Sunday, October 31, 2010

The Children of Lake Wobegon vs the Bell Curve

Normal Distribution
Lots of phenomena in nature and human experience, when charted, creates a classic bell curve*, human height, for one. There are a few giants running around, some little people, but most of us are clumped together toward the center of a chart which plots the numbers of people on the x axis and their heights on the y axis.

Intelligence is supposedly distributed normally, but there is a ton of controversy about that. And there is also the body of research that suggests that intelligence is plastic, that we can get smarter--or more stupid. (Of course, grade school, jump-roping girls have always known that "Boys go to Jupiter/To get more stupider.")

NCLB, State Standards, and Critical Thinking
Every U.S. state tests its students on standards that each state invented. Some states have EASY standards, a few, like California, have TOUGH ones. Take a glance at this comparative study done by the Fordham Foundation of all the states--it's revealing:

Here are how California's content standards were rated:

Because each state is measuring different items, we can't accurately compare states' student performance. California may appear to be scoring lower than, say, Massachusetts, but since California's standards are so much tougher, are the students really less educated? If the students swapped tests, would the MA kids ace the CA test? Would the CA students suddenly become more proficient?

Educators are always crying about how bad it is to "teach to the test." I argue that if you have a test worth teaching to, quit crying; for math and science, "teaching to the test" is probably a good thing. But I do have grave doubts about English and history--unless you believe that history is just names and dates (and not decision making about abstract, fuzzy, controversial concepts such as power) or that reading is mere decoding (ignoring tone, irony, inferences, word choice, and creativity). How can a multiple choice test measure such nuanced and HUMAN subjects?

To further complicate matters, here are three of the goals of No Child Left Behind (the Federal Register, 3/6/02):
1) All students will reach high standards, at a minimum attaining proficiency or better in reading and mathematics by 2013-2014
2) By 2013-2014, all students will be proficient in reading by the end of the third grade.
3) All limited English proficient students will become proficient in English. [Wow, even the newly arrived speakers?]

See why this gets tricky? If the bell curve reflects truths about human performance, then goals that "all will be proficient" are nearly impossible: "Any test that meets ordinary standards produces an approximation of...a bell curve--because achievement in any open-ended skill such as reading comprehension or mathematics really is more or less normally distributed," according to Charles Murray (WSJ, 7/25/06). "All the children cannot be above average. They cannot all even be proficient, if 'proficient' is defined legitimately." In other words, it is a self contradiction to say, as goal #1 above does, that all will reach "high standards."

Now reading is a skill, and skills are arguably teachable, but everyone knows that people master skills at different rates. If a teacher waits for 100% mastery of any skill before moving on to the next....hmmm. In order to not bore those who are ready to move on, each student will need a personally tailored educational path to help her move on only when she is ready; I can't imagine there is any way a teacher of 36 algebra students could do this on his own without computerized instruction. Very well, there are such reading and math computer programs that might be able to do this. We are trying a math program at our school this year. It'll be interesting to see what happens on the math portion of the CST. Good luck, though, trying computerized instruction with the critical thinking components of problem solving, and more good luck plus TInkerbell dust if you try to subtract the human element from teaching the elements of English and history that demand critical thinking.

K. Is Moving
All of this because I am feeling guilty about my reaction upon hearing that K.'s last day is on Monday. She is transferring to another school--and she is perhaps our lowest performing student who is not in a special day class. That's right, kids, she is on the far left end of that bell curve. No matter how I teach my guts out, K. seems to lose information and knowledge gains almost instantly. It is awful. We spend extra time with her, provide services, develop relationships--but K. persists in her gnat-like attention span, and her interest in boys and fashion do not make for academic motivators except as they are a reason to stay in school.

She is being left behind, despite all our efforts. Our good little school gets punished because the K.s of the world prevent us from meeting goal number 1 of NCLB as stated above. I wish K. the best, but the reality for public schools is we have to take ALL the kids on our softball team, not just the all stars. And dang it, K. is an "easy out."

We don't have a problem acknowledging that we are differently endowed athletically, that some of us are faster than other, for instance. But NCLB doesn't acknowledge that perhaps the same might be true intellectually; I love the social reasons for demanding the same standard for all, but practically, there are some issues.

* bell curve
A symmetrical bell-shaped curve that represents the distribution of values, frequencies, or probabilities of a set of data. It slopes downward from a point in the middle corresponding to the mean value, or the maximum probability. Data that reflect the aggregate outcome of large numbers of unrelated events tend to result in bell curve distributions. (from thefreedictionary .com)

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