Lessons for Today

Today in math class, they would be learning how to factor quadratic equations. Miss Gracie, called Mrs. G by her students, knew this because she had the lesson planned out meticulously across three-and-a-half sheets of college-ruled notebook paper, which sat neatly in a folder before her. She knew because, like with all her lessons, she had recited it in front of her dressing mirror last night, right before bed.

She glanced at the clock. Ten minutes left until class. Its tick, tick, tick was the only sound in the room.

She looked around the room. Nothing but the equation charts that she covered with long sheets of colored paper during tests (always to the dismay of the students) and Tu fui, ego eris. Latin. What you are, I was; what I am, you will be. She stared at it. She had written it out on a sheet of white cardstock and stuck it to the wall with blue tape on her first day. It seemed like a kind and encouraging quote, a reflection on how ideally, the student would someday become the master. Only yesterday did she learn that it was actually a phrase that had been written on tombstones.

Her students seemed not to notice the phrase. Nor did the administrator, who walked in one day without warning to see “how well you were teaching the material.” The administrator had eyes the color of sour apples, and a mouth that was puckered like she’d eaten a sour apple, and had told her that she couldn’t teach proofs because they a) weren’t in the curriculum and b) wouldn’t be on the state exams and were thus irrelevant, all in the disgruntled voice of someone who’d expected a sweet apple but gotten a sour one.

Irrelevant! Miss Gracie breathed in sharply. The word seemed to be everywhere. When she handed out her weekly quizzes, which no one was allowed to use calculators on, the students always complained. Miss, how is this relevant to our real lives? We can just use a calculator in real life. That’s what one student said. She said there wouldn’t always be calculators. But there’s one on my phone, he said.

The administrator would probably tell her to go ahead and let them use calculators, because they could on the state exams. The parents who phoned her every time progress reports went out probably would say the same. Never mind that the quizzes were composed of arithmetic questions like 25 x 80 and not higher algebra.

What were they studying today? Quadratic equations, and no one would be allowed to use calculators. They were very simple quadratic equations, really, that required logic and a basic sense of how numbers fit into each other, like (x + 2)(x -3) = x² – x – 6. Everything in math can be boiled down into how numbers fit into each other, she’d told the class one day. That’s why I have you take these quizzes, to build up your number sense. They’d sat and stared at her without seeing her. In the back row, one student played with her phone under her desk.

Her quizzes had a reputation in the school. Before the administrator walked in and told her proofs were irrelevant, she had also sometimes included proofs on the quizzes. Nothing complicated, just questions like Prove that if n is an integer such that n² is even, then n is even too. She’d even walked them through a very similar question the other day. It was all algebra. Why weren’t proofs relevant? But her quizzes were infamous, and on the day the administrator told her proofs were irrelevant, one student had cheered.

Tick, tick, tick. Five minutes until class began.

At this moment, she could have been studying for her doctorate in mathematics, probably bent double over a desk and sometimes straightening to sip a cup of hot tea, like she liked to in college. (She liked to think that she would have attended Columbia.) But she had chosen to take Mathematics in Higher Education instead of Applications of Higher Mathematics and go right to teaching before pursuing higher degrees because she had wanted to “make a difference.” Maybe she should have taken Teaching Elementary Mathematics instead. Maybe that would have made a difference.

It probably wouldn’t, her mind added.

She closed her eyes. Time seemed to crawl; she breathed in, a slow gasp, feeling her lungs expand. She’d never noticed how tight her ribs were before. Above her the clock tick, tick, ticked like dripping water, slower and slower. Tick, tick, drip. The dry air sandpapered her throat on the way down. She breathed out, exhaling too small an amount of air.

What were the teaching plans for today? She tried to remember without looking at her notes. Something about factorials… no, factoring. Factoring of quadratic equations. Factorials were years later, in calculus. So were proofs. Tick, drip. Yes, that was it. She needed to get herself together before her students arrived. They would come in here, and while she thought, they would hide their homework under their desks and copy off of each other. All while she tried to remember what her lesson plans were. What kind of teacher was she?

What would the administrator say when her class’s state exam scores came back in? Abysmal. She would look at her with those beady sour apple eyes. The parents would phone her, asking why she’d let their children fail.

Miss Gracie tried to think about quadratic equations, and (x + 2)(x -3) = x² – x – 6. But all she could imagine were tombstones, little white tombstones in the shape of rectangles and narrow trapezoids and triangles in overgrown grass, tombstones all inscribed with “Tu fui, ego eris.” Dozens and dozens of tombstones, as far as the eye could see.