The Age of Educational Innocence Shall End, But When?
Since my retirement as a professor of mathematics, ten years ago, I have somehow acquired a second career, having to do with mathematics education in the schools, from Kindergarten through high school. I began this unexpected career commissioned by an educational foundation to report on the adequacy of those documents called "Standards" by our states, and the Standards printed by some cities and foreign countries as well, and I have in consequence been in correspondence with, and indeed cooperation with, professionals in public education in both the states and in Washington. Outside of officialdom, too, I have become acquainted with both teachers of children and professors of those destined to become such teachers. I have also participated in other studies and projects, constructing syllabi or examinations for states, or models for such things. Serving on committees with me have been all sorts of professionals in education, from mathematicians to psychologists, from those who know nothing of mathematics (nor pretend to) to those who do know something of mathematics (or pretend to). Thus I have seen up close a good number of representatives of the educational establishment, and have debated policy with them, both grandly and in detail. And I have read extensively in their literature, both current and outdated, foolish and wise, most of it being literature I would once have avoided.
One such paper, by an educational psychologist, examined the problem of how a devoted teacher might overcome a common sort of resistance from a student or class; it attracted my attention because resistance to instruction is one of the great stumbling blocks math educators face, or so it seems to those with classroom experience. I and a few colleagues were discussing this paper in our email discussion group, and one of us, a college teacher himself, commented that the paper we were discussing was perhaps inverting the problem. That is, he wrote, the paper was “a strange combination of cynicism with respect to students and idealism with respect to teachers. That psychologist assumes the worst about students and the best about teachers. Why not the opposite: the students want to learn something and the teachers (and educrats) want only to seem competent and survive till retirement. This is equally realistic. Even in the case with students who want only to get out of this class with a passing grade, we should ask who taught them this.”
The third party mentioned only parenthetically above, neither "the teachers" nor "the students" but the education establishment itself (“educrats” was his derisive term), is in many ways neither teacher nor student, though its members are largely drawn from former teachers and current professors of education. My own experience in K‑12 math education has been almost entirely via this third class, since I have myself have taught only in universities, and have spent the past ten years studying, consciously or not, the behavior of the K-12 professional education establishments, state, federal and guild.
My correspondent’s comment on the attitudes of students and teachers towards the work of the day in the teaching and learning of mathematics has therefore raised in my mind more the question of the structure of the establishment that has generated these attitudes than the question of the attitudes themselves. How teachers view their tasks, and how students do, appears to me to have more to do with the institutions governing the schools than with the choices teachers and students seem to have freedom to make once in the classrooms.
For example, to speak of the motives of "the students" is to speak too broadly, for while some of them are anxious to learn, almost all of them are anxious to appear to learn, even the good ones. Thus, students are driven by conflicting motives within themselves: should they dig deep, following their interests and natural desire to understand, and in consequence risk missing a bet by not knowing some trifle that will appear on the next exam; or should they spend their time studying the list of answers to previous exams of that level as fed them by typical teachers ‑‑ under District instructions oftentimes ‑‑ during the periods, ever lengthening, called "test preparation"? Here the structure of the examination system probably is decisive for most participants, however much they enjoy mathematics, or understand it.
To speak of the motives of "the teachers" is also to speak too broadly, for they too are made up of all types: time‑servers waiting for retirement, enthusiasts who love children more than they love mathematics, other enthusiasts who know mathematics better than they know children, and so on. Whatever their personal preferences might be, or might have been when they entered their profession, they are today under very severe instructions to generate the appearance of successful teaching, for new federal pressures for discernable "results" are now causing them, via the demands from their Principals and Supervisors, to behave as they might not behave if they were simply doing "their best" as measured by some moral criterion of their own.
The motivation of the "new class", the educational establishment itself as I have seen it in its works of recent years, seems much clearer than that of the teachers in the field. In particular, the evidence of the Standards the states have created, driven by a political deadline in most cases, and the consequent examinations, whether statewide, district-wide or a national assessment such as NAEP, is already conclusive, though of course an entire class has within it some variation. That motivation ‑‑ apart from careerism which one finds in some degree in all walks of life – is partly politically driven, but is mainly a product of the zeitgeist of "equity", along with a few other sociological components having to do with compassion, shame, and all that used to come under the heading of "guilt‑trip".
The education of a professional educator is heavily laced with the “progressive” doctrine of the 20th Century, with lessons taken from psychoanalysis, Marxism and Sunday supplement compassion. A distinctive culture has emerged from the schools of education and is now omnipresent in all corners of the world of education, and its nature is captured by its most prominent professional symptom: Every action in the name of education is now directed at assuring the non‑failure of all individual students. This non-failure, were it possible, would sound like what is also called “equity”, so that while compassionate teachers generally believe their efforts towards making students pass their exams are in the direction of what was once called education, political considerations have changed the meaning of the terms. “Non-failure”, under the regime of incessant examinations, now means “non-failing-grade”, since while other forms of failure are visible to parents and observant teachers – and future employers -- they are invisible to a school system, and it is the system that faces the public.
"Tough questions" therefore must not appear in examinations, memorization must not be demanded in Standards, formula pages and hand calculators must be part of the exam-day equipment, proofs must be "informal" in geometry and absent in algebra. Easy exams imply easy instruction, of course. And exams are not the only driving force behind the race to mediocrity, for progressivist principles of classroom instruction have, even in the absence of a trivialized exam regime, been gaining strength for a century or so, becoming literally de rigeur, i.e. enforced in many classrooms today, with student-discovery taken as more virtuous than learning what past generations have found to teach us. Without particularly knowledgeable teachers and ideal classroom management these principles are already a recipe for diminished content in the curriculum.
Concerned parents have always wanted their children to "do well" in school, but while doing well was correlated with learning well, fifty and a hundred years ago, it is today measured by exam grades, which are no longer (though they could be) a valid measure. Thus we have the short‑cuts of grade inflation and low or vague standards, all covered over by the language of concern for how children really learn (deep‑down, in some non‑measurable way, if one can get away with it until retirement time). With well‑chosen words all this can be made -- for a time -- to sound virtuous. For many years, in fact, it has been unassailable.
Easy exams and grade inflation solve the problem of teaching in a manner exactly analogous to the populist solution of the problem of economic inequality, and poverty, a solution of which we have so many historical examples, all accompanied by genuine democratic enthusiasm: Peronism has been the most striking example in our neighborhood in recent times. Inflation will appear to make everyone rich, and the popularity of rising wages and falling taxes is unbounded for a while -- until one realizes that the dinner table is not in fact heavy with food, and the electricity is subject to frequent and unaccountable cutoffs.
Ultimately, though delayed by injections of foreign credit from richer governments themselves concerned more with temporary appearances of stability than with long‑run solutions, the inevitable monetary crash requires a currency reform, “land reform” or the expulsion of some minority population guilty of profiteering. If the country is lucky it gets through it without a new tyrant immediately emerging to begin again at zero and run through the routine once more.
Sometimes, as in the great revolutions of 1789 and 1917, the distress can be apparently cured for the moment by dispossession of those who seem to have 'more than their share', but as we see again and again this cure also does not last. Sometimes ethnic cleansing helps, too, as in Uganda and Zimbabwe, where those who had all the wealth happened to be Indians or English, hence expendable. In many countries the dispensable class has been the Jews, though in the far east it has usually been those of Chinese origin. What remains constant through all these humanitarian revolutions is the professed concern for the common man, for the dispossessed, for the so-called failures. The common cure is the abolition of failure by fiat.
In education it is only in recent years that analogous phenomena have appeared, because until perhaps the last hundred years, maybe two hundred in the West, education has not been a public matter at all. Indeed, a lack of formal education did not distress a most of the population because it was not seen to correlate with poverty or other ills. But today the analogy is quite clear. Those responsible to "the people" must look successful in providing them with education as much as in providing them with employment at high wages directly.
Since language has a certain inertia and doesn't change overnight, the old words for educational success can fool the people in the same way as the old words for money or economic success. For a few years the Peronist peso sounds like money, and the printing presses can keep the electorate happy until at least the next election. Then follows currency reform and worse, and when the truth can no longer be hidden, those responsible must resort to tyranny: What cannot be hidden can at least be silenced. This can go on in the most successful cases for 75 years, as in the Soviet Union, though in modern times one generation or two is the maximum ‑‑ in a given country. Strangely, one country sometimes does not learn from the example of its neighbor, so that this process can be going on somewhere in the world at any given moment.
In American public education we are in the late stages of this process today. The educational establishment is still struggling to make the old words, such as "high grades", "real understanding", "rigorous standards" and "accountability", maintain their old magic, while at the same time the printing presses are putting out standards that are not standards, examinations that do not examine, and leadership that does not lead (though it claims to “guide from the side”). This is not to say the establishment is entirely insincere; I believe, in fact, that most people today covering educational failure with such jargon believe what they are saying, even as the apologists for the Soviet system were not only numerous when the system collapsed, but are still with us, even in Russia itself, despite having seen the failure with their own eyes.
One must allow, however, that no analogy is perfect. Despite all that is evident in today’s educational environment, my experience of the past few years has made me optimistic, at least for the country I know. There is a real public out there in the United States that is not ashamed to acknowledge that some people will learn more than others and thereby become more productive -- and richer – and that whatever one says about inequity and oppression, past or present, some people will fail. The unproductive will not be raised to productivity and prosperity by inflationary devices; a drastic redistribution of the marks of success, whether grades of A or paper money by the bagful at the end of the week, will not redistribute success itself, and worse, will in time kill success altogether.
There is a large public that sees this truth, even if in the colleges of education the reverence for progressivist rhetoric hides it from the professionals. That public is hiring tutors when the schools make a mockery of curriculum, or sending its children to private schools, or teaching them at home, but while all this augurs ill for public education, and is certainly driving us further in the direction of a two-class society, it does show that a large part of our population is not deceived by the trappings of education on exhibit as real education. As it increases in self‑awareness, and gains confidence in the justice of its cause, this public may yet teach the necessary lessons back to that part of the public still deceived by the mockery, teach them by the example of those who have not been deceived, that they are being bought off with trivial examinations, cheap report cards, and diplomas as phony as the affectation of Latin they are written in.
A free public, unlike those politically deceived by a revolution that has taken control of their thoughts and words, can, I believe, once it sees that the professionals in charge of education have feet of clay, regain confidence in themselves: that asking effort of children is not a disservice to their "childhood", and that “everyone passes” can never be an absolute guarantee any more than the unemployment rate can be zero. The public must recognize, and it can, that real knowledge can be distinguished from psychobabble, and that real teachers can be educated to provide such knowledge to children without agonizing over the inevitable failures.
The time will come again when it is admitted that it is adults who must teach the young, and not the young each other. The time will come when geography lessons will require the young to locate countries, lakes, mountains and cities on unmarked maps, even to draw such maps on blank paper, a time when speeches from Shakespeare and Lincoln will be memorized, and children will take handwritten notes from dictation in standard English spelling, a time when "science" will say more about molecules than about the destruction of the environment (by big business, not their parents’ vans), and when mathematics will again concern itself with the rationale of computation along with the way such computation mirrors the behavior of the marketplace and of the natural world. And that will also be a time when it will be admitted that while all men are created equal they do not all make equal effort or have equal desires in the direction of their own lives.
Failure exists whether announced or not, just as poverty exists however many pesos are printed and handed out equally and compassionately to all citizens; but as the evils of poverty are only exacerbated by the illusions that currency inflation provides, the evils of ignorance are only exacerbated by the pretences of today’s schooling. But the evidence of the counterproductivity of current educational orthodoxy can not be hidden forever, unless we ignore it too long, and permit it to last so many generations that nobody will be left to recognize ignorance at all. Should our society fall into such a state, a new dark age having nothing but bootstraps by which to raise itself might endure a thousand years. There are some differences between today and the latter days of the Roman Empire, however, that cause me to take a brighter view of the future than this.
Ralph A. Raimi
13 May 2003
Revised 2 November 2005