An earlier version of this article appears in educational Horizons Summer 2006

EVERY CHILD ABOVE AVERAGE
Achieving the Lake Wobegon Vision

©2006 Edward G. Rozycki, Ed. D.

Salagadoola mechicka boola bibbidi-bobbidi-boo
.
It'll do magic believe it or not, bibbidi-bobbidi-boo.
--- J. Livingston (Cinderella)

RETURN
edited 11/13/08

Too Quick to Judge?

Hardly dragging a foot, the American Public has rushed to embrace the vision of No Child Left Behind; presumably, because no one wants any child left behind. "Left behind what?" says the cynic. "Stop quibbling!" we admonish. "Being left behind is no joking matter" (Remember poor little McCaulay Culkin left behind by his family in the 1990 movie Home Alone? It shouldn’t happen to anyone, let alone a child left alone.)

Similarly heart-warming as "NCLB" has been the mantra, All Children Can Learn, although other skeptics raise questions as to what it is they might be able to learn and under what conditions.[1] So essential to effective teaching has ACCL been recognized to be, that some school boards in this Land of the Free require -- as a pre-condition of satisfactory evaluation -- public avowal by teachers of this inspiring formula!

All well and good for NCLB and ACCL. But a knowing wink crinkles the crowsfeet when Garrison Keillor’s confection, “Every Child Above Average,” is brought up for discussion. Everyone knows that not every child -- not even in Lake Wobegon -- can be above average. But do they really? Might it not be possible to make every child above average?

I propose, in the space of this very short essay, to demonstrate how ECAA can be accomplished. That is, I will show how every child can be brought to being “above average.”

Test Yourself

I have constructed a series of simple problems to help the reader begin to understand how the Lake Wobegon Effect might be achieved. In April 2006, these four simple problems were posed in a survey to 30 graduate students in different occupations, both corporate and educational. You will be able to compare your answers with theirs.[2]

Problem A -- the best grade package

Consider the following situations:

a. ten out of ten students in a class get a 75 on their math exam;

b. one student in a class of ten gets a 100, the other nine get a 75; and finally,

c. one student in a class of ten gets a 20, the other nine get a 75.

Which is the best situation? Which is the worst.

If you are like the great majority of the thirty people I recently gave the survey to then you found b to be the best situation and c to be the worst.

Problem B -- above or below the class average

Now, consider these situations:

a. ten out of ten students in a class get the class average grade on their math exam;

b. nine students out of ten are below the class average; and finally,

c. nine students out of ten are above the class average.

Which is the best situation? Which is the worst?

Now, for these situations, if you are like the great majority of the thirty people I surveyed, then you found b to be the worst situation and c to be the best.

A Perplexing Situation

These are very strange results for Problems A and B. They are self-contradictory. The situations a, b and c can be the same in problems A and B, yet they are described by those surveyed as polar opposites. Consider chart 1.

chart 1

Survey results for Problem A indicate situation b to be the best; situation c, the worst.

Yet, survey results for Problem B indicate situation b to be the worst; situation b, the best. Why is this the case?

To Continue

Problem C -- a sequence of tests

Suppose now that we give a class a sequence of tests. Which of the following possible scenarios describes the best outcome; which, the worst?

a. the class average does not change over the series of tests and everyone is at the average;

b. the class average changes; at the end, 90% of the class is below average;

c. the class average changes; at the end, 90% of the class is above average;

The people in my survey identified b to be the worst situation and c to be the best.

Problem D -- Student descriptions

Of the students described below, who is the best student; who, the worst?

a. Mary’s test scores are above average 90% of the time;

b. Sam’s test scores are always average;

c. Bob’s test scores are always slightly below average.

The people in my survey identified Mary as the best student and Bob as the worst.

More Anomaly

For Problem C which deals with a series of tests, we could take the series on the one hand to be described by a move from situation a to situation b. This clear improvement shown on chart 1 was indicated on the survey to be a change for the worse.

A transition from situation a to situation c, clearly for the worse when we look again at chart 2 , was indicated by those surveyed as a change for the better.

chart 2

 

How are these contradictions possible? It is clearly because there are two different concepts of “average” at play here. Let’s examine this.

Colloquial vs. Technical

Many words have both a colloquial usage and a technical usage. Educators work in a field which uses many words that share such ambiguity. Take the word, “abnormal.” Colloquially, this is often used to indicate something undesirable. Technically, speaking, it indicates something that deviates from the norm with no connotation, necessarily of undesirability. (Note how “deviation” itself carries a colloquial burden of dysvalue.) High intelligence, or talent, or perfect pitch, and the like, though highly valued in our culture are technically characterizable as “abnormal.”

“Average” is one of those words. Colloquially, “average” means “OK,” “acceptable,” “so-so,” “not worrisome,” etc. “Below average” means “something to worry about,” “not good;” “above average” means “good,” “praiseworthy,” “something worth pursuing,” etc. Also, many people carry around in their heads a rough letter-grade equivalent for these words: "average = about a C;" "D = below average;" "really good = A." This is schooling custom; not mathematics.

The technical meanings of the phrases, “average,” “below average” or “above average” do not carry any of the colloquial connotations. To evaluate a technical average, values have to be specifically introduced. For example, if a test average for a class is 25, where 69 is a failure, then being above average at 50 is still not good. If the class average is 95 and I am below average at 90, that is still good.

As more students make higher and higher exam scores, pulling the average up, then more and more students are likely to fall below class average and still be quite good. Conversely, as the class average falls, more and more students may end up above average and still be in a bad situation.[3]

Mixing colloquial and technical usages, a common practice in education, generates all kinds of controversy and no little practical mischief, as NCLB high-stakes testing illustrates.[4]

Every Child Above Average

Problem D above which identifies the best student as one who is consistently “above average” suggests a technique for achieving the Lake Wobegon Effect.

The process will involve our equivocating between colloquial and technical usages of phrases involving the word “average.” The process is simple.

Clearly, a student whose tests are above the class average 90% of the time is an above average student.

Suppose we have a class of ten students to whom we plan to give ten tests. Exempt one student from participation -- from attendance, even -- and from study for a particular test. Let us call this student, “the vacationer.” We prep the rest of the class for the exam.

All students take the exam. The vacationer gets by far the lowest grade on the exam,[5] thereby rendering his or her classmates above average for that particular test.

For each test a different “vacationer” is chosen. In this manner, each student will end up “above average” 90% of the time -- according to our definition of an “above average” student as indicated by Problem D.

Educators are likely to underestimate the practical power of invoking such a confusion. But every demoleader -- excuse me, leaderogogue -- recognizes the potency of ambiguity and understands that carefully defining terms wastes time in the pursut of Excellence.

I showed members of the survey group how the same nine students could have scores which would all be either above or below average depending upon whether just one classmate received a 100 or a 20. One of the persons surveyed protested that I had done some sort of trick. Intuition couldn’t possibly be overridden by arithmetic!

Thus we achieve the Lake Wobegon vision by promoting mathematical illiteracy. This is a tradeoff many would accept.[6]