The Substitute

1 The substitute in Room 114 was the smallest adult I had ever seen at the front of a classroom. She wore a gray cardigan buttoned to the top, and when she wrote MRS. ALBRECHT on the whiteboard in small, careful letters, half the class never looked up. Jace Kowalski leaned across the aisle and declared the class a free period, and nobody bothered to argue. Our regular math teacher had left us a worksheet on equations, and in the corner of the board was a bonus problem that nobody had solved all week.

2 She read the directions twice in a voice as thin as tissue paper, then settled into her chair and folded her hands. For twenty minutes, the room hummed with conversation and the crackle of snack wrappers. Then Jace pointed at the corner of the board and called out, "Hey, want to try the bonus problem? Our teacher said even he needed an hour." A few people snickered, since everyone knew he was only trying to fluster her.

3 The substitute stood up, read the problem once and picked up a marker. It asked how many handshakes there would be if all twenty-eight students in the room shook hands with one another exactly once. "Each of you would shake twenty-seven hands," she said quietly, writing as she spoke, "but that counts every handshake twice, once for each person." She multiplied, divided by two and underlined the answer, 378, in less time than it had taken Jace to ask. Then, almost apologetically, she explained that she had spent thirty-one years calculating the paths of weather satellites, and that puzzles like this one had been her lunch-break entertainment. "Next time, try drawing four people and counting their handshakes first," she added. "The pattern does the rest."

4 Nobody snickered this time. Jace lowered his hand slowly, as if it had suddenly become heavy. Then Maddie Sorensen raised her hand, which nobody ever does for a substitute, and asked what a satellite's path looked like on paper. After that, the questions arrived one after another: how satellites stay up, whether she had ever watched a launch, why they don't simply fall. She answered every one patiently and never once raised her voice, because she never needed to.

5 When the bell rang, my worksheet was still blank, but my notebook was full of circles and arrows that I actually understood. On the way out, Jace stopped at her desk and said, "Thanks, Mrs. Albrecht," and for once he didn't say it like a joke. I looked back at the small woman in the gray cardigan and wondered how many other people I had written off before they ever said a word.