One of my strengths as a test prep instructor was spotting weird mental glitches that was interfering with a student’s success. I miss this part of the job, but every so often I get the chance in classroom teaching. In this case, summer school trigonometry. I taught first semester in block 1, second semester in block 2, but I taught the same material in both classes.
I had about eighteen kids in the two classes, but eight of them took both classes, meaning they’d failed both semesters. All eight students repeating both semesters were stronger than the three weakest students repeating the second semester, and the weakest student just repeating first semester. Remember what I said about GPAs? Shining example, right here.
So this is a conversation I had with Warren on the next-to-the last day of class. Before you decide I’m a rotten bully, understand that I had raised this issue several times with Warren, but the message had, like everything else, rolled right off his back like whatever water does with a duck.
He was taking the final test, and had asked me to check it over before he turned it in. (This is a normal part of my class routine).
“OK, you’ve got quite a few cases where I’m asking for onions and you’re giving me a Jeep.”
“No, you don’t. Like question 5. You’re using the Pythagorean theorem on a question asking you to understand and evaluate a trigonometric model.”
“No, you don’t.”
“I get it.”
“No, you don’t.”
“Yes. I see now.”
“NO YOU DON’T!” The class was now snorfling quietly, not out of mockery of Warren, but amusement at me. I was playing my aggravation very big.
“YOU DON’T UNDERSTAND HOW TO DO THIS PROBLEM.”
” Then why are you done with the test? This one is not just mildly wrong. It’s Jupiter and we’re Earth.”
“STOP SAYING THAT.”
“I understand what you’re saying.”
“No, you don’t.”
“No, it’s not OK!”
“OK..I mean, I know…Oh, sh**.” Warren is no longer a duck, but a deer, frozen.
“Listen to me.”
“No, see, already you’re not listening. Don’t try to make me happy. Don’t try to give me what I want. You’re trying to figure it how to make me happy and that one task is consuming all your brain cycles. JUST LISTEN.”
“I know…no. OK. I get it.”
Half the class was howling by this point, and I shushed them.
“This problem is incorrect. Not mildly incorrect. Way off. DON’T SAY A WORD. Continue to listen. Cover your mouth if you must. Say nothing until I ask you a direct question.”
Warren stood. Affect way off, smiling nervously.
“You came up here, telling me you were done, asked me to just look through for minor errors. But as I look through the test, I see that you have no idea how to do at least three of the eight problems. SAY NOTHING!” Warren closed his mouth. “In two cases, you came up here earlier and asked me for help. I gave you guidance, you said ‘I know’, I told you no, you didn’t, tried again, got nowhere. And now you’re up here saying you’re done. We have an hour left of class. You are MANIFESTLY not done. When I point out an error, you say ‘I know’ but you clearly don’t mean it because you are up here saying that you are finished! No–I haven’t asked a question. Stay put.”
Warren stood. But I could see the panic fade a bit. He was starting to actually listen.
“This is a trig modeling question. It’s about temperature in a room. Max and min temp. 24 hours in a day. Yet you are using the Pythagorean theorem. Why, Warren, are you using the Pythagorean theorem? That is a question. You can answer.”
But Warren stood mute. I waited. The class snickered and I ferociously signaled them to stop.
“I….I don’t know what you want me to say.”
“EXACTLY! That’s it. Exactly. Perfect. Now, continue to listen. The reason you are confused, Warren, is because you are uninterested in math at this particular second, and entirely interested in making me happy because you think it will help your grade. But I want you to learn. And that involves asking questions. It involves thinking. It involves furrowing your brow and asking for clarification. Normally, you ask your friends for help, or copy what they’ve done and think you understand the math. Sometimes you do. Mostly, you don’t.You just know how to go through the motions.”
“But I asked for help.”
“No, you didn’t. You asked me to ‘look through’ the test. Earlier, you asked for help and ignored my response. You aren’t asking for feedback. You are going through a self-imposed ritual in the hopes that I will be impressed with your effort. Then after each conversation, you return to your work to try another random approach to a problem you don’t understand, as completely clueless as you were before you came up. You only know the math that triggers a routine in your brain. And when I try to fix that, you nod or say ‘I know’ but you have absolutely no conception of the possibility that I might be able to help you! In your learning world, friends are for help. Teachers exist to be placated and grade your work so you can get an A.”
Warren’s eyes widened. Apparently, he thought we teachers weren’t onto his scheme.
“But Warren, talking to me–talking to any teacher–is a conversation. A process. It is your job to communicate your confusion. It’s my job to try and give you clarity and undertanding. Our conversations are not mere rituals mandated by the Chinese American education canon. So let me ask the question a different way: When you were modeling trigonometric equations all this week, what pieces of information were relevant?”
Warren answered readily, “Amplitude. Period.”
“If I gave you the maximum and minimum points, how would you find amplitude and period?”
“I would sketch them and look for the middle.”
“Which is also the…..”
“OK. Now. Look at this problem. Do you see how this problem fits into that format? It describes the temperature in a corporate office. So what I want you to do now is go back and think about this problem. Think about how you could describe temperature in terms of max and min. Think about relating it to the time of day, hours past midnight. And then see if you can figure out how to work the problem.”
Warren obediently took the test and started to return to his seat, but stopped. “OK, but here’s what I don’t get. You’re asking us to solve an equation. But modeling is just building the equation. How come you’re asking us to solve the equation?”
I looked at the class. “Whoa. Did you hear what I heard?”
“A QUESTION!!!” and we all clapped loudly and genuinely for Warren, who smiled nervously again.
“Warren, I mentioned this over the past couple days: Trig equations don’t just occur in a vacuum. We build the equations to model the world. Then we look to the model to predict outcomes, which we do by solving for outputs given inputs, or vice versa. The problem covers both. It asks you to evaluate and explain the given model, then it asks you to use the model as a trigonometric equation. In this case, I actually used function notation because I want to see if you understand it, but at other points, I’m using verbal descriptions.”
“Um. No. I don’t know how to start.”
I waited. The class waited.
“Could..could you give me a suggestion on how to start?”
“Is there something you could do to the given equation that might give you some insight?”
“I could…graph it, maybe?”
“There’s a thought. Then look at it, look at the multiple answers, and see how it goes.”
As Warren walked back to his desk, I mimed collapsing in fatigue. “And now, everyone, entertainment’s over. Get back to work.”
Warren worked on the test for another hour. He forgot and said “I know” and “OK” reflexively a few times, but stopped himself before I could, to both of our smiles. He came up each time with a specific question. He listened to my response. He went back and worked on the problem based on my response and his new understanding.
On the last day of class, after the final bell rang, Warren came up to chat with me.
“Thanks for yelling at me.”
“You know, I was working towards a good cause.”
“You were right. I was coming up to ask you questions because that’s what other kids did, so I figured that’s what you wanted. I never really thought about getting help from you. I just kind of…work through something using whatever I remember, until I’m done.”
“Don’t be a zombie.”
“Okay–wait. What’s a zombie?”
“Don’t just work problems without any sense of what’s going on. That’s why you flunked Trig the first time, I’ll bet.”
“Yeah. I didn’t always understand Algebra 2, but I could follow the procedures. But Trig, I just couldn’t do that.”
“Yeah. Zombie thinking. Don’t do that. I mean–zombie thinking is what you’re doing in math. You get the answers from friends, you don’t care about understanding the math. You just go through the motions. The driving me crazy saying ‘I know’ stuff, that’s different. Plenty of zombies do a better job of asking for help!”
“I understand math a lot more the way you teach it, but I also….I couldn’t always figure out your tests.”
“That’s why you ask for help. And not from your friends. Look–school is about more than getting an A. It’s about more than giving teachers what they want so you’ll get an A. It’s about learning how to learn. You have to start communicating with teachers–good, bad, indifferent–and learn how to figure out what they’re telling you. That starts with asking for what you need. If you can’t communicate with a teacher right away, don’t just ask a friend. Half the time, they’re just doing what you do! Find teachers you can work with. You’re a really bright guy. Don’t let school ruin you.”
And then we talked about his college plans where–no joke–he asked me for advice.
Ten minutes later, as he walked out, he said: “Thanks again. I mean it.”
He knew a lot of math, and worked his way out of being a zombie. I gave him an A-.