doctor. They chat, he pays his bills, and then he’s on his way. Every single day there’s a new group of patients—more small talk to be made, stories to tell, and lives to catch up on.

It’s interesting to take note of the things that people deem important enough to share about their life in the small amount of time they’re given. If you had ten minutes to talk to someone that you haven’t seen in half a year, what would you say? Some people go all in, giving short narratives of every trip and experience and meal they’ve had for the past several months, complete with a slideshow. Others passionately discuss the latest football game. Others make small talk and nothing else.

Sometimes I wonder. What kinds of things would I tell people if I only had a short amount of time? Would I tell them about my life? What’s happened recently? How can you possibly satisfactorily summarize the past half year into 5-10 minutes? Would I even talk about my life, or would I talk about something else?

The dynamic of the patients that come to the dental office each day is truly marvelous. Some are introverted, others highly extroverted. Some crack jokes; others would just like to get the business done and be on their way. Sometimes I can’t help but outwardly laugh or snort or snicker at the conversations going on—some people are the level of witty and benevolent and charming that I aspire to be one day. It truly is something, listening to the stories of this broad variety of people of different ages, from different backgrounds, different hometowns and childhoods and jobs, different personalities and goals and dreams, all united by a single commonality: the possession of teeth.

And at the end of every single appointment, the patient makes his next appointment, and goes on his way. Some, after scheduling their next appointment, leave with the frequent joke of “see you then! Hopefully not before!” and leave, others rush out as quickly as possible. But the months pass, and before you know it, each patient resurfaces, with new life experiences and stories to share.

“Before you marry someone, look through their birth records and family history so you know what kind of a mess you’re getting into. I wish I did that with my husband–now look at me. It’s too late.”

–Best piece of advice I’ve ever received from a patient

(PSA: You should go to the dentist at least twice a year)