Much Ado About a Box of Beans

We are going to bed early this week, eating good breakfasts, being careful not to watch too much TV. Brain-racking homework has been put on hold, lest it sap our intellectual energy.

For my kids--and millions of California students--this is the time for Stanford 9 and ERBs (the private school equivalent of the Stanford), the week when our well-fed, well-rested children will rack up the numbers that help determine not just their academic standing but how much money their schools will get and what their teachers will be paid.

Most of us remember the exams from our childhoods . . . those sharp No. 2 pencils; the daunting little circles to be colored in; the teacher’s voice marking the hours with “You may begin!” and then, light-years later, “Put your pencils down!” Today those tests have become the focus of our national obsession with educational accountability, the linchpin in a desperate campaign to lift our schools from mediocrity.

Principals are rewarded or demoted, teacher pay is calculated, children are held back or promoted according to what the test scores say.

The testing frenzy is not without controversy. There are whispers of coaching or outright cheating; concerns that real learning suffers when teachers try to “teach to the test.”

And I worry whether our preoccupation with percentiles obscures the reality: that so many factors influence learning, and not all students learn at the same pace, or display their knowledge in the same way.

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They are, the testing company’s brochure explains, “norm-referenced, standardized” exams, intended to measure not only what your child has learned but how he or she compares with millions of others nationwide.

Administered over several days, they test reading, spelling, grammar, math, science, social studies and problem-solving skills.

So, first-graders could be asked to look at a list of words and to mark the one spelled incorrectly, or to pick which should begin with a capital letter. In math, they might be shown a puzzle with a missing piece and asked to choose which of several shapes would fit.

By fourth grade, the vocabulary test includes words like “clambered,” which means either “leaped, fell, scrambled or peered.” In science, they might have to use a chart listing the density of dogwood, glue, resin and quartz, to figure which will float in water.

“It is important to understand,” the brochure claims, “that no one ‘passes’ or ‘fails’ [the] Stanford.”

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Then why do I feel like such a failure when I am stumped by this problem from a hypothetical third-grade exam:

There is a picture of a box, labeled “Mixed Beans,” with a multicolored collection of beans spilling from it. “If one more bean spills from the box,” the question asks, “what kind of bean will it most likely be?”

I count the beans already spilled. There are six dark ones, three gray ones, two white ones, and one with stripes.

My head starts to hurt. . . . I don’t know the answer.

Is there some formula for figuring out what bean would come next, some math equation, a form of statistical probability that they teach today’s kids in third grade?

I stare at the picture, counting the beans . . . I suppose it could be a striped bean next. Since only one of them has fallen out, there must be several more inside.

But then it could be a dark bean, since there are six of them already out. Maybe they’re heavier, so whenever you tip the box, they’re the first beans to tumble out.

And how do you know if the box ever contained the same number of beans of each color, anyway? Maybe all the beans left inside are gray!

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I give up, then try to imagine how each of my children would try to solve this tricky question.

The oldest--methodical, a slave to logic--would embark on some complicated formula, with striped beans equaling A, white beans equaling B and some probability resulting from X times Z.

The middle one--plodding but persistent--would never move beyond this problem and would spend the rest of the test session staring at those confounded beans.

And the little one--my lawyer-to-be--would consider every possible option, then refuse to answer, scribbling a note instead in the test booklet’s margin, pointing out the inconsistencies.

Three different children, three different processes, three different answers . . . each reflecting not just what they’ve learned, but who they are.

And who they are--though it may not be measured in their test scores--is ultimately what carries the day.

Sandy Banks’ column is published on Sundays and Tuesdays. Her e-mail address is sandy.banks@latimes.com.