The Achievement Gap

Sometimes educators talk about "closing the achievement gap" which separates high and low performing students.  There are documented gaps in educational outcomes on the basis of e.g. economic classes, race, etc.  Some of these gaps lead to serious social problems down the road.  But even if we somehow produced a society which had equal outcomes for every factor in the current Politically Correct List of Superficial Ways to Classify People™, there would still be high-performing students and low-performing students.  Educators don't like this sort of situation, because they don't want to feel like they are failing some of their students.

Now, there are two ways to close a gap.  One is to take the students who are doing badly, and teach them better.  The other way is to take the students who are doing better, and teach them worse.  Or at least, don't pay any special attention to them, since the goal is to produce equality.  This shows the danger of adopting equality as a goal.  Inequality is defined as a difference between two people.  Adopting equality as a goal means you are trying to benefit one person as compared to another.  If all better-off students were worse off, there would be less to feel bad about.

Instead, we ought to adopt the goal of benefiting all students.  But especially the ones who are most capable of benefiting from education.  This is, primarily, the more intelligent and motivated students.  People with (small "d") democratic sensibilities don't want to hear this.  But as St. Lewis writes in an essay on "Democratic Education":

Equality (outside mathematics) is a purely social conception. It applies to man as a political and economic animal.  It has no place in the life of the mind.  Beauty is not democratic; she reveals herself more to the few than to the many, more to the persistent and disciplined seekers than to the careless.  Virtue is not democratic; she is achieved by those who pursue her more hotly than most men.  Truth is not democratic; she demands special talents and special industry in those to whom she gives her favors.  Political democracy is doomed if it tries to extend its demand for equality into these higher spheres.  Ethical, intellectual, or aesthetic democracy is death.

A truly democratic education—one which will preserve democracy—must be, in its own field, ruthlessly aristocratic, shamelessly `high-brow'.  In drawing up its curriculum it should always have chiefly in view the interests of the boy who wants to know and can know.  (With very few exceptions, they are the same boy.  The stupid boy, nearly always, is the boy who does not want to know.)  It must, in a certain sense, subordinate the needs of the many to the needs of the few, and it must subordinate the school to the university.  Only thus can it be a nursery of those first-class intellects without which neither a democracy nor any other State can thrive.

The goal of leaving No Child Left Behind sounds enlightened, but leaving some children behind is in fact a necessary logical corollary of teaching children difficult subjects.  If your only goal is not to abandon the children who are behind, then you will abandon those who are ahead: the ones who are actually interested in learning.  Most people, believe it or not, forget most of what they were made to learn in school.  The future philosophers, scientists, authors, judges, and so on will actually remember (part of) their education and apply it.

This is not to say that education is unimportant for the masses.  A certain quantum of literacy and comprehension is necessary to survive in the world.   By definition, a democracy has votes, and a certain degree of education is necessary to vote wisely.  When broad sections of society are deprived of a good education, and become a permanent underclass, society suffers.  The heroic teachers who try to remedy this, by volunteering to teach failing students, are worthy of our respect.  It is a valuable project, but it ought not to have such an exclusive monopoly on our thinking that we forget the need to teach those most capable of learning.

But aren't those students going to be learning anyway, in pretty much whatever environment you put them in?  To some extent, yes.  But it makes a difference what you think is the point of education.  The current goal is to produce a system in which any student can succeed if they really try.  This means lots of busywork, and a hefty amount of grade inflation (rewarding the consistently effortful, and punishing those who take chances on difficult subjects).  It does not necessarily mean teaching critical thinking.  Teaching people to be "good at school" can mean be a sort of slave-mentality, while the goal of a liberal arts education is to produce people who can think for themselves.  This involves a sort of paradox: you have to teach people to teach themselves.  Ignoring a student's needs is one way to try to encourage this, but it is not the best way.

Let me be autobiographical for a moment, just to give a concrete example. I hope that I am now old enough and fulfilled enough to be beyond any resentment, but I feel that a specific example will be helpful, and I am the example I know best.

In the area of mathematics, I was "left ahead" as a child for pretty much my entire school career before I started taking college classes.  The teachers recognized my knowledge, but none of them did what was required to give me sufficiently advanced material.  I suppose they probably had their hands full with the students who needed more help with the assigned curriculum.

Eventually, in the 7th grade, someone put me into the 8th grade Algebra class.  It was too late—I was already starting to do Calculus by then.  I was too bored by the subject to do any homework, so the teacher failed me, even though she knew I knew all the material.  She thought I was lazy and needed study skills, which was true, although this was hardly the correct motivator to produce them.  I had to repeat the class again in 8th grade.   I was mortified, but fortunately none of my classmates knew about the situation.  I still didn't do any homework (through guilt-ridden procrastination and deception, not through a firmly decided upon rebellion), but this time she recommended me into the Honors Geometry class in the 9th grade.

This time homework was only 10% of the grade, but the extremely formulaic and tedious standards for proofs docked me another 10% or so on the exams.  (See A Mathematicians Lament for an important critique of the way we teach Geometry and other mathematical subjects.)  That got me to a C+.  As a result I was looking at having to take the non-honors version of the next course in the sequence Algebra II.  (Los Altos High School had a policy against skipping classes).  Bear in mind that, on my own, I was learning Maxwell's equations,  General Relativity, and Quantum Mechanics at this point.

There was a standardized test to overcome the C, but in a school full of overachievers it was deliberately designed to be impossible.  Too many questions in too short of a time.  I knew immediately, before getting the results, that it wasn't going to fly.  I was going to be steamrollered under the wheels of an formalistic bureaucracy which was unable to make a plain human diagnosis of the sort of student I was: lazy but brilliant.  I was terrified that I would never receive the help I needed to succeed at what I already knew I wanted to do in life: theoretical physics.

 Some wandered in desert wastelands,
finding no way to a city where they could settle.
They were hungry and thirsty,
and their lives ebbed away.
Then they cried out to the Lord in their trouble,
and he delivered them from their distress.
He led them by a straight way
to a city where they could settle.
Let them give thanks to the Lord for his unfailing love
and his wonderful deeds for mankind,
for he satisfies the thirsty
and fills the hungry with good things. 
(Psalm 107:4-9.  Read the whole thing!)

So I cried out to the Lord to save me, and he rescued me from my afflictions.  The instruments of his salvation were as follows: Although I complained of the inhuman bureaucracy, in fact there was an excellent academic counselor at the school who knew my situation and advised me to apply to the Foothill Middle College Program, basically a way to flunk out of high school into the local community college. They only take Juniors and Seniors, so I had to skip my Sophomore year.  No regrets!

When I went there, Foothill finally gave me an actual placement test, and I got the highest result and so placed into Calculus 1A (I made an arrangement with the prof to skip the classes and take the final: with Calculus 1B I finally got to new material).

My weird education story doesn't end there, but this was a critical turning point.  It happened because at some point certain educators cared enough design and implement a program for people like me.  For this and many other gifts I give thanks to the Head Teacher:

I love the Lord, for he heard my voice;
he heard my cry for mercy.
Because he turned his ear to me,
I will call on him as long as I live.
(Psalm 116:1-2)

About Aron Wall

I am a Lecturer in Theoretical Physics at the University of Cambridge. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.
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