Confessions of a Reluctant Teacher

March 12, 2010

Math Anxiety

I had a funny realization this weekend at my second job as an SAT preparation tutor.

I realized that the students I was tutoring knew just as much about math as I did, if not more. I was on the “slow track” for math in school: I did make it to pre-calculus in my senior year, but I have completely blocked it out (are there diagrams involved in calculus? I seem to vaguely remember graphing things). I also never took a math class while I was in college. I had only gotten about as far as they had: junior-year algebra. And yet when they faced a difficult math problem in the homework or on a practice test, they brought it to me and I could usually figure it out without finding the answer in the back of the book.

I couldn’t understand why, if they weren’t able to do these problems, I was. It wasn’t because I had done the problem before–I’ve only taught this course a few times, and there are so many practice problems, I hadn’t even begun to work my way through them all. It wasn’t because I am instinctively good at the SAT style of testing math, the way I am with the SAT style of testing reading and writing. In fact, my own SAT math score was so low, it almost disqualified me from being hired by this tutoring company. When I do figure out how to solve the problems, I can never quite believe I did it. It always surprises me. I wondered what could possibly account for the ability gap between me and my students?

How Math is Tested on the SAT

In order to understand the disparity, you have to understand a few things about how the SAT tests math. If you’ve taken the SAT, you may remember that the easiest questions come first, with each subsequent question getting harder, until you reach the end of the section, where the highest difficulty questions are. Surprisingly, the highest difficulty questions are solved using the same basic math skills that are used to solve the easy questions: no need to know trigonometry, calculus, or game theory to answer these questions. The only thing that makes them “harder” is that there are more steps–more chances to trip up, to make an error, to get confused.

Another surprise is that there are often little tricks and ‘hacks’ built into each problem. I tell my students that if they’re looking at a problem and thinking, “Oh man, this is gonna take forever to solve,” they are probably missing something. See, the SAT rewards those who think flexibly about numbers. If the test designers really wanted to evaluate math skills, they wouldn’t let students bring calculators. Especially when you get into more difficult questions, SAT math is all about strategy and how you think about math. If you can figure out what they’re asking for, and mentally create a mathematical map to find it, you can solve the problem. How you approach the problem is the key.

What Are You Trying to Prove?

I have the luxury of approaching the problems with an open, curious mind. I even look forward to the challenge of solving an unfamiliar high-difficulty problem. I know that if I can’t figure out, I’ll just look it up in the back of the book and walk the student through the book’s explanation. All that my students are able to think about is the effect their SAT score will have on their college admissions, or how disappointed their parents will be if they get a low score. They believe that if they can’t figure it out, the implicit judgement will follow them around for the rest of their careers.

It became very clear to me that other people’s expectations of us affect our performance, for better or for worse. When I look at a difficult test question, I generally think, “Oh no…this one looks really tough. Maybe I should just flip to the explanation in the back now.” But then I take a deep breath and remember: I am the teacher. I am supposed to be smart enough and capable enough to figure this out; that’s why this company decided to hire me. So even if I feel confused or intimidated, that vote of confidence gives me the motivation to put pencil to paper and muddle through. It gives me the courage to try, and keep on trying until I get the right answer (or at least several wrong ones).

My students, on the other hand, are approaching the problem from a very different perspective. First of all, while I know that I am there to help, my students know that they are there to be helped. This may encourage them to view themselves as, well, helpless. Secondly, the process of being tested puts students in the uncomfortable spot of having to prove their own intelligence. When they get to the high-difficulty questions, the test is whispering to them, “Here’s where we separate the smart kids from the dumb ones. So go ahead, see if you can solve it. Which pile will you end up in?”

Brain Freeze

In his book How Children Fail, John Holt talks about the tension we experience when we are trying to finish something without making any mistakes. He realizes that some of his students are making mistakes on purpose to break the tension.

“Worrying about mistakes is as bad as–no, worse–than worrying about mistakes they have made. Thus, when you tell a child that he has done a problem wrong, you often hear a sigh of relief. He says, “I knew it would be wrong.” He would rather be wrong, and know it, than not know whether he was wrong or not…When the paper was turned in, the tension was ended. Their fate was in the lap of the gods. They might still worry about flunking the [test], but it was a fatalistic kind of worry, it didn’t contain the agonizing element of choice, there was nothing more they could do about it. Worrying about whether you did the right thing, while painful enough, is less painful than worrying about the right thing to do.”

I think this same relief of tension manifests in SAT takers when they leave an answer blank. Whenever the student brings their question to me, the rest of the problems may be marked up, with their work written out, but the difficult problem is always spotless. I admit I haven’t been doing this very long, but I have never seen a student get stuck in the middle of one of these math problems. When I have faced really difficult problems in my student years, it always felt like some kind of mental paralysis: I’d try frantically to figure out what to do, but all I could think was, “I don’t know. I just don’t know!”  I couldn’t figure out where I was going, how to get there, or even how to begin.

Solving a difficult SAT math question hinges on approaching it properly: you have to look at what the problem says, what it asks for. You have to think about how to use the information given to get from point A to point B. You have to clear your mind and let the numbers and figures speak to you. If you can’t get to that open, curious, relaxed-yet-alert state of mind, you won’t be able to figure out how to approach the problem, and you’ll be sunk. You’ll hand me your paper, saying helplessly, “I didn’t know where to start.”

Thawing Out

I think the only thing that really helped me out of my math anxiety was knowing that I’m no longer judged by my math skills or lack thereof. I’ve relaxed enough to be able to treat them as intriguing challenges, fun ways to stretch my mind. I hate that I can’t give my students the same permission not to worry about it so much. Also, since I haven’t prepared the problem ahead of time, I can’t really “lead” the student through it. I kind of turn the problem over and over in my head, and then once I’ve got it, I hand it to the student and say, “There.” I don’t think that’s really the eye-opening learning experience they need.

Have you suffered from math anxiety? Have you ever helped any one through it? What are your strategies for helping students move from fear to curiosity to delight?

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August 5, 2009

Never ask students a question you already know the answer to

Filed under: Behind the Desk — christinag503 @ 11:15 pm
Tags: , , ,

Unless you want to make them feel like children, bore them to tears, create desperation and confusion in the classroom, and cause them to resent you. Let me illustrate.

I remember when our dean of students at my small, private prep school “guest taught” my 10th-grade English class. We were studying Phillis Wheatley, a young slave who became the first published African American poet. He asked us some question about the man who decided to publish Wheatley’s work. I think it was, “What was the most significant thing about him?” or some other incredibly open-ended question. So we started tossing ideas out there….he worked for a newspaper. “No.” He was from Virginia. “No!” I can’t remember now all of our answers, but I do know this charade went on for about ten full minutes, with us growing increasingly confused and desperate as he got angrier and angrier. He started giving us “hints.” “It has to do with what he looked like.” We were pretty confused. How were we supposed to know what he looked like? They didn’t have cameras then. Did he have a beard? “NO!” Than he said, “It begins with a W.” Somebody guessed that he was a writer, and he hotly reminded us that it had to do with the man’s physical appearance, not his work. I think by this point we were all sick of guessing out loud and then being screamed at, so we just sat and stared at him. After a little while, he realized we weren’t going to talk anymore, and he bellowed, “HE! WAS! WHITE!” I don’t know whether he got carried away and lost his temper, or if he thought he was being a good teacher by demonstrating enthusiasm for his subject, but all it impressed upon me was that this man had just wasted twenty percent of our allotted class time to yell at us about something that wasn’t really even that important. (Of course, all these years later, I still remember what the dean said. I don’t remember the man’s name, what the dean’s point ultimately was, or even what question had been asked, but I remember that Phillis Wheatley’s publisher was white.)

I really, really loathe the “fishing for answers” that some teachers indulge in. Sometimes known as the “asking leading questions” technique, I have become convinced that it is nothing but an exercise in wasting time and condescension, frustrating both teacher and student. In most curricula, however, it’s the major teaching strategy. “Asking leading questions” is supposed to engage the students, and encourage them to think about the material presented. I suppose it is preferable to only lectures, all the time. But as a teacher and a student, I feel strongly that ‘leading questions’ do not engage the mind in a critical thinking capacity. There are two different ways leading questions can be used, according to the material being presented, and they are not helpful in either case.

For questions that deal with facts and problem solving (like asking what the next step is in a math problem): If the student has been paying attention to the material, he’ll grasp the concept without leading questions. Asking such questions will waste time and make the student angry at teachers who seem to think he’s dumb. If the student hasn’t been paying attention to the material, they won’t be able to answer the leading questions. Asking them will waste time and make the student feel ashamed and humiliated, which is really unnecessary in a low-stakes game like School.

For questions that are of a more subjective nature (like asking what effect a certain battle had on a war, or something about the symbolism in a novel): asking leading questions is like implanting your thoughts (which are not really even yours, but belong to the group who designed the curriculum) into the student’s head. She is not allowed to grapple with the primary text and draw her own conclusions. Therefore, she is deprived of the chance to think for herself and instead learns to unquestioningly accept how authority figures instruct her to interpret data. We can see the repercussions of this effect when Americans blindly believe the rantings of political pundits, or they succumb to a high-pressure sales pitch and sign up for a mortgage they can’t afford.

Leading questions presume there’s only one way to get to the right answer. “Think how I think,” you’re saying. “Otherwise it’s wrong!” A few times I was embarrassed at the board when doing math sections with my SAT prep class. I’d ask the students, “What next?” or “What approach should we use here?” and one of the students who was rather stronger in math than I was would give me an answer other than the “right” one I was expecting. I’d say, “No, I don’t think that would work.” And she’d patiently walk me through it to show me that there was, in fact, more than one way to solve this problem. Pretty humbling. When we dictate how students should think about a problem, we encourage standardization of thought, which in turn produces a homogeneous, manageable population with the exact same inevitable blind spots.

In addition, it is condescending to ask someone a question you already know the answer to. You’re not asking the question for your own edification, or because you’re interested in the student’s unique perspective. You’re asking in order to test her. You’re asking her to prove her intelligence to you, over and over. It implies a lack of trust in her capabilities. And when a teacher implies that a student’s intelligence is not reliable, that student loses trust in herself as well.

Leading questions do not foster real learning. They merely turn an eager student into Clever Hans–you know, the horse that could supposedly do math, but who had actually learned to respond to visual cues provided by his trainer and the audience. John Holt made the case in his excellent book, How Children Fail, that most students, instead of learning the subject matter, learn how to please the teacher. While this can be a useful skill, I don’t think a generation of sycophants will serve society well in the future. Raising children to be responsible citizens and independent adults requires that we allow their thinking processes to develop in their own time. If we constantly “lead” our students, they can only learn how be followers.

July 31, 2009

Celebrity Chefs: the End of Civilization as We Know It?

Initially, I was sucked in by the photo of what Julia Child’s famous cooking show, “The French Chef,” was like behind the scenes.  I love how there are five professional-looking adults sitting on the floor around her, hiding behind the counter.  I always thought Julia looked a little distracted from time to time, like something was going on off-camera, but she wasn’t supposed to say what.  Now I know!

“I really should be writing something new for ‘Confessions’,” I thought.  But the aformentioned photograph, plus my mounting excitement over the upcoming “Julie & Julia” movie, seduced me into “taking a quick peek” at Michael Pollan’s article about the rise of the cooking show.

It turns out that in Mr. Pollan’s hands, a story about Julia Child and the rising popularity of cooking shows becomes a cautionary tale about an industrialized culture of passive consumers who spend more time watching celebrity chefs on TV than actually cooking for themselves.  As he observes,

“It’s no accident that Julia Child appeared on public television — or educational television, as it used to be called. On a commercial network, a program that actually inspired viewers to get off the couch and spend an hour cooking a meal would be a commercial disaster, for it would mean they were turning off the television to do something else.”

John Taylor Gatto predicted this in his 1991 essay, “The Six-Lesson Schoolteacher.”  I’m thinking of the fourth lesson this New York State Teacher of the Year taught his students: dependency.  By being the voice of authority that decided where children must direct their attention and what tasks they should be performing at all times, he robbed them of a chance to learn self-directed thought and action.  He taught them “that [good people] must wait for other people, better trained than ourselves, to make the meaning of our lives. It is no exaggeration to say that our entire economy depends upon this lesson being learned.”  He goes on to explain, “The food services, restaurants and prepared-food warehouses would shrink if people returned to making their own meals rather than depending on strangers to cook for them…We’ve built a way of life that depends on people doing what they are told because they don’t know any other way.”

Michael Pollan has the research and the proof that corporations have a vested interest in cultivating the helplessness of American consumers:

“Those corporations have been trying to persuade Americans to let them do the cooking since long before large numbers of women entered the work force. After World War II, the food industry labored mightily to sell American women on all the processed-food wonders it had invented to feed the troops: canned meals, freeze-dried foods, dehydrated potatoes, powdered orange juice and coffee, instant everything. As Laura Shapiro recounts in “Something From the Oven: Reinventing Dinner in 1950s America,” the food industry strived to “persuade millions of Americans to develop a lasting taste for meals that were a lot like field rations.” The same process of peacetime conversion that industrialized our farming, giving us synthetic fertilizers made from munitions and new pesticides developed from nerve gas, also industrialized our eating…It took years of clever, dedicated marketing to break down this resistance and persuade Americans that opening a can or cooking from a mix really was cooking.”

Around this era was when compulsory schooling really started to mold the next generation of Americans into consumers rather than citizens.  Eventually, schools stopped requiring students to take Home Economics.  Have you noticed that schools no longer teach any skills to prepare children to live independently?  I’m sure we’ve all heard stories about college freshman hauling weeks’ worth of dirty clothing on visits home because they have no clue how to do their own laundry.  Or the young adult in making his first home-cooked meal for his sweetheart (normally they’d just get take-out but he promised her something special for Valentine’s Day), and having his mother on the phone to walk him through the steps of preparing food.  Not only do these kids not learn basic life skills in school, but homework and extracurricular activities (that they need so desperately to succeed in life—or at least to get in to a good college) keep them too busy to learn these things from their parents.  And Schools are clamoring for still more hours of our children’s lives!

And since I’ve already quoted abundantly from the article, here’s one more passage for the road:

“The Food Network (blogger’s note: AND SCHOOL!) has helped to transform cooking from something you do into something you watch — into yet another confection of spectacle and celebrity that keeps us pinned to the couch. The formula is as circular and self-reinforcing as a TV dinner: a simulacrum of home cooking that is sold on TV and designed to be eaten in front of the TV. True, in the case of the Swanson rendition, at least you get something that will fill you up; by comparison, the Food Network leaves you hungry, a condition its advertisers must love. But in neither case is there much risk that you will get off the couch and actually cook a meal. Both kinds of TV dinner plant us exactly where television always wants us: in front of the set, watching.”

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