Circular Reasoning

A math teacher tries and fails.

There was a bell ringer on the board when the children came in. Mr. Ivan had written out a short list of equations (A=LW, A=1/2BH, and ) and he expected the students to tell him the use for each one.

“Look up here and tell me what these are,” he said, his booming voice carrying easily. He had the stature of a retired football player and the volume to match.

The children were still finding their seats and missed the instructions, despite their decibel. 

“Before Christmas, preferably,” Mr. Ivan said.

Three hands shot up. Kaylee, a tiny brunette who sat in the farthest corner, waved her hand around with barely contained insistence. When Mr. Ivan looked at her, her grin showed every tooth. 

“Alright, Kaylee.”

“They’re letters.” 

Mr. Ivan stood by the front podium holding the whiteboard marker in one hand and the eraser in the other. “Well, yeah, obviously, but what do they represent, Kaylee?”

“Formulas.” This from Franklin, Pine Hill’s only Puerto Rican student. Most of the other kids just called him black because they hadn’t yet experienced the distinction between races.

“It’s amazing how Kaylee can say the answer in that boy’s voice without her lips even moving,” Mr. Ivan said.

Franklin clapped a hand over his mouth.

“Formulas!” Kaylee echoed.

“Too bad you won’t have Franklin whispering in your ear on the state assessment in two weeks.”

At this, Franklin clicked his tongue and pointed a finger at Kaylee like a movie star. “I got you, girl,” he said.

“But what are they formulas for?” Mr. Ivan asked, his thunder drowning out Franklin’s cheekiness.

No one volunteered this time.

“No one knows?”

There were fifteen children in the class"six boys who sat at the back table, seven girls who sat on the side by the windows, and two boys who sat alone. Still, no hands rose.

“Okay, what about the first one? A=LW? Whenever we see two letters together with no space in between, what does that mean?”

“Multiply,” said Logan from the back, except that he mumbled it so only his tablemates could hear.

“What was that, Logan?”

“You multiply,” Logan repeated.

“So, A=L times W. What is that a formula for?”

“Area of a rectangle,” said Logan in that same quiet voice.

“I can’t hear you, Logan. Come on, speak up.”

“AREA OF A RECTANGLE.” He was a wrestler and too smart for his class, but disorganization and apathy kept him from moving to the higher math group.

“Good, Logan. And what about this one?” Mr. Ivan said, pointing to the next formula on the board. “Cameron?”

Cameron, one of the two boys who sat alone, squinted at the equation. “Area of a… triangle?” Between his severe ADD and the fact that he was a new student, it was a miracle any time Cameron got a right answer.

“Area of a triangle. Awesome, Cameron. And the last one?” said Mr. Ivan, moving on to the equation for a circle.

They had been on the briefest of triumphant streaks, but now there was silence again. 

“Come on, you know this. What is the formula used for?”

“It’s pi,” said Justin, not waiting to be called on.

Mr. Ivan let it slide. “Yeah, pi is used in it, but what is the whole formula for?”

“Radius?” From Terry this time. Justin hadn’t gotten in trouble for talking out, so now the others felt more freedom. 

“No, radius is in it, but what is it for?”

“Diameter.” Cameron.

“Not diameter, no.”

“Polygon!” Franklin.

“Circles aren’t even polygons, Franklin.”

“To find around the sides!” Kaylee.

“What did I just say? Circles aren’t polygons. They don’t have sides.”

“Perimeter?” Franklin again.

The students were all laughing now at the number of wrong answers. Answer, rebuttal, answer, rebuttal. The exchange was, to the students, like a volleyball match where one person constantly swings and misses.

“You have got to be kidding me,” said Mr. Ivan. The change in his tone brought the laughter to a halt, even though smiles still lingered on their faces. “We have been learning this stuff since September. How can I possibly teach you new information when you can’t even remember the most basic formulas?” The more he talked, the angrier he got. “I thought we were going to be okay on this test in two weeks, but now I’m getting pretty scared. I don’t know how else to do it, folks. I just don’t know.” He threw the whiteboard marker and eraser on the ground. “I am trying to help you, but I can only do so much.”

The smiles slowly faded from their faces.

“What frustrates me most is that we don’t know and we’re laughing about it. Stupidity,” he slammed the textbook closed on the podium, “is not funny. Stupidity is never a joke.” 

They were properly chastened now. They watched Mr. Ivan’s every movement with eyes wide and lips pressed tight.

“I’m mad because you’re better than this. You are better than this.” He sat on top of an empty desk a few feet away from the long table of girls and bowed his head. “You have to understand, what you do now will follow you. Some of you think school is boring and you come here staring off into space, happy to let everyone else answer for you. You may be content right now to just barely pass, but I’m sorry to tell you, when you get to the end of high school, that attitude isn’t going to earn you the diploma you’re hoping for. You’ll get a certificate saying your butt was in a chair. But then, when you go out to apply for a job, if it comes down to you and a person with a high school diploma, they’re going to take that person with the diploma over you every time. 

“I am trying to help you, folks. You’re free to hate school if you want, but when you come in here, I want to see effort.” He walked back to the board and pointed at the last equation. “Now, open your notes, find where you originally wrote this down, and tell me what it is.”

Fifteen notebooks opened. Each student flipped through scribbled pages, hoping that someone would find the formula so they’d all be saved from further lecture. Logan’s hand was the first to rise, but Mr. Ivan didn’t call on him. A few moments passed before others began rising as well.

“What is it, Logan?” Mr. Ivan finally said.

“The area of a circle.”

Mr. Ivan reached for the whiteboard marker and uncapped it. “Area of a circle. Exactly. When we see pi,” he underlined pi for emphasis, “we’re always talking about circles.”

The lesson continued, unfolding at an elementary pace as Mr. Ivan introduced a new formula--for finding distance, rate, and time--and spiraled back to older concepts. Outside the window, a gym class played kickball. The students in Mr. Ivan’s room chanced furtive looks in that direction whenever he turned back to the board. Most of them watched him teach, their notebooks left untouched, but a few little hands did push pencils across their papers"students who had no desire to one day lose a job to that candidate with the high school diploma.