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X = Karin (Johnny) > 95%

What does it take to learn algebra? First you have to master the fundamentals.

February 04, 2006|Karin Klein | KARIN KLEIN is an editorial writer for The Times.

JOHNNY PATRELLO was a greaser. I was a dork. And yet, despite our rigidly stratified school culture, we came together in the spring of 1968 at Walt Whitman Junior High School, where I tutored Johnny in algebra.

I thought about Johnny again as I read The Times' series this week on L.A.'s dropout problem. Algebra, the reporters found, is an insurmountable stumbling block for many high school students.

What struck me was that the reasons why Johnny can't do algebra in L.A. today are remarkably similar to why Johnny Patrello couldn't do algebra almost four decades ago in Yonkers, N.Y.

Johnny and I were brought together by Mrs. Elizabeth Bukanz, the algebra teacher. Mrs. Bukanz wore her sandy hair in a frizzy French twist and her glasses on a chain. But she was gentle and smiling, and she had passion -- at least for what she called "the beauty of algebra." I, too, loved its perfect logic and tidy solutions, so unlike my messy teenage life.

But Johnny was deaf to algebra's siren song. He was flunking, and Mrs. Bukanz hoped that if I used my study halls to tutor him, he might score at least 65% on the New York State Regents exam. Passing the exam allowed even failing students to move on to high school, which started in 10th grade; otherwise, Johnny would be left behind.

Johnny wore his leather jacket in class despite the spring warmth, and he habitually tilted his face toward the floor so that when he looked up at me, he seemed embarrassed. Yet for such a cool guy, he was surprisingly friendly and committed to giving this a try.

Things looked pretty hopeless to both of us those first couple of sessions, as Johnny stumbled through algebra problems while I tried to figure out exactly what he didn't understand. Then, as we took it down to each step of each little calculation, the trouble became clear: Johnny somehow had reached ninth grade without learning the multiplication tables.

Because he was shaky on those, his long multiplication was error prone and his long division a mess. As Johnny tried to work algebraic equations, his arithmetic kept bringing up weird results. He'd figure he was on the wrong track and make up an answer.

This discovery should have made us feel worse. How could we possibly make up for a dearth of third-grade skills and cover algebra too?

But at least we knew where to start.

We spent about half of those early sessions on multiplication drills. Seven times eight, eight times seven -- Johnny could never remember. As an adult, in memory of Johnny's struggles, I would rehearse my kids at an early age in that one math fact. Get that 56 down, I would tell them, and the rest of multiplication is a snap.

Today's failing high school students, though plagued by more poverty and upheaval than Johnny or I ever knew, bring the same scanty skills to algebra class, according to The Times' series. They never quite grasped multiplication tables, but still they moved on to more complicated math.

Who can focus on the step-by-step logic of peeling back an equation until "x" is bared when it involves arithmetic that comes slow and slippery, always giving a different answer to the same calculation?

Yet in all these decades, the same school structure that failed Johnny goes on, dragging kids through the grades even if they don't master the material from the year before. This especially makes no sense for math, which is almost entirely sequential.

Leaving children back isn't a solution; it simply makes them feel stupid. They learn, like Johnny, to look at the floor. The floor can't embarrass them.

What I learned from Johnny -- aside from the fact that greasers could be sweet-natured and very, very smart -- is that schools are structured to help administrators feel organized, not to help children learn.

Young children's skills are all over the map, yet we corral them into second grade, third grade and so forth, where everyone moves at one pace in all subjects. Better to group them according to their skills in each subject, without the "grade" labels, and let them move on to the next skill when they have mastered the one they were on. If they're not getting it, give them extra tutoring, but don't push them forward until they're ready. This way, there is no failure -- only progress.

It requires a sea change in thinking, but it's not impossible or even all that hard. Back before standardized tests put classes in lockstep, some progressive schools already were using team teaching to do this in math as well as reading and writing.

Johnny finally nailed seven times eight, then with amazing quickness worked his way through basic "x" problems up to multiple variables and beyond. Still, I couldn't quite catch him up to a year's worth of work in a couple of months. And on a sweltering June day, with humidity that neared 100%, the regents exam came, faster than we felt ready for it.

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