I had not thought that the tsars of education could possibly have come up with another idea as inhuman or stupid as have been their many innovations in the past – the New Math, the basal reader, the consolidated school, look-see reading, “creative” spelling, Social Studies, “pods,” feeding “speed” to boys to jam those pegs into uniformly tooled holes, pornogogical health classes – but the mills of the netherworld grind on. They have indeed come up with something every bit as horrible as all of that. What that is, I’ll discuss in coming essays. For now, I’d like to point out that only a vast system of compulsion can impose bad ideas on millions of people for years at a time. That is especially true of bad educational ideas. Mothers and fathers naturally want their children to learn, and are in a good position to notice, if they take the trouble, when they aren’t learning much of anything at all.

Let’s take for example the New Math. It staggers the mind, to look back on it. The Old Math was remarkably successful, after all. If you but glance at advanced arithmetic books from the 1800s, you’ll see that boys and girls were led to understand exactly *why *the rules of various operations worked, so that they could then use that understanding to skip steps and to simplify complex problems. It allowed them to perform calculations in their heads, at a snap. Multiply by 81? No, never. Multiply by ten, subtract the multiplicand; multiply the product by ten in turn, and subtract the product. Or, 13 is 39 % of what? Get out the calculator? Never. Notice the relationship between 13 and 39. The answer is obviously 33 1/3. The pitcher gave up 2 runs in 5 2/3 innings. What’s the ERA? Throw up your hands in despair? No. Understand what’s going on. Make the numbers easier, keeping the relationship the same: 6 runs in 17 innings. Work from that: 3.18.

That’s the really easy stuff. Take a look at instructional manuals for railroad mechanics, or electricians, or ham radio operators, circa 1930. They don’t require calculus. They do require very sophisticated calculations, arithmetical, algebraic, or trigonometric. They require a real *feel *for numbers and ratios, for what they mean, and how we use them, and why our algorithms work. Old fashioned instruction in arithmetic was designed to instill that familiarity. Small children would memorize the multiplication tables at an early age, not because the schools were in a rush, but because children have excellent memories, and it was just as well to get the tables out of the way, so that you could learn to use those tools to solve real problems.

Then came the New Math. All such things are precipitated by “crises.” We’re falling behind the Soviets – a crisis. No, it’s the Japanese – a crisis. We must be Leaders of Tomorrow, and drag that lizard out of his den by main force. What children really needed was not sing-song tables, and not familiarity with numbers such as most people need for most of the practical things they will do throughout their lives. They needed the Cutting Edge. They needed Set Theory.

One cannot overstate how wrongheaded and, yes, inhuman this approach was. A child learns to count. He sees that three blocks and two blocks make five blocks. In short order he intuits that three and two make five, and that two and three make five, because the order in which you count them doesn’t make a difference. Three and two make five.

At this point, the old instructors in arithmetic would build upon that intuition, and show the child that by the same reasoning, nine and two make eleven; and from there it would be only a few short steps to learning how to add 923 and 292. There wasn’t a rush about it, but there was also no backtracking, no needless ideation, no absurd abstraction, no fancy terminology – just the same kind of familiarity with numbers as a budding little carpenter will learn with a hammer and nails and wood.

And at this point, the commissars of the New Math veered perversely away from the child’s nature and away from the parent’s expertise. They went backwards. The important thing, they thought, was not that the child moved from the three blocks to three, but that he returned from three to the three blocks. Every number was to be conceived as a *set. *“Three,” then, means a *set of three. *But that wasn’t perverse enough. A child might think of three dogs or three blocks or three trains. But Set Theory knows nothing of dogs or blocks or trains. “Three,” more precisely, means a *set of three elements.
*

What happens when we add three and two? Do we get five? Not so fast. We *unite *a set of three with a set of two, and we get a set of five, so long as none of the elements in the first set is the same as either of the elements in the second set. At this point, parents would scratch their heads and squint; only their cultural predisposition to defer to teachers kept them from rising up with five-tined pitchforks.

Now, the child knows – he sees, in a wonderful act of intuition – that three and two are five. He sees that that also implies that two and three are five. He’s ready to go. But no, the New Math must frustrate him here. It must burden him with abstraction and terminology. He must learn about the Commutative Property of Addition. You see, some operations are commutative and some aren’t. If you divide five blueberry pies among three boys, each lad will get a lot more than if you divided three pies among five boys. Rather than simply asking children to advert to that interesting fact when they begin to learn division – something they should simply see, and have done with, as when you first see that red paint and yellow paint make orange paint, or that ice is slippery, or that blacktop in the summer sun gets very hot – they mystified what should have been straightforward and immediate.

It got worse. Let’s say you’re teaching children to multiply. Let’s say you want them to *feel *the numbers, and intuit what they mean. Take a simple problem, like 17 x 6. If you’re an old fashioned instructor, you say, “Let’s split the problem into two parts, in our heads. We’ll do the ten first, then the seven. Six tens are sixty. Six sevens are 42. Our answer is 102.” We understand intuitively that this is correct. If I’m doubling a canister of sugar with a small measuring cup, I know that I have to fetch an additional cup for every cup I take out of the canister. I double each thing by turns. If I need three pencils for 134 students, I can give three to the first hundred (300), then three to the thirty (90), and three to the last four (12). All this, a bright child will “learn” just by seeing that it makes sense. But the New Math came to stick a label on it. It was called The Distributive Property of Multiplication over Addition. And the child had to learn that label. The child had to say, when he was doing a simple operation (or trying to do it; often, trying to undo it, to split back into baby-bites what he had seen at a glance), that such and such was true because of the Commutative Property of Multiplication or because of the Distributive Property, and so forth.

Needless to say, the parents couldn’t manage the garble, and that provided material for much jesting. But maybe that was part of the purpose of the verbiage. The innovators wanted a wholly different approach to mathematics. They knew better, and they wanted the parents out of the way. They wanted to produce the next Peano or Cantor or Hilbert, I suppose; the Soviets had established a Set Theory Gap which we must close forthwith, or be damned to submission forever.

What’s odd, though, is that this madness could have lasted more than a week, anywhere in the country. It lasted for years – and I believe we are still laboring under the misery, because it broke the links between the generations, so that the ordinary know-how of the parents could not be passed down to the children, and then to the children’s children. No one is surprised now by a cashier who can’t give back the correct change when somebody gives $10.12 for an item costing $9.62. It lasted, because it had the clout of compulsion. It had the publishers, the professors of education, the school superintendents, money, and a largely captive and helpless public.

As a teacher of college remedial math (that speaks volumes about this essay, doesn’t it?), I want to share one of my favorite stories from the history of math education. It can be found on pp. 14-15 of the PDF file at

http://www.deliberatedumbingdown.com/MomsPDFs/DDDoA.sml.pdf

or, in case this doesn’t work, it can be linked to from the author’s homepage

http://www.deliberatedumbingdown.com/

Long ago in my undergraduate days, my Philosophy of Religion professor challenged the class to imagine the next stage of human evolution. I do not remember the context of the challenge, but I will never forget the winning concept: Losing their individuality, human beings will merge into one large brain, connected by the dendrites of modern technology–a new spin on the Gaea theory. The year was 1985; how prescient was that student (I think his name was David). Desktops, laptops, Androids, iPhones, iPods, tablets–connective devices abound so that 1 billion neurons can watch Psy’s “Gangnam Style” and tweet about it. Even this neuron writes to you on a laptop in a living room aglow with WiFi (almost everything has its redeeming quality–thank you, FPR). I have read Professor Esolen’s entire “Compulsion” series to date, and each essay speaks in its own way to this enervating uniformity, an encroachment that no one seems to mind because life is much easier than it used to be. People will say that every generation has its complaints about progress, but I think that the stakes are higher than they have ever been. Just a partial list of history’s great shifts–The Fall of Rome, the Rise of Christianity, the Reformation, the Industrial Revolution–reveals much cataclysm, but men have always been able to keep their own counsel. Now, we know almost everything about everyone, and we impose conformity on each other by happily sharing advice, passing judgment, and, remarkably, playing the fool; that strange enthusiasm extends to the school house.

As a teacher, I witness the submission to compulsion every day. We may call it twenty-first century education, skills-based curriculum, problem-solving, or just plain progress, but in the end it really is submission. To what? I think of the phrase “keeping up with the Joneses.” No one wants to be left behind, to be considered the dolt, the Luddite, the bumpkin, or–for a more techno-savvy word–the dinosaur. Conversely, no one wants to be the hero, the lone defender of principle who just lost his job for insubordination or incompetence (You can’t make a Prezi on Shakespearean tragedy? Really, Ken, your techniques are outmoded). The gurus tell me that my students will be more enthusiastic about writing if they can jazz it up with gadgetry, but after I read their papers I just want to tell them where their commas go, and why. Professor Esolen mentions grade-school students of generations past acquiring a “feel for numbers” by learning basic computation; in a similar way, their contemporary counterparts should have a feel for writing, and only a firm understanding of the mechanics of language will yield that result.

If, FPR, you publish these rambling thoughts, I will be grateful, and if you like my contributions–presumptuous as they may be in the company of the heavy-hitters on your website–then keep publishing Professor Esolen’s work because he never fails to make me do absurd things like spending New Year’s Eve blogging about education while my friends work on their excruciating hangovers.

Most sincerely,

Kenneth Cote

Mr. Cote,

Community, i.e. persons in communion in families, in churches, in associations and in natural polities, had been replaced by the collective, a counterfeit community. The way from community to collective has been the emergence of the would-be, so-called autonomous individual, the Promethean self, with his abstract rights. This process of atomization has been aided and abetted by the emergence of the Hobbesian state and the emergence of the every-more powerful technologies which complement the growing power of the state, among them those technologies which you outline in your post supra. The notion of the Borg is not farfetched at all.

I am the headmaster of a small private school dedicated to the classical Christian tradition as embodied in what is called Western Civilization, sometimes wondering if we are the last fools mistaking the flotsam and jetsam thereof as a viable ship of spiritual and intellectual commerce. The big task for us is finding and maintaining a point of teaching commensurablity with our pupils who come to us out of the morass of modernity. They bring few to no traditional or cultural reference points for the hard work of acquiring, internalizing and living out fundamental skills in formal and informal venues. Transfer students coming into the middle school cannot write in cursive; they cannot pen complete sentences; they do not command fundamental arithmetic skills; and they lack cultural reference point. The most disturbing trend which is emerging is that they do not retain even after rigorous drill and study.

What exactly is a basal reader?

Mr. Peters,

Thank the gods for Prometheus because I love a good barbecue. Kidding aside, I believe in individuality as Christ revealed it, that each person is unique, each person is sacred, each person has a soul, and each person has an opportunity for redemption. The binding agent is not technology but God’s love, which we express through community or, to use my preferred word, neighborliness. In short, I agree with your comments.

Happy New Year and God Bless,

Ken

The notion of the “individual” is a modern and quite abstract concept. We are embodied souls, persons, who even in our fallen state reflect the Imago Dei, and who exist, not as atomized “individuals” but as creatures, even fallen, in communion with God, with family, with Church and with other associations which make up the social order of which we are a part. The Imago Dei must be by the very nature of God – Triune- an image of man in communal relationships. To idolize the “individual” is to embrace a false understanding of man and to go down the road of attempting to make him a god. Christians cannot allow themselves to be driven into yet another corner of false dichotomies. Our embodied souls are not, on the one hand, subsumed and annihilated into some “Oneness.” That is anti-Trinitarian. Neither, or we, on the other hand, a race of atomized individuals with our wills as our god; that, too, is anti-Trinitarian. Faith, which itself is a gift of God, along with attendant humility,and not the individual will, shoots the gab between all of the false dichotomies with which we are regrettably beset.

Mr. Peters,

I think you and I are in accord. If it has no other value, technology has at least allowed us to discuss God across some unknown distance on New Year’s Day.

Best,

Ken

James, the “basal reader” was designed to pare readers down to a base level, a very limited number of words and only a few kinds of constructions. It took the common sense notion that very small children, when they’re first learning to read, can’t tackle Tolstoy, but can make their way through the tales in the first-level McGuffeys, and went insane with it. The result was readers that were absolute wastelands, utterly inane, insipid, terminally boring to any child who mastered the elements of phonics (I just ignored it all). This approach to reading, along with the anti-intuitive “look-see” method, produced a nice generation of kids uncomfortable with sophisticated language. It was incredibly stupid and wholly artificial. See Spot run. Run, Spot, run! Oh, oh! Spot has the ball….

Reminds me of what said Einstein said “It is high time that the ideal of success should be replaced by the ideal of service ”. Only ours is an aesthetic crisis. We serve our own comfort, self-esteem, and ‘happiness’ living in a consumeristic bubble of narcissism and feel good platitudes. How many people today could even understand what it could mean to instead ‘serve beauty’ ? “The object of education is to teach us to love beauty.” –Plato

As a mathematics tutor in a town that boasts of having one of the best public school systems in the great State of Connecticut (an accolade whose grounding is the fecund soil of standardized testing–there’s some nutritious fodder for the next article, peut-être?), I have witnessed first-hand the degradation of the study of mathematics, a degradation that owes as much to the inane encroachments of technologies in the service of “distraction” (as though Lotus-eating were the loftiest aim of man) as it does to the vanity of the “educators.” While I don’t wish to make too hasty a generalization–after all, there are, somewhere out there, some good teachers in bad school systems–one of the most disturbing problems in mathematics pedagogy is that many mathematics teachers have turned it into a mimetic science; that is, one can only uncover the solution to a problem through set processes prescribed by a veritable deity, a deity from whom all mathematical and logical truth issues.

I have always argued–against not a little resistance–that mathematics is a science that is both rigorous and aesthetic; it involves formulas, observations, and creativity; it is not merely a genus or kingdom under which falls a finite number of axioms, postulates, and formulas; mathematics is, above all, a study of patterns, patterns that have been discovered by men of genius, at which men labored tirelessly, without the assistance of a calculator, a monstrous device with which one is compelled to be familiar, lest he fall behind the rest of the class.

The peddling of mathematics that we see nowadays is only natural, given the overall academic environs it finds itself in at present. What need have we for creativity, when the machines can do it all for us? “Why should we only toil, the roof and crown of things?” (I regret to end my comments here, would that I had more time to elaborate and polish)

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