Trying to solve the math problem; is it instruction?

By Michele Herman

Here’s a math problem: a New York City couple gives birth to a child, and X years later, they have a second child. As the years go by, they are pleased with the spread. But then the first child turns 13, and they discover a fatal flaw in their family planning. Solve for X.

The answer: the kids are three years apart, and the flaw is that this fall, the family has to submit applications for middle school (assuming they’re sending the kids to public schools) for the 10-year-old and high school for the 13-year-old. This means that in the next two months, they will have to pull their kids out of school at least 10 times (if they’re lazy) and up to 30 (if they’re hyper-diligent like some Manhattan parents) to go on school tours, and strategically rank a minimum of 17 schools in order of preference (five for the middle-schooler and 12 — count ’em — for the high-schooler). If the 13-year-old is a serious student, they will also face the decision of whether to sign up for the three-hour October test that provides the sole criterion for admittance to one of the eight highly reputed specialized “science” schools, including Stuyvesant, Bronx Science and Brooklyn Tech. If they decide to try for one of those schools, some serious test preparation is all but necessary, because, as many families in Manhattan’s District 2 will tell you, the district is notorious for its “fuzzy” math curriculum.

As you may have guessed, we are such a family. I don’t usually spend much time thinking about math, but right now, looking ahead to a grueling fall full of scheduling conflicts and decision-making, math is very much on the table. Oh, math has always been an issue in District 2, where the war between old math and new rages on into its second half-century. Around here you can walk into a group of parents and start a fight by uttering the word “algorithm.” This is code for “old math,” which to some people means meaningless boring rote learning with no understanding of the concepts behind it, while to others it means giving students the benefits of math’s accumulated historical wisdom rather than forcing them to reinvent the discipline for themselves — a possibly rewarding but prohibitively slow process.

I’ve taken on some educational issues over the years, but math has never been my cause. As much as I enjoyed my own math education — at least up until calculus — my mind doesn’t naturally travel along a path of numbers. When I recall algebra, geometry and trig, I inevitably veer from the actual math to the textures and personalities surrounding it. I see the yellow cover of our SMSG textbook (which everyone knew was short for either “Some Math, Some Garbage” or “Some Mad Scientist Goofed”). I try to call to mind those wonderful side-angle-side theorems for proving the relative area of triangles but, alas, as much as I adored those puzzles at the time, I gravitate to the double-knit pantsuits our geometry teacher wore, and the then-pressing question of the effeminate algebra teacher’s sexuality. I can still say “multiplicative inverse of the co-efficient of the variable” really fast, but I would need some review before I could define it.

As with my own education, I confess that I’ve paid less attention to my sons’ math instruction than to their humanities. Only rarely do I review their math homework. This is in part because reviewing their writing gives me a much fuller window onto their character and progress, and it’s in part because, as a writer, I feel in a better position to evaluate the quality of their English instruction than that of their math. I’ve also managed never to attend a single math night, and you’d be surprised how often math night comes around. My rationale is that I’ve already been to enough meet-the-teacher nights that have devolved into heated debates over math education. In fact, maybe all those math nights imply a certain defensiveness on the part of the education establishment; I’ve yet to be invited to a social studies night, or science night to explain the educational theory behind the teaching.

You’d think any sensible school system and curriculum would balance the two: spend some time letting the kids discover their own ways of understanding numbers and solving problems, and some time teaching them to use quick, time-tested, foolproof equations and formulas toward the same end — any worker needs incentive and a sense of relevance and mastery, but without good tools these other goals are hard to meet.

But I have another reason for being lax about math: I married into a family full of mathematicians. My husband’s father, brother and uncle have all had distinguished careers as math professors, at Princeton, the University of Virginia and Berkeley, respectively. I brought some decent math and problem-solving genes from my own paternal line to the marriage (with a father who claimed he chose his friends according to the number of dimensions they could think in), and so I figured the math would take care of itself.

For the most part, it has. Both my kids have always been comfortable with numbers and problem solving. When I do check their math, I’m always pleased by the quantity of word problems and by their teachers’ efforts to personalize and enliven the problems by using actual situations and names. On the other hand, I’ve always worried that an essential second step was lacking: providing formulas to help them evaluate and solve these problems efficiently. I remember a problem a teacher once gave my older son, one of those X-minus-1 jobs that would take hours to solve with arithmetic but minutes with algebra. My son was hungry, even desperate, for a formula to help him. I apologized because I didn’t remember enough to show him how to convert the words into a more manageable equation. I told him algebra was surely on the way, and that he would love it as I had, for the way it pared big complicated problems down to simple elegant ones. I crossed my fingers and hoped that algebra was indeed on the way, much as I prayed for an English teacher to give him some instruction in grammar to deepen his understanding of the workings of language (and I’m pleased to report that in seventh grade, this finally happened).

Now we have the specialized high school test looming. It’s full of algebra and geometry and, sure enough, it turns out that my son is not as well prepared as he should be. We’re lucky. My retired father-in-law, the Princeton math and economics professor (the Kuhn of the Kuhn-Tucker theorem), graciously agreed to tutor him, saving us from the other, less desirable options: not taking the test, winging the test, working his own way through the prep materials, paying a tutor or tutoring company more than $1,000 to drill him, or being invited to take the free but terribly long and time-consuming course offered by the Department of Education.

As I feared, my father-in-law says my son has not been prepared well for high-school math. “I asked him to write down as many formulas as he’s learned: diameter of circles, area of triangles, etc.,” he says. “He’s got to know those cold. I find they haven’t really been emphasized. Not that they haven’t been treated, but not treated enough that they’re at the tips of his fingers. Algebra as a technique has been very weakly treated. The formal handling of symbols using algebraic rules has not been covered.”

The two of them meet on Saturdays while our other son is busy fencing. Slowly and methodically they’re working their way through the practice tests. Grandpa gives him weekly homework, which they review at their next session. They understand each other well, and when they finish their session, they play cribbage and have a good laugh over some of the dumber sample questions from previous tests, like the one that begins: “Mrs. Smith has precisely four children.”

Like many of our friends whose kids are planning to take the test, we’re not even sure that one of the specialized high schools would be a good fit, at least not until the frenzy of touring begins in late September. But, like any parent, we want our children’s education to open up worlds of possibility.