The statistical problems with sample size

Imagine for a moment that some agency, in an attempt to establish the average Body Mass Index for Americans, used players in the NFL as the original “sample”. After carefully establishing the range and the mean for BMI in the entire league, would it be reasonable to look at the rest of the American population and declare that the human species was shrinking

The absurdity of the proposal is staggering.

However, just such a scenario has been played out for years with the Scholastic Achievement Test when newspapers decry our nation’s “plummeting” SAT scores.

The validity of this standardized test for anything other than determining the socio-economic status of those sitting for the exam might be the topic of a future article. Cost is listed as one of the major impediments to sitting for the exam.

Today, however, alarmist headlines are inexcusable when, for decades, the SAT was normed against and administered to America’s academic elite, the upper quartile of high school students.

We are moving, albeit at a glacially slow pace, toward a society that discourages the concept of disposable children. As we come closer to furnishing all children the opportunity to compete against their peers, we are inexorably increasing the sample size.

Statisticians will confirm that the “average” score will invariably fall as the sample size increases. Except in the case of a totally randomized sample, it is foolish to expect otherwise. The SAT has yet to be normed on a random sample across the spectrum of all American students.

Yet, such realities do not hinder ideologues from using such erroneous data analysis as political fodder to question the effectiveness of our public schools.

Diane Ravitch clearly illustrates in Reign of Error how student achievement and academic performance have been steadily improving for decades according to a host of of alternative measures. More students know more about more subjects, and at earlier ages, than ever before in our history.

Moving forward will require that irrelevant soundbites and erroneous headlines not drive the debate around educational egalitarianism.

 

[This Commentary appeared originally in the now defunct Prince George’s Gazette on 10/23/2014.] 

Letters from the front

Dear Parents,

On the grandest of scales, everything I ever needed to know about Public Education, I learned watching a situation comedy that frequently explored the angst of our human condition.

“M*A*S*H” introduced me to the concept of triage in a Mobile Army Surgical Hospital. Derived from the French verb trier (to sort), triage is a medical protocol designed to cope with the prospect of too few doctors caring for too many casualties on the battlefield. Different from what we currently experience as triage in a modern Emergency Room, trained army medics make life-or-death decisions about which patients might be saved with the resources at hand. Occasionally, the most severely injured are left to die if the heroic measures required to save them might ultimately cost more lives among the less-seriously-injured casualties forced to wait too long for their care. Multiple acute arterial bleeds from numerous shrapnel wounds to internal organs? Sorry, soldier…even attempting to save you will cost the lives of these three less-severe trauma cases over here.

Welcome to life reduced to the existential absurdity of intolerable working conditions adversely affecting the desirable outcome of a maximal effort to save every wounded soldier. Imagine yourself simply administering analgesics and condemning one broken body to death in order to facilitate saving others. How can medical professionals function under such conditions and maintain their sanity? Regrettably, however, this heart-wrenching process has become a metaphor for the modern system of public education.

Today, if teachers are to survive a career in the classroom they must become adept at Educational Triage. Never furnished adequate resources, time or circumstances to reach every student, teachers must all too often cut their losses by occasionally giving up, albeit reluctantly, on students who do not exhibit sufficient resilience to thrive in the classroom. Not enough of a self-starter to crack your book and get your assignments done? Sorry, student, the hours spent arriving at minimal participation will negatively impact the many classmates ready and willing to perform.

Much like the doctor in a battlefield hospital, teachers confront a long roster of  students that is, at best, daunting. Not only is the caseload overwhelming, but far too many of the students on their rolls present perhaps insurmountable challenges. Hence, teachers are frequently forced to choose the interests of the many over the interest of the one. These decisions are not the result of malice, sloth or incompetence. They derive from judicial duress. In the state of Maryland, a judge ruled -and was upheld- that class size “is not a working condition” and therefore “non-negotiable” in the collective bargaining process. Specious legal reasoning may stand up as a narrow interpretation of the law, but it certainly withers under the scrutiny of reason and experience for classroom practitioners.

But surely,” you might exclaim, “our children are far better off than someone lying wounded in a field hospital!”

Truthfully, too many of our children can be tallied among the walking wounded, because the community to which they belong does not currently exhibit the will to lift them from their circumstance and prepare them adequately for the information age.

Neither the county nor the state has demonstrated sufficient resolve to furnish the resources that might transform schools into the one safe place where at-risk children can feel connected in this age of rampant alienation and dissociation. Children are the disenfranchised victims of societal indifference to their plight.

Were your child in legal trouble, would you hire a law clerk who had yet to pass the bar exam? Were your child ill, would you even consider a visit to an unlicensed practitioner? No, you would be looking for the most qualified professional you could find. How has it become acceptable anywhere in America that children can spend more than 1,100 hours each year with inexperienced or marginally-qualified educators?

The demographics suggest that it has become tolerable because it is most consistently the problem of poor children of color and poor children of recent immigrants. We see schools with 100 percent participation in the free/reduced lunch program; coincidentally, those schools also have higher percentages of inexperienced educators. For some reason we have not sufficiently pressured our political leaders to institute the changes necessary to achieve real equity in those schools.

Like it or not, the issue is funding. Affluent jurisdictions almost always manage to fund their schools; they grease the political wheels; they buy influence. Jurisdictions with soci0-economic challenges are seldom able to accomplish that feat.

If a community aspires to no more than the educational equivalent of meatball surgery, then our mission has been nearly accomplished. However, if teachers are to do more than sort those who choose to learn from those who appear unwilling, then we must find an effective and equitable manner by which to fund completely our most challenged schools.

Perhaps you’ve heard the old inspirational saw often trotted out to encourage educators. Two children are walking on the beach. They find hundreds of starfish washed up on the shore. The first child throws one back in the ocean. His companion wonders what possible difference saving one starfish could make. The erstwhile triage specialist responds, “It made a difference to that one.”

A poignant parable… unless your child is among those left as detritus on the beach.

Sincerely,

A beleaguered teacher

 

[Updated from an early Commentary 5/6/99 in the now defunct Prince George’s Journal. Despite enacting the Bridge to Excellence Act in Maryland inspired by the Thornton Commission’s findings, staffing ratios remain approximately 20% lower than our neighbors.]

“Underfunded schools: Push rock up hill; start over”

After having the temerity to outwit the gods and deny them their vengeance, upon his death Sisyphus was condemned in the afterlife to an eternity of rolling a boulder up a mountainside. In his landmark essay The Myth of Sisyphus, Albert Camus claimed that Sisyphus was superior to his fate in the moments of respite after the boulder crossed the summit and rolled back to the base of the mountain. Camus further suggested that, in those moments of rest before the next bout with his eternal labor, we must imagine Sisyphus as joyful.

The logic of that last proposition can prove elusive, but the fate of Sisyphus effectively demonstrates the existential conundrum of each individual forging meaning out of the perceived absurdity of meaninglessness. As Sisyphus purchases a few moments of repose by his grueling labor, he becomes the ultimate existential hero. He conquers the absurd by finding a purpose in a situation that appears hopelessly futile.

The Sisyphus myth is an apt metaphor, albeit an imperfect one, for the fate of teachers today. It is imperfect because Sisyphus discovers purpose in a futile task while teachers often discover futility in work most meaningful.

The latter seems infinitely more cruel.

Teachers, at least those committed to optimizing educational opportunities for children, are the spiritual stepchildren of Sisyphus. Their mountain takes three decades to climb and the boulder seems to grow inexorably by accretion. The constants in the professional life of teachers are requests, directives, and even longings, to do ever more for their students, accompanied by the illogical corollaries that fewer resources will be allocated and less time will be allotted.

At least Sisyphus knew how he had offended Zeus to arrive at his fate.

Teachers scratch their heads and wonder how their neighbors can stand by and silently witness what is happening to those charged with awakening young minds. Teachers also wonder how their neighbors can acquiesce to a community bent on funding conditions in our schools that promote little more than intellectual Darwinism for our children.

At least teachers do not labor for all eternity. Teachers can exercise free choice and walk away from this sublime torture called teaching at any time. Most do just that within six years. But for many, that act of surrender is a worse fate than pushing the boulder could ever be.

To no avail my parents always advised me to be careful when I wished for something. Like many children I did not heed them. All I ever really wanted to do was teach.

Now, it seems that teaching is just about all I do. My participation in outside interests has declined precipitously across my years in the classroom.

The martial arts are out. Lobbying elected representatives and fighting for school funding takes precedence.

Music is out. Once a constant companion, that old guitar in the corner has not been touched in years while my computer keyboard has nearly become an added appendage.

Sustained Silent Reading for pleasure is out. That never-ending pile of papers always beckons for correction.

Astronomy is out. Stargazing on distant mountaintops unfortunately involves remaining awake well past sunset after somewhere between eleven and fourteen hours have been devoted to my livelihood.

How has it come to this? That is a simple question. Teaching is a to-do list that grows by twelve items a day with only sufficient time to eliminate five, and three of those five items have nothing to do with organizing instruction or assessing its effectiveness.

According to Camus, the gods “…quite reasonably thought that there is no more terrible punishment than futile and hopeless labor.” Sisyphus, however, still has some small chance at hope. He can accomplish his assigned task and earn a momentary reprieve from his punishment. Sisyphus can still put his shoulder to the boulder, acquire purchase, and achieve the summit. It would be a far worse punishment if the boulder never moved.

Compare that to the lot of teachers. Ideally, our goal is to make a scholar of every child. Failing that, the teacher’s mission is to inspire children to make maximum use of their talents. Not having the means to accomplish these noble goals leads to feelings of frustration and futility.

A normal day for a typical teacher comprises more than 9,000 teacher/student minutes. Nearly three-dozen children arrive periodically for a daily total of 270 minutes of instruction. If the instruction is to be dynamic, tack on 4 ½ hours of planning time. If teachers are to hold students accountable for their learning, marathon sessions of correcting papers must occur. The daily grind is interminable.

The non-instructional time of the contracted day is largely consumed by other-duties-as-assigned. Do not forget to be at your door before the school day begins and between classes. Do not neglect to be at your duty station. Prepare to stand in a long line at the photocopier as colleagues deforest the planet to cope with textbook shortages and obsolete materials. Watch those “quick” phone calls to parents become 45 minute planning-period-killers. During lunch, students come with résumés in search of letters of recommendation, or to make-up a quiz, or to seek help. It never ends.

Teachers are systematically denied the necessary time, resources and circumstances to achieve the desired goal of preparing children for this new century.

To paraphrase some homespun southern wisdom: sorry, but that rock just don’t roll.


[This is a slightly revised reposting of a 2001 Commentary in the now defunct Prince George’s Journal.  Things have changed for the worse in the intervening years thanks to No Child Left Behind (NCLB) and Race to the Top. ]