The boy across from Mia Boyle, Larry Corsets, stood from his chair, prim and proper. "A n is equal to F two n minus one, B n is equal to two F n F n minus one, and C n is equal to F n, squared, minus F n minus one, squared," the child said. He gave a great big smile and sat as the other students applauded.
"Well done Larry!" Mia said, clapping. "For homework everyone go home and take measurements of the perpendicular sides of right triangles you can find and see if you can figure out the last side using the details of the Fibonacci sequence we've discussed today. Tomorrow we're going to talk about some of the real-world applications of the Fibonacci sequence, including Euclid's algorithm. I'll see you all then!"
The students filed out, saying goodbye to Mrs. Boyle as they left, orderly and clean. Then she woke up to her alarm, dragging her out of her sweet sleep with a sound like nails on a chalkboard. She rolled and slapped it off.
Instead of the bright, clean room like had been in her dream, the clouds outside obscured the sun and made her bedroom a dark, sad place. She got up, showered, and began to get dressed. Her husband was only rubbing his eyes when she was eating breakfast.
The dream was a common one, though it didn't always work out the same way. Sometimes, the children had turned in all their homework on time. On bad enough days they were simply able to show up and say nothing as she went through her lesson. A dream similar to the one she'd had an hour ago, when she was able to teach the eighth graders complicated ideas like Fibonacci or hexadecimal numbers, occurred only after a day of trying to get them to understand something like simple algebra. Her husband put a cup of coffee in front of her as she ate toast.
"I know that look," he said, sitting across from her. Mia wanted to dunk her head into her coffee cup. "Chin up," he continued. "It's Friday. They'll be happier."
"They always want to do something fun," Mia said. "But there's no space in the curriculum. I have to tell them every week that it'll just be the same stuff. And then they get grouchy."
"Well..." her husband hesitated. "It's Halloween. Candy?"
"They'll be getting plenty of sweets. The last thing they need is me giving them more." Mia went to the sink and rinsed her plate. She stood there for a second. "You know Mr. Newton, the shop teacher, taught the kids to make automatic light switches they can use with remotes? I wish I could do that. Show them something really cool. I just don't think it can happen that way with math." She sighed. "I'd better get going. I told them I'd be there early in case anybody had problems with the homework."
"All right," her husband said. "Have a good day." She kissed him on the forehead and took her stuff to the car. The leaves dropped as she drove, cut from their stems by the chill late-October air. Halloween decorations littered yards. Buses rumbled to and fro with clouds of exhaust rising from their tailpipes. Mia could see inside some of them, and saw a very familiar look on the faces of some of the children: I'm going to school again.
"I had to go to school just to go back to school," Mia muttered to herself. "I went to college to teach you!" She nearly shouted it.
She reached the school and pulled herself to her windowless classroom. She knew she had a few minutes of silence to think and get ready for the day, but before she knew it there were small bodies in her room. They asked her about algebra, frightened or angry or tired. As she helped them she thought to herself children always seemed to be flying from one emotion to the other. They were never content, or at a baseline feeling. They had to be upset with something, or excited about something. They couldn't just be.
But she remember what eighth grade had been like for her. A flurry of hormones running into her toes and fingers and the tips of her ears. It was like a minefield with no path; eventually it will blow up in your face.
She was able to convince the students asking for help what it all meant. Algebra -- such a strange thing to worry over. How many of them would ever use it once they got out of college? Or once they even got to college?
The five-minute bell for first period rang, and all the students began to slink into their chairs. A packed class, she noticed. They all had the at-odds I'm tired but excited that it's Friday look on their faces. A few had drooping eyelids already.
The class bell rang and she stood up. She'd had an idea. "Morning everyone. Before today's lesson, I want to ask if anyone has questions about yesterday’s material." No one spoke up. "Come on now, don't be shy. I know some of you have questions." Still none of the students said anything.
She almost smiled. "Good. I'm very glad that all of you know exactly what you're doing with this. It can be complicated; I know. But I think you're ready to move on to...discrete mathematics.
"Discrete math is the study of sequences of numbers that are not continuous, almost like how a hilly area goes up, down, up, down...you understand. Now, discrete objects -- that is, a set of numbers in a sequence -- can often be enumerated by integers. You all know about integers after learning about algebra."
She went on, using terms like cryptography, automata theory, combinatorics, p-adic analysis, and names like Wolfgang Haken, Yuri Matiyasevich, and David Hilbert. At the conclusion of drawing a diagram, she dropped the chalk on the tray and clapped her hands together. "In a few weeks we'll start on infinitary logic."
Every boy and girl in the class was staring at her with a gaping mouth. Some looked like they were close to weeping. One child in the front row had started copying down her diagrams but stopped halfway through because his pencil lead broke.
She let out a half-laugh, half-sigh. "What's Halloween without a few scares?" She said as she started erasing the graph on the board. "Don't worry, we'll be sticking with algebra today. Let's see how your homework went."
The class ended well. The children, still somewhat shell-shocked, didn't have the energy to screw around, and for the most part sat quietly, listening to her. A few students who normally wouldn't have asked questions. They wandered out when the bell rang.
Mia felt rather good. The little jump she'd given the students had done even more for her; it had reminded her what is was like when she was in college, learning both complicated mathematics and how to light a fire under student's bottoms. She had her hands pressed down onto her desk as the next class came inside. She tried to collect herself as they sat and talked. It was a seventh-grade class trying not to fret too much about geometry. A thought came to her and she picked up the sheets from her first class.
"Morning, everyone. I had a few of you talk to me about the homework; that's to be expected. I know that sometimes math can seem like a different language. I'll give you an example." She took a look at a homework sheet from her first class. She wrote: x/2-5 = 0.
"Can anyone solve for x?" she asked. The class was silent. "Does anyone know what x equals?" Still nobody said anything. "This is algebra. You won't get to it until next year. My eighth-graders had this very same problem on their homework from last night. It might look complicated, but as soon as you learn what it means, it'll be simple. Let me tell you: nobody from my first class got this problem wrong," she lied. "Now, somebody give me a question from their homework. Anything you need me to explain."
A girl asked about parallelograms, and their angles. A boy didn't understand how to figure out the area of a triangle. A few started yelling about circles, circumferences, radii, pi, and on and on. Mia, energized, answered their questions the best she could, and then started moving on to the inside area of irregular triangles. Even the brightest students looked downtrodden. Mia slowed down and went over it again. She dolled out homework from the book and the bell rang. Mia liked to think the children left a little happier than they entered.
There were fifteen minutes until the next class. For a brief amount of time, Mia had some time to think. She had to keep going, and continue this streak of different thinking. For the last few weeks she'd felt like a black-haired Ms. Krabapple, but now she felt a interesting cool heat; energy in her hands. She was a bit dizzy. Third period was algebra again. Should she pull the same trick?
No, this was a school, eighth graders acted as washerwomen. They'd have already talked. Mrs. Boyle scared us this morning by giving us some really hard math! She was just kidding, though.
The eighth-graders getting ready to join her class thought they had a leg up on her. Well, she thought, I'll see about that.
They trudged in. At her desk, she could see a few furtive glances her way. Yes, they knew. She wasn't going to be able to trick this squad of sharp crayons.
"Morning everyone. Before we start with today's lesson, are there any questions from yesterday's homework?" None of their hands went up. She recognized a few faces from before class; it seems two hours had given them the time they needed to figure everything out. "Good. That's good.
"Well, today we're going to start on something a bit more complicated." She went to the chalkboard. Through the back of her head, she saw some of the students exchange knowing looks. With her face to the board she smiled.
"This is the quadratic formula," she said, after putting the chalk down. "It looks complicated, yes, but it's actually quite simple..."
And she explained it. The x, the constants, the quadratic equation's shape on a graph. She turned and saw some of the students smirking. They think they know what's coming, she thought.
"This is algebra. By the end of the year, you will have to know how to use this to figure out x for quadratic equations. Yes, it will be on your final."
With contained glee she watched their faces drop. From one step ahead of Mrs. Boyle to one step behind, they faltered. "No need to get started on it right away, of course," she said. "This won't be popping up again until late in the year." She wiped it away and drew one of the homework equations on the board. "Makes this little solve-for-x seem pretty easy, right?"
Color was entering back into the students' faces. "Who wants to take a stab at this? None of you had any questions on your homework," she added, "so you must all be able to do it."
A hand raised, quivering slightly. "I...I didn't understand all of it, Mrs. Boyle," the boy asked. "I don't understand how to equal the sides. Like the multiplying and stuff."
"Yes!" Mia said, looking at the equation. "The multiplying and stuff! Something that a lot of students will struggle with at first. What are we trying to do with this formula?" She asked.
"Get the x on its own," a student answered.
"Right! So if there's an x/2, that means we have one half of an x. We need a whole x. We have to multiply both sides by the same amount, to keep the equal sign true. So, if the other side, here, is one, and we multiply both sides by two, we find that x equals two."
Several students' eyes opened. "So you have to multiply both sides?" a girl asked. Mia nodded. "Because otherwise the equals sign would be lying!"
"It'd be a dirty liar," Mia said. She felt a rush. The class continued perfectly. Better than perfectly; perfectly meant no problems, and not only were there no problems, but there were encouragements, and laughter, and excitement. She felt almost one hundred percent certain every student in the room understood algebra better. They were replaced with another group of seventh graders, and Mia wondered briefly if she should try the same trick again. She felt like she was honing in on the perfect tactic.
Then, just as the bell rang, she wondered if she could do without it. She could feel herself thinking around the normal blocks of teaching. She had energy, and motion; she wasn't about to stop.
She attacked the class with her fervor, and their pre-lunch exhaustion melted in the face of her surprising volume. She had them off-balance and she liked it. She hadn't even used any tricks to get their attention; she got it on her own. They took some of her energy and turned it into progress.
The class ended and the students, through the class faster than normal, exited for lunch. Mia stepped out of her room during the thirty minute break and went across the hall to Katherine Olmstead's room.
"Katy!" she said, peeking her head in. "I've had the best morning!"
"That's surprising," Katy said over her bowl of soup. "What's gotten into your bonnet?"
Mia explained the morning, started with the dream, moving to the tired drive to school, and then the split-second decision to give her first-period students a jolt, and finally the following classes.
"I feel so good!" She said when she finished. "I barely even feel hungry!" Her stomach growled. "Well, a little."
"I can't believe you did that!" Katy said, laughing. "Even letting those kids know that discrete math exists almost warrants some kind of punishment!"
"Oh, I know, it was terrible of me. But it's Halloween! I was able to get through fourth period just on pure energy; I didn't need to do anything other than that. But it seemed to work so well with first period...the kids will be sleepy after lunch, just like in the morning...it'd be the perfect time to do it again." She looked up. "I'd love to do something like that in my last period. It's eighth-graders again. It's my worse class of the day and it's always the one that I go home thinking about."
"That's the class with Larry Corsets, right?"
Mia nodded. "That's it. Something to shut him up. I need something good. Something big."
"Word's spread by now," Katy said. "You won't be able to catch them off-guard with the same tricks."
"I figured that. What if I..." Mia stared into a corner of the room. This sort of creative thinking wasn't her forte. Her mind was changing into a blank even as she searched through it.
"What if you didn't do anything?" Katy asked. "What if you just relied on word-of-mouth to make them think something's up when there really isn't?"
"That's perfect!" Mia exclaimed. "I could make them think a few things, use a few tricks..." She smiled. Her stomach growled again, and she glanced at the clock. "I'd better go eat. Thanks again."
Katy was right. The children were on edge. Four periods had already passed and it was enough time for the whole school to hear about what she had been doing. Even the simple, yet energetic, fourth period had given pressure to the story that something was up with Mrs. Boyle today. Would she dump something terrible on them? Show them what the future held? Or simply overpower their senses?
At one point Mia began to draw an equation on the board. It was too complicated, the students noticed. They looked at each other as she had her back to them. Would this be next year? Next week? A decade away? They tensed.
Mia suddenly halted and stepped away from the board, looking at it quizzically. "Oh, sorry," she said, picking up the eraser. "That's for algebra. Silly me." She erased it.
For the students, this was worse. It was like in a monster movie when the hero opens a cracked door and an old hat rack falls on him. He'll get up, laugh it off, turn around, and-
But there was no monster. Mrs. Boyle never discussed anything horribly complicated -- or, at least, more complicated than things already were. She went through the homework, egging questions on with the same kind of energy powering her during the fourth period, talked through the day's lesson -- every child hung on her words, ready for the monster. When she explained what they would be going through the next week, several of them cringed, but it was nothing, just work to build on what they had already learned. She dolled out homework, the bell rang, and they left, feeling slightly dizzy and confused, wondering if they had all missed the monster. Sunday afternoon, when they would sit down and look at their homework, they would realize how much they remembered of her lesson.
Sixth period, now, Mia thought. I can do the same thing again and make them think something will come at them, but I really do need to do something for seventh period. Her tongue rummaged in her mouth, as if the answer might be found there.
She came to realize it was.
Sixth period didn't go exactly the same as fifth. She pulled the same trick on them, making them think something was up when there wasn't. With ten minutes left in the period she handed out homework. "I have to prepare something," she told the class. Several of the students' eyes widened. "Everyone get started on your homework; I'll be back in a few minutes."
As soon as she shut the door she heard the students talking. She went up to the second level of the school and peeked her head into Mr. Oshiro's art room. Inside, paintings and drawings and masks from his travels to Japan covered the walls.
"Can I have a minute, Jon?" She asked. "I'd like to cash in a favor."
"Favor?" Jon asked. His students stared glumly down at limestone hunks they were supposed to turn into animals. "Why do I owe you a favor?"
"I helped you get all those canvases into your room last spring. You told me you owed me."
"Ahh." Jon looked at his class. "It depends, I suppose. What was it you wanted?"
Mia explained. "Between classes. I have to talk to a few more people."
As the bell rang for seventh period, Mia's students saw Mr. Oshiro leave, wiping chalk dust from his hands, and Mrs. Boyle enter, stand by the light switch for a moment, then walk to the middle of the class. Six periods of talk echoed in their ears as they took their seats. The projector screen was pulled down over the blackboard. Mia watched them sit and squirm with a big smile.
"Afternoon everyone," she said. She spotted Larry Corsets in the front, chewing gum and watching her. "I'm sure you've heard of some of the things that have been going on in this room today. Don't worry, I won't do those things to you. It's just going to be a nice, normal, seventh period."
She went through a class so standard the students began to think they were safe. A small bit of her previous energy still slipped through, as well as her impatience for the end of the class. She drove toward the end of the day, looking forward to it even more than the students. She introduced the next lesson, handed out homework and, with about ten minutes left in the day, directed the students' attention to the projector screen.
"Very last thing," she said, switching it on. A runny red problem shined on the screen. "I've written a slightly more complicated algebra equation on the board. I think with all the practice we've gotten today, you should be able to solve it. If x is the number of monsters that will sneak in the classroom tonight and leave you all candy, and 3x - (3^2 - 3) = 0, how many monsters will sneak into my classroom tonight?"
The students leaned forward. It wasn't too hard. They should be able to figure it out. A few went to their notebooks, scribbling. You subtract, and then add, and then divide.
A student next to Larry Corsets raised her hand. "Is it one and a third, Mrs. Boyle?"
"No Jen, You have to resolve the square first," Mia said. Larry Corsets grinned, smacking his gum in the girl's direction. "Larry. We don't you give it a try?"
Larry leaned back in his chair. "Naw."
"Go on. You can do it."
Larry was moments away from protesting once more, but he saw a flash of something in his teacher's eyes. They gazed at him unwavering. He leaned forward, working his mouth to figure out the problem. He leaned back, and smiled. "I got it. It's two."
"Care to explain?"
"Well, three squared is nine. Nine minus three, since it's in the brackets you do it first, is six. Then you gotta add six to both sides like you told us, to keep it equal. Then you just divide each side by three." Larry tapped his finger in the air to punctuate each of the next words. "X equals two."
At the last word Mia yanked the projector screen down, revealing the art Mr. Oshiro had drawn, and pressed the button on Mr. Newman's remote-controlled light switch. At the same moment, Katy Olmstead burst into the door, wearing a huge, hairy, wrinkled demon's mask. Behind her, select members of the school's seventh-period band collided musically into one destructive, discordant note. It sounded as if steel spikes were being dragged down the chalkboard in the dark, windowless room. The board showed a monster with long, sharp fangs, drawn with chalk, seeming to reach out at them, with the projected equation in the place of the eyes. The runny red ink she'd used dribbled.
The snap of the screen and appearance of the monster, the sudden darkness, and the loud and startling appearance of Ms. Olmstead in her mask, together, made all of the students jump. Larry Corsets fell out of his chair, swallowing his gum. He pushed himself backward.
"Thank you, Larry," Mia said when the loud note had died away. "That's correct. X equals two. Happy Halloween, everyone."
At four-thirty Mia got home, beaming. At five-thirty her husband arrived and found her happily making dinner. "Looks like your day turned around," he said, and then he spotted bags on the table, which Mia had picked up after school. "What's all this?"
Mia laughed. "I owe the kids some candy."
"Well done Larry!" Mia said, clapping. "For homework everyone go home and take measurements of the perpendicular sides of right triangles you can find and see if you can figure out the last side using the details of the Fibonacci sequence we've discussed today. Tomorrow we're going to talk about some of the real-world applications of the Fibonacci sequence, including Euclid's algorithm. I'll see you all then!"
The students filed out, saying goodbye to Mrs. Boyle as they left, orderly and clean. Then she woke up to her alarm, dragging her out of her sweet sleep with a sound like nails on a chalkboard. She rolled and slapped it off.
Instead of the bright, clean room like had been in her dream, the clouds outside obscured the sun and made her bedroom a dark, sad place. She got up, showered, and began to get dressed. Her husband was only rubbing his eyes when she was eating breakfast.
The dream was a common one, though it didn't always work out the same way. Sometimes, the children had turned in all their homework on time. On bad enough days they were simply able to show up and say nothing as she went through her lesson. A dream similar to the one she'd had an hour ago, when she was able to teach the eighth graders complicated ideas like Fibonacci or hexadecimal numbers, occurred only after a day of trying to get them to understand something like simple algebra. Her husband put a cup of coffee in front of her as she ate toast.
"I know that look," he said, sitting across from her. Mia wanted to dunk her head into her coffee cup. "Chin up," he continued. "It's Friday. They'll be happier."
"They always want to do something fun," Mia said. "But there's no space in the curriculum. I have to tell them every week that it'll just be the same stuff. And then they get grouchy."
"Well..." her husband hesitated. "It's Halloween. Candy?"
"They'll be getting plenty of sweets. The last thing they need is me giving them more." Mia went to the sink and rinsed her plate. She stood there for a second. "You know Mr. Newton, the shop teacher, taught the kids to make automatic light switches they can use with remotes? I wish I could do that. Show them something really cool. I just don't think it can happen that way with math." She sighed. "I'd better get going. I told them I'd be there early in case anybody had problems with the homework."
"All right," her husband said. "Have a good day." She kissed him on the forehead and took her stuff to the car. The leaves dropped as she drove, cut from their stems by the chill late-October air. Halloween decorations littered yards. Buses rumbled to and fro with clouds of exhaust rising from their tailpipes. Mia could see inside some of them, and saw a very familiar look on the faces of some of the children: I'm going to school again.
"I had to go to school just to go back to school," Mia muttered to herself. "I went to college to teach you!" She nearly shouted it.
She reached the school and pulled herself to her windowless classroom. She knew she had a few minutes of silence to think and get ready for the day, but before she knew it there were small bodies in her room. They asked her about algebra, frightened or angry or tired. As she helped them she thought to herself children always seemed to be flying from one emotion to the other. They were never content, or at a baseline feeling. They had to be upset with something, or excited about something. They couldn't just be.
But she remember what eighth grade had been like for her. A flurry of hormones running into her toes and fingers and the tips of her ears. It was like a minefield with no path; eventually it will blow up in your face.
She was able to convince the students asking for help what it all meant. Algebra -- such a strange thing to worry over. How many of them would ever use it once they got out of college? Or once they even got to college?
The five-minute bell for first period rang, and all the students began to slink into their chairs. A packed class, she noticed. They all had the at-odds I'm tired but excited that it's Friday look on their faces. A few had drooping eyelids already.
The class bell rang and she stood up. She'd had an idea. "Morning everyone. Before today's lesson, I want to ask if anyone has questions about yesterday’s material." No one spoke up. "Come on now, don't be shy. I know some of you have questions." Still none of the students said anything.
She almost smiled. "Good. I'm very glad that all of you know exactly what you're doing with this. It can be complicated; I know. But I think you're ready to move on to...discrete mathematics.
"Discrete math is the study of sequences of numbers that are not continuous, almost like how a hilly area goes up, down, up, down...you understand. Now, discrete objects -- that is, a set of numbers in a sequence -- can often be enumerated by integers. You all know about integers after learning about algebra."
She went on, using terms like cryptography, automata theory, combinatorics, p-adic analysis, and names like Wolfgang Haken, Yuri Matiyasevich, and David Hilbert. At the conclusion of drawing a diagram, she dropped the chalk on the tray and clapped her hands together. "In a few weeks we'll start on infinitary logic."
Every boy and girl in the class was staring at her with a gaping mouth. Some looked like they were close to weeping. One child in the front row had started copying down her diagrams but stopped halfway through because his pencil lead broke.
She let out a half-laugh, half-sigh. "What's Halloween without a few scares?" She said as she started erasing the graph on the board. "Don't worry, we'll be sticking with algebra today. Let's see how your homework went."
The class ended well. The children, still somewhat shell-shocked, didn't have the energy to screw around, and for the most part sat quietly, listening to her. A few students who normally wouldn't have asked questions. They wandered out when the bell rang.
Mia felt rather good. The little jump she'd given the students had done even more for her; it had reminded her what is was like when she was in college, learning both complicated mathematics and how to light a fire under student's bottoms. She had her hands pressed down onto her desk as the next class came inside. She tried to collect herself as they sat and talked. It was a seventh-grade class trying not to fret too much about geometry. A thought came to her and she picked up the sheets from her first class.
"Morning, everyone. I had a few of you talk to me about the homework; that's to be expected. I know that sometimes math can seem like a different language. I'll give you an example." She took a look at a homework sheet from her first class. She wrote: x/2-5 = 0.
"Can anyone solve for x?" she asked. The class was silent. "Does anyone know what x equals?" Still nobody said anything. "This is algebra. You won't get to it until next year. My eighth-graders had this very same problem on their homework from last night. It might look complicated, but as soon as you learn what it means, it'll be simple. Let me tell you: nobody from my first class got this problem wrong," she lied. "Now, somebody give me a question from their homework. Anything you need me to explain."
A girl asked about parallelograms, and their angles. A boy didn't understand how to figure out the area of a triangle. A few started yelling about circles, circumferences, radii, pi, and on and on. Mia, energized, answered their questions the best she could, and then started moving on to the inside area of irregular triangles. Even the brightest students looked downtrodden. Mia slowed down and went over it again. She dolled out homework from the book and the bell rang. Mia liked to think the children left a little happier than they entered.
There were fifteen minutes until the next class. For a brief amount of time, Mia had some time to think. She had to keep going, and continue this streak of different thinking. For the last few weeks she'd felt like a black-haired Ms. Krabapple, but now she felt a interesting cool heat; energy in her hands. She was a bit dizzy. Third period was algebra again. Should she pull the same trick?
No, this was a school, eighth graders acted as washerwomen. They'd have already talked. Mrs. Boyle scared us this morning by giving us some really hard math! She was just kidding, though.
The eighth-graders getting ready to join her class thought they had a leg up on her. Well, she thought, I'll see about that.
They trudged in. At her desk, she could see a few furtive glances her way. Yes, they knew. She wasn't going to be able to trick this squad of sharp crayons.
"Morning everyone. Before we start with today's lesson, are there any questions from yesterday's homework?" None of their hands went up. She recognized a few faces from before class; it seems two hours had given them the time they needed to figure everything out. "Good. That's good.
"Well, today we're going to start on something a bit more complicated." She went to the chalkboard. Through the back of her head, she saw some of the students exchange knowing looks. With her face to the board she smiled.
"This is the quadratic formula," she said, after putting the chalk down. "It looks complicated, yes, but it's actually quite simple..."
And she explained it. The x, the constants, the quadratic equation's shape on a graph. She turned and saw some of the students smirking. They think they know what's coming, she thought.
"This is algebra. By the end of the year, you will have to know how to use this to figure out x for quadratic equations. Yes, it will be on your final."
With contained glee she watched their faces drop. From one step ahead of Mrs. Boyle to one step behind, they faltered. "No need to get started on it right away, of course," she said. "This won't be popping up again until late in the year." She wiped it away and drew one of the homework equations on the board. "Makes this little solve-for-x seem pretty easy, right?"
Color was entering back into the students' faces. "Who wants to take a stab at this? None of you had any questions on your homework," she added, "so you must all be able to do it."
A hand raised, quivering slightly. "I...I didn't understand all of it, Mrs. Boyle," the boy asked. "I don't understand how to equal the sides. Like the multiplying and stuff."
"Yes!" Mia said, looking at the equation. "The multiplying and stuff! Something that a lot of students will struggle with at first. What are we trying to do with this formula?" She asked.
"Get the x on its own," a student answered.
"Right! So if there's an x/2, that means we have one half of an x. We need a whole x. We have to multiply both sides by the same amount, to keep the equal sign true. So, if the other side, here, is one, and we multiply both sides by two, we find that x equals two."
Several students' eyes opened. "So you have to multiply both sides?" a girl asked. Mia nodded. "Because otherwise the equals sign would be lying!"
"It'd be a dirty liar," Mia said. She felt a rush. The class continued perfectly. Better than perfectly; perfectly meant no problems, and not only were there no problems, but there were encouragements, and laughter, and excitement. She felt almost one hundred percent certain every student in the room understood algebra better. They were replaced with another group of seventh graders, and Mia wondered briefly if she should try the same trick again. She felt like she was honing in on the perfect tactic.
Then, just as the bell rang, she wondered if she could do without it. She could feel herself thinking around the normal blocks of teaching. She had energy, and motion; she wasn't about to stop.
She attacked the class with her fervor, and their pre-lunch exhaustion melted in the face of her surprising volume. She had them off-balance and she liked it. She hadn't even used any tricks to get their attention; she got it on her own. They took some of her energy and turned it into progress.
The class ended and the students, through the class faster than normal, exited for lunch. Mia stepped out of her room during the thirty minute break and went across the hall to Katherine Olmstead's room.
"Katy!" she said, peeking her head in. "I've had the best morning!"
"That's surprising," Katy said over her bowl of soup. "What's gotten into your bonnet?"
Mia explained the morning, started with the dream, moving to the tired drive to school, and then the split-second decision to give her first-period students a jolt, and finally the following classes.
"I feel so good!" She said when she finished. "I barely even feel hungry!" Her stomach growled. "Well, a little."
"I can't believe you did that!" Katy said, laughing. "Even letting those kids know that discrete math exists almost warrants some kind of punishment!"
"Oh, I know, it was terrible of me. But it's Halloween! I was able to get through fourth period just on pure energy; I didn't need to do anything other than that. But it seemed to work so well with first period...the kids will be sleepy after lunch, just like in the morning...it'd be the perfect time to do it again." She looked up. "I'd love to do something like that in my last period. It's eighth-graders again. It's my worse class of the day and it's always the one that I go home thinking about."
"That's the class with Larry Corsets, right?"
Mia nodded. "That's it. Something to shut him up. I need something good. Something big."
"Word's spread by now," Katy said. "You won't be able to catch them off-guard with the same tricks."
"I figured that. What if I..." Mia stared into a corner of the room. This sort of creative thinking wasn't her forte. Her mind was changing into a blank even as she searched through it.
"What if you didn't do anything?" Katy asked. "What if you just relied on word-of-mouth to make them think something's up when there really isn't?"
"That's perfect!" Mia exclaimed. "I could make them think a few things, use a few tricks..." She smiled. Her stomach growled again, and she glanced at the clock. "I'd better go eat. Thanks again."
Katy was right. The children were on edge. Four periods had already passed and it was enough time for the whole school to hear about what she had been doing. Even the simple, yet energetic, fourth period had given pressure to the story that something was up with Mrs. Boyle today. Would she dump something terrible on them? Show them what the future held? Or simply overpower their senses?
At one point Mia began to draw an equation on the board. It was too complicated, the students noticed. They looked at each other as she had her back to them. Would this be next year? Next week? A decade away? They tensed.
Mia suddenly halted and stepped away from the board, looking at it quizzically. "Oh, sorry," she said, picking up the eraser. "That's for algebra. Silly me." She erased it.
For the students, this was worse. It was like in a monster movie when the hero opens a cracked door and an old hat rack falls on him. He'll get up, laugh it off, turn around, and-
But there was no monster. Mrs. Boyle never discussed anything horribly complicated -- or, at least, more complicated than things already were. She went through the homework, egging questions on with the same kind of energy powering her during the fourth period, talked through the day's lesson -- every child hung on her words, ready for the monster. When she explained what they would be going through the next week, several of them cringed, but it was nothing, just work to build on what they had already learned. She dolled out homework, the bell rang, and they left, feeling slightly dizzy and confused, wondering if they had all missed the monster. Sunday afternoon, when they would sit down and look at their homework, they would realize how much they remembered of her lesson.
Sixth period, now, Mia thought. I can do the same thing again and make them think something will come at them, but I really do need to do something for seventh period. Her tongue rummaged in her mouth, as if the answer might be found there.
She came to realize it was.
Sixth period didn't go exactly the same as fifth. She pulled the same trick on them, making them think something was up when there wasn't. With ten minutes left in the period she handed out homework. "I have to prepare something," she told the class. Several of the students' eyes widened. "Everyone get started on your homework; I'll be back in a few minutes."
As soon as she shut the door she heard the students talking. She went up to the second level of the school and peeked her head into Mr. Oshiro's art room. Inside, paintings and drawings and masks from his travels to Japan covered the walls.
"Can I have a minute, Jon?" She asked. "I'd like to cash in a favor."
"Favor?" Jon asked. His students stared glumly down at limestone hunks they were supposed to turn into animals. "Why do I owe you a favor?"
"I helped you get all those canvases into your room last spring. You told me you owed me."
"Ahh." Jon looked at his class. "It depends, I suppose. What was it you wanted?"
Mia explained. "Between classes. I have to talk to a few more people."
As the bell rang for seventh period, Mia's students saw Mr. Oshiro leave, wiping chalk dust from his hands, and Mrs. Boyle enter, stand by the light switch for a moment, then walk to the middle of the class. Six periods of talk echoed in their ears as they took their seats. The projector screen was pulled down over the blackboard. Mia watched them sit and squirm with a big smile.
"Afternoon everyone," she said. She spotted Larry Corsets in the front, chewing gum and watching her. "I'm sure you've heard of some of the things that have been going on in this room today. Don't worry, I won't do those things to you. It's just going to be a nice, normal, seventh period."
She went through a class so standard the students began to think they were safe. A small bit of her previous energy still slipped through, as well as her impatience for the end of the class. She drove toward the end of the day, looking forward to it even more than the students. She introduced the next lesson, handed out homework and, with about ten minutes left in the day, directed the students' attention to the projector screen.
"Very last thing," she said, switching it on. A runny red problem shined on the screen. "I've written a slightly more complicated algebra equation on the board. I think with all the practice we've gotten today, you should be able to solve it. If x is the number of monsters that will sneak in the classroom tonight and leave you all candy, and 3x - (3^2 - 3) = 0, how many monsters will sneak into my classroom tonight?"
The students leaned forward. It wasn't too hard. They should be able to figure it out. A few went to their notebooks, scribbling. You subtract, and then add, and then divide.
A student next to Larry Corsets raised her hand. "Is it one and a third, Mrs. Boyle?"
"No Jen, You have to resolve the square first," Mia said. Larry Corsets grinned, smacking his gum in the girl's direction. "Larry. We don't you give it a try?"
Larry leaned back in his chair. "Naw."
"Go on. You can do it."
Larry was moments away from protesting once more, but he saw a flash of something in his teacher's eyes. They gazed at him unwavering. He leaned forward, working his mouth to figure out the problem. He leaned back, and smiled. "I got it. It's two."
"Care to explain?"
"Well, three squared is nine. Nine minus three, since it's in the brackets you do it first, is six. Then you gotta add six to both sides like you told us, to keep it equal. Then you just divide each side by three." Larry tapped his finger in the air to punctuate each of the next words. "X equals two."
At the last word Mia yanked the projector screen down, revealing the art Mr. Oshiro had drawn, and pressed the button on Mr. Newman's remote-controlled light switch. At the same moment, Katy Olmstead burst into the door, wearing a huge, hairy, wrinkled demon's mask. Behind her, select members of the school's seventh-period band collided musically into one destructive, discordant note. It sounded as if steel spikes were being dragged down the chalkboard in the dark, windowless room. The board showed a monster with long, sharp fangs, drawn with chalk, seeming to reach out at them, with the projected equation in the place of the eyes. The runny red ink she'd used dribbled.
The snap of the screen and appearance of the monster, the sudden darkness, and the loud and startling appearance of Ms. Olmstead in her mask, together, made all of the students jump. Larry Corsets fell out of his chair, swallowing his gum. He pushed himself backward.
"Thank you, Larry," Mia said when the loud note had died away. "That's correct. X equals two. Happy Halloween, everyone."
At four-thirty Mia got home, beaming. At five-thirty her husband arrived and found her happily making dinner. "Looks like your day turned around," he said, and then he spotted bags on the table, which Mia had picked up after school. "What's all this?"
Mia laughed. "I owe the kids some candy."