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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September 28, 2009

How Standardized Tests Punish Nonconformity

In a previous post, I linked to an article by a former standardized testing grader, Todd Farley. He has an op-ed piece in the New York Times today entitled “Reading Incomprehension,” which is also very eye-opening. He talks about the difficulty of scoring open-ended items on a standardized rubric and he gives a few examples of especially confounding student responses.

I disagree, however, with his opening claim that “the problem [with standardized testing] is not so much the tests themselves–it’s the people scoring them.” Open-ended questions are inherently subjective and therefore difficult to grade according to a rubric.  Even if the scoring was done “only by professionals who have made a commitment to education,” a lot of the results would still be influenced by personal bias.  For example, take the review of the X-rated “Debbie Does Dallas” which Mr. Farley encountered.  While he described it as well-written and hilarious, normally qualities that would merit a 6 (“genius”) grade, it ended up being given a 0 because it discussed a pornographic movie.  This student obviously possessed a sense of humor, the ability to think independently and question authority, and enough writing skill to craft a “comprehensive analysis” that was “artfully written.”  Yep, sounds like that kid needed to be put in his or her place with a big, fat zero.  Would a “professional who was committed to education” have made a different call?  It would depend entirely on the individual professional.  While one who appreciated the student’s wit and individualism might have given it a higher grade, one who was offended by children and teenagers exploring their sexuality might have given it the same zero.

In another example, Mr. Farley tries to decipher whether a drawing of a child wearing a helmet while riding a bike over a flaming oil spill properly demonstrated “an understanding of bike safety.”  Since the student had just read a passage about bike safety, and most children don’t encounter walls of fire while tooling around the neighborhood, I would say, “Yes, of course.  The kid in the picture is wearing a helmet.  He’s just trying to inject some humor into the lifeless, eternally dull process of taking a standardized test.”  Mr. Farley, however, was stumped as to how many points he should assign.  The experience showed him that “the score any student would earn mostly depended on which temporary employee viewed his response.”  I think that the student’s score would depend, not on the scorer’s background or “commitment to education,” but on the scorer’s “commitment” to enforcing conformity and punishing those who color outside the lines.  The scorers are hired to judge, not to educate.  Because of the way standardized tests are set up, we can’t just ask the student about their intentions with the drawing.  That would require a sense of humor and respect for a child’s thought process.  I’m sure the test designers thought that having the students draw a picture in response to a reading passage would be a creative learning exercise.  I hope that child wasn’t penalized too harshly for being creative in the wrong way.

Ultimately, Mr. Farley and his colleagues had trouble with some of these responses because the rubric doesn’t work if the student refuses to conform, not necessarily because they were only “temporary employees.”  The problem is still with the test and what it demands of students, not with the people who score it.

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July 27, 2009

Extreme Credentialism

Paul Graham’s essay on credentialism, which I linked to and wrote about last week, points to imperialist China as the birthplace of testing. He argues that testing/earning credentials displaced nepotism and bribery as a method of selecting government officials. While that was a beneficial change, the tests were indicators of wealth as much as of knowledge and skill–only the privileged would have the opportunity to study classical literature. In time, such tests gave rise to ‘cram schools,’ where those who could afford it were able to learn how to get a good score on the test, rather than taking the time to build the skills that were supposed to be measured by the test. (SAT prep, anyone?)

Modern-day Chinese students have recently stumbled upon a new permutation of ‘test hacking’: identity theft. According to an article that appeared in the New York Times yesterday, all Chinese students have a personal file that contains their grades, test results, peer and teacher evaluations, diplomas, etc. These files are physical and supposedly kept under lock and key by government agencies. Lately, however, the files of students from poor families have been ‘vanishing.’ These students suspect corrupt government agents of selling the records of their achievements to young people from wealthy families. The victims of this scam are sentenced to low-paying jobs, as they are virtually ineligible for government or private-sector employment without their files. All the time and money they invested in their education has been completely and utterly lost, for while they still have all the knowledge and skill they worked so hard to develop, potential employers only care about credentials. I especially appreciated Tony Z.’s comment (it’s #6) on the ramifications of this crime for Chinese society. He writes, “[Don’t] ask why these corrupt officials weren’t caught. Ask why on earth is a man’s life predicated on one file? Ask what happens to a society when it prizes the Gold medal over the discipline to achieve it legitimately?”

On the other hand, the Chinese economy seems to be thriving. Perhaps it’s an indication that all the specialized knowledge that universities claim only they can bestow, is not really necessary. Only time will tell.

It is only more evidence that the system of credentialism can be, and often is, skewed to favor the wealthy. This means that wherever an individual’s ability to earn income depends on the pieces of paper they possess (and whether those papers are name-brand), there exists a society where the rich get richer and the poor stay poor. It is a shame that the bright future these students traded their youth for has been denied to them, due to the greed of others. I am encouraged by Paul Graham’s assertion that the American marketplace is moving towards rewarding performance rather than credentials. I hope that these young students will live to benefit from a similar trend in China, although, as Tony Z. suggests, credentialism seems to be an ingrained part of Chinese culture. As he says, “If you’re Chinese, ask why you care more about a number on a piece of paper than the man in front of you.”

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