Teacher: “Johnny, I’m sorry to tell you, but you received another low score on the last math exam.”
Johnny: “Sorry, Mrs. Arse. Which problems did I get wrong?”
T: “Well, you didn’t get any of them wrong, but that’s not the issue. I’ve told you countless times that you must show your work.”
J: “So I got a hundred percent?”
T: “No, you earned a sixty percent because you lost points for not showing your work!”
J: “Oh. Sorry.”
T: “Sorry? Is that all you have to say young man? Why can’t you be more like the other students?”
J: “Did any of them get all the problems correct?”
T: “Don’t be impertinent, young man! You’re completely missing my point. Look at Sammy here. He got an 88 because he carefully explained his thought process on each and every question.”
J: “But he only got half of the problems correct.”
T: “Yes, but he explained his thinking.”
J: “But isn’t it more important to get the problem correct, rather than have a convincing explanation for the wrong answer?”
T: “Johnny, you’re still very young and naive to the ways of the world. It’s far more important in life to sound convincing, rather than to silently stand there with the correct view. Nobody will believe you. In every field of life: politics, economics, psychology, religion, you name it, the important thing is to sound convincing. That’s the key to success in life. Nobody really knows the answers to most questions anyway, so being correct has nothing to do with it. It’s the persuasive communicator that people will believe.”
J: “So, getting the wrong answer but explaining it convincingly, is better than quietly getting the right answer?”
T: “Exactly! Besides, how do I know you didn’t just copy the answers from your classmate?”
J: “Well, I sat next to Badass Billy. I must confess that I did look at his paper. Some of his doodle pictures were really cool!”
T: (sigh) “Johnny, please try your best to understand. You can’t go through life being right about everything. People will hate you. It’s much better to be popular and convincing. Take the lead! Express yourself! Explain the logic of your position.”
J: “Even if it’s the wrong logic? I dunno. Maybe I should sign up for the debate team? Or take a course in illogic? Do they teach illogic here?”
T: “Of course we do! It’s one of our most popular courses. Students love it! Illogical thinking is very common these days.”
J: “Well, thanks for setting me on the right path, Mrs. Arse. I’ll try to do better. I’ll spend less time figuring out the truth of things, and focus instead on my speaking skills.”
T: “Trust me, Johnny. You’ll be a much better person for it. Besides, why not just take the time to explain your answers and show your work? You handed in your paper halfway through class, so don’t tell me you didn’t have time.”
J: “But, I don’t know where the answers come from.”
T: “What? Don’t joke with me, young man! You’re just being lazy because you don’t want to take the time to explain yourself. As I have stated time and again, you need to show your work. That’s why I penalized you.”
J: “But I really don’t know, teacher. The answers just come to me. I see them in my mind.”
T: “Johnny, math doesn’t work that way. You must memorize the correct formulas, and then enter the numbers into your calculator.”
J: “Sorry, but I didn’t use a calculator. And I don’t recall memorizing any formulas. I just sort of reason my way through the problem.”
T: “That’s ridiculous! Never in my life have I encountered such insolence! I’m insulted that you’d even dare to think that I’d believe such nonsense!”
J: I’m really sorry, teacher. I don’t mean to be rude. But, you see, I practice hours of math every day because I love it so much. After a while, things just come to me. It’s sort of an unconscious process, I guess.”
T: “Johnny, be serious! What exactly do you think math is, anway? Some kind of game?”
J: “Well, to me anyway, math is a game. Like golf or tennis, math is a skill. If you practice it enough, it becomes second nature. Most good athletes say that if you think too much about your playing, it’ll get worse. The conscious mind needs to step aside and let those unconscious years of practice come to the fore. That’s what skill is all about. Math is the same way. It isn’t about memorizing formulas or using calculators. It’s about practicing your reasoning skills over and over again on many different problems until it becomes second nature. That’s how math is to me, anyway.”
T: “But if you don’t make your reasons explicit, and clearly explain them to others, no one will believe you. Have you already forgotten our earlier conversation?”
J: “I understand what you’re saying, teacher, but for me, math solutions just pop into my mind. I see the problem in front of me and somehow I know what to do. After all that practice, I guess my unconscious mind has learned how to think logically all by itself.”
T: “Well, young man, you’ve just earned a note home to your parents. Hopefully they can talk some sense into you, because it obviously isn’t working for me.”
J: “Okay, but they’re away this week.”
T: “Away?”
J: “Yes. At a math conference. They’re college math professors.”