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To Learn or Not to Learn: A Derivative Lesson TaleA story of turmoil, chaos, and derivatives.NOTE: This story is not meant to offend people who love sports, drama, school, the SCA or twins. WARNING: Stereotyping is at its best! As the bell rang, students rushed out of Ms. Rowling's AP Calculus AB class. However, Ms. Rowling was expecting a group of students to stay afterschool, since they had just missed class to go to an SCA General Assembly meeting. The 6 students had missed a very important lesson: introduction to derivatives. First to arrive at 2:01 p.m. sharp was Emma Watson, a girl intent on learning anything she misses and focused on grades. Emma took a seat and immediately took out her notebook, paper, calculator and textbook. Soon her desk looked as if she was ready for math war. Next to come at 2:07 p.m. were the Taylor twins, Melody and Veronica. The twins didn't enjoy being twins- they absolutely loved it. They did everything together, except when it came to the fine arts. Melody's true enjoyment was in chorus while Veronica was inclined to art. At 2:09 p.m. came Rupert Grint, the devoted drama student, apparently rehearsing lines to himself while finding a seat. The drama department was currently in the process of doing a parody of Hamlet, and Rupert had the lead. Next came Lisa Attson. Seemingly normal as they come, she sacrificed a Key Club meeting to attend her make-up lesson in calculus. She always held that school came first before any other extracurricular activity. Then as the afterschool bell was ringing at 2:15 p.m., Dean Jordan walked in and went straight to Ms. Rowling, asking her how long the lesson would be as he had soccer practice in 20 minutes. "Okay! Since we're all here, today we start derivatives," announced Ms. Rowling with a smile. Almost immediately, without any hesitation or pause, everyone started speaking out of turn. "What is a derivative? What is it like?" asked Rupert in his fake Shakespearean accent. "Well that's what I'm going to expl--" "Is it hard?" the twins chimed in before Ms. Rowling could finish. "Well, I-- " "Of course it isn't hard! Math is really easy, and--" Emma's english accented voice retorted but was cut off by Dean. "How long will this take?" Dean asked. "Well, it should only last--" "What is a derivative?" Rupert repeated. Soon the entire room of only 7 people was louder than a class of 30 as everyone began talking at once. Suddenly, Lisa does a whistle to catch everyone's attention. "Why not let Ms. Rowling talk, okay? The sooner we learn, the sooner we understand and can ask questions, then the sooner you all can leave, okay?!?" Lisa reasoned. Silence. "Thank you, Lisa," Ms. Rowling thanked with a sigh of relief. She began to continue," Now as I was saying... today we are learning about derivatives. Normally I would go into great detail about what it is and where the derivative comes from mathematically using graphs, but since we're on a time crunch, I'll just tell you all a definition that everyone knows. Lets see.. a derivative is the slope of the curve, and --" "Whoa!!" the twins interrupted. "A curve has a slope?!?" "Yes, it does. Now everyone copy this down, and I'll explain after you finish writing. The limit of a function as h approaches 0 is..." "Whoa!!" the twins interrupted again. "What is h?" asked Ron as he continued his accent. "Well, I'm going to explain it in a second, just as soon as everyone copies this down for now." Everyone continues to write as Ms. Rowling recites the formal definition of a derivative, intent on explaining it to her students. However, the order doesn't last for long. "How much longer is the lesson?" Dean asked, looking at the clock. "Yeah, we have cheerleading practice...." the twins added. "Rehearsal," Ron nodded in. Ms. Rowling looked at the clock herself. Fifteen minutes had already passed. She had to think quickly. "You know, since everyone's so pinched for time, how about I show you the short cut instead? You're not supposed to learn it until next class, but just for today, as long as you don't tell anyone-- I just want you all to do your homework at least-- a derivative is simply taking the function, looking at the power of x, multiplying by the coefficient and reducing the power by 1. For example, if I had 3x², the derivative would be 6x because the power of x is 2, and 2 times coefficient 3 is 6. Then the power of x, which is 2, is reduced by one so instead of x to the second power it is now x to the first power. Does that make any sense?" "Perfect sense!" Emma beamed in a convincing tone. The twins, Rupert, and Dean gave uneasy smiles and nodded their heads; they just wanted to go. "Oh, all right then.. if that's okay, then you all can go--" Before Ms. Rowling could finish, Dean, Rupert, Veronica and Melody all rushed out of the room. Ms. Rowling felt uncertain about the pop quiz she had planned for the next block. Lisa and Emma were still in the room. "Brilliant lesson!" Emma exclaimed. "I asked someone in your Calculus BC class to tell me about it, then I looked at my mom's old college textbooks and learned it myself. Really, I wish that the BC class wasn't already full, because it sounds so interesting and I think learning at a fast pace is absolutely fabulous! I don't really understand how anyone could fall behind in that class... Oh, I already did the homework for the night, so would you like me to hold it or show it to you next class?" "Uh, could you wait until next class? It'll be less confusing for me, if you don't mind.." answered Ms. Rowling, caught off guard by Emma's speedy explanation. "Oh, alright. I'll be going then, thanks!" Emma zoomed out of the room in a flash, leaving both Lisa and Ms. Rowling in shocked expressions at Emma's fast-paced personality. "So, Lisa... how are you doing on the lesson? Don't you want to leave like everyone else?" Ms. Rowling asked. "Actually, I have lots of time... if you don't mind, I was wondering if you could explain this definition of a derivative that you've had us copy down..." Lisa began. Ms. Rowling smiled at Lisa's enthusiasm to learn. "Of course." |
