The case against Algebra II

In 1545, Girolamo Cardano, a doctor, a wearer of magical amulets, and a compulsive gambler, published a math book in Latin called Ars Magna.

In 1545, Girolamo Cardano, a doctor, a wearer of magical amulets, and a compulsive gambler, published a math book in Latin called Ars Magna.

But the algebraic rules Cardano described and codified are variants of the techniques that millions of students are taught, with varying degrees of success, today.

But the algebraic rules Cardano described and codified are variants of the techniques that millions of students are taught, with varying degrees of success, today.

It offers seemingly superhuman powers of interlinkage.

Its foliage is in the atmosphere of abstraction; its inflorescence is the outburst of the living imagination.

Its foliage is in the atmosphere of abstraction; its inflorescence is the outburst of the living imagination.

From its dizzy summit genius takes its flight, and in its wealth of verdure its devotees find an everlasting holiday.

From its dizzy summit genius takes its flight, and in its wealth of verdure its devotees find an everlasting holiday.

Grant Wiggins, an educational consultant and former teacher, told me it was a “nasty gatekeeper course”: the compulsory Greek grammar of the modern era.

But many math conscripts are angry, many resigned, and some have reached states of real panic or despair.

“I only survived by gnawing one of my own legs off.”

PRAY FOR THE GIRL IN PERPETUAL ALGEBRA HELL.

The homework is unrelenting, the algorithms get longer and trickier, the quizzes keep coming.

(Last week was a strenuous forced march through logarithms.)

(Last week was a strenuous forced march through logarithms.)

Arne Duncan, the U.S. secretary of education, wants everyone working their asymptotes off, learning about rational functions and their points of discontinuity.

Your state has benefited from a federal Race to the Top grant that has encouraged your school to buy many copies of this new, expensive textbook, along with the associated workbooks and software licenses, all of which conform on every page and every screen to the guidelines spelled out in the new Common Core State Standards for math, now adopted throughout the country.

The textbook’s cover is black, with a nice illustration of a looming robotic gecko.

There’s nothing about surface tension or walking on water in Chapter 8 — and indeed, the caption would puzzle an expert on reptilian locomotion, since basilisk lizards don’t actually rely on surface tension to run on water.

The real miracle of the basilisk lizard is that it can scamper over Costa Rican rivers (and over laboratory tanks at Harvard’s Museum of Comparative Zoology) by relying on the momentary inertia of the boluses of water beneath its fleet, long-toed feet.

The real miracle of the basilisk lizard is that it can scamper over Costa Rican rivers (and over laboratory tanks at Harvard’s Museum of Comparative Zoology) by relying on the momentary inertia of the boluses of water beneath its fleet, long-toed feet.

Next you are presented with a salient feature of discontinuous functions:

To reinforce your learning — to make it really bake itself in your mind, so that you’ll be able to call upon it in times of quantitative uncertainty in the years to come — there are some exercises to do.

It’s a highly efficient engine for the creation of math rage: a dead scrap heap of repellent terminology, a collection of spiky, decontextualized, multistep mathematical black-box techniques that you must practice over and over and get by heart in order to be ready to do something interesting later on, when the time comes.

It’s a highly efficient engine for the creation of math rage: a dead scrap heap of repellent terminology, a collection of spiky, decontextualized, multistep mathematical black-box techniques that you must practice over and over and get by heart in order to be ready to do something interesting later on, when the time comes.

In 2011, Duncan — a broad-shouldered, well-meaning, Harvard-educated former basketball player from Chicago who occasionally scrimmages with President Obama — gave a speech under a spotlighted infinity symbol at the annual meeting of the National Council of Teachers of Mathematics (NCTM).

“Rigor” is Duncan’s watchword — he used it several times in his speech.

Distressed that students were doing so poorly in math, he instituted something called “double-dose algebra,” which required every incoming ninth grader who had a below-average score on a placement test to take not one but two back-to-back periods of algebra each day.

Algebra II, he believes, is the mystic portal to prosperity.

Algebra II, he believes, is the mystic portal to prosperity.

These micromanagerial, misbegotten, joy-stunting standards are, said Duncan, a “real game changer,” and will be rolled out nationwide this academic year.

You need it for the burgeoning field of high-tech, but that’s not all the jobs.

We’ve eviscerated vocational-training programs over the past fifteen years.”

Programs in graphic design and the building trades have disappeared, he notes, while billions are spent on math enrichment and testing.

We are, of course, but what percentage of our students can see it, however dimly?”

Cornell’s Steven Strogatz, a mathematician of crowds and swarms and oscillating bridges, told me that he agreed with much of what Hacker wrote.

Cornell’s Steven Strogatz, a mathematician of crowds and swarms and oscillating bridges, told me that he agreed with much of what Hacker wrote.

We should, I think, create a new, one-year teaser course for ninth graders, which would briefly cover a few techniques of algebraic manipulation, some mind-stretching geometric proofs, some nifty things about parabolas and conic sections, and even perhaps a soft-core hint of the infinitesimal, change-explaining powers of calculus.

Kids don’t hate smelting, or farming, or knitting, or highway design, or portrait painting, or neurology, or juggling rubber balls, or sonnet-writing, because they don’t have to take three years of instruction in any of these arts.

If Algebra II were an elective and colleges didn’t ubiquitously demand it, fewer people would learn it.

And those for whom Fourier analysis is a joy and a marvel, a way of hearing celestial music, would be in classes with other students who get a similar buzz.

Life’s prerequisites are courtesy and kindness, the times tables, fractions, percentages, ratios, reading, writing, some history — the rest is gravy, really.

No study, he claimed,

has supported the contention that the abstractions of algebra, geometry, and trigonometry, which so many students are required to learn, are practical in any general sense, except for a small number of occupations.

Smith published it instead in the Phi Delta Kappan, where it inspired a barrage of mail, some supportive, some enraged.

Stolp told me that although he loves teaching algebra, he doesn’t believe children should be compelled to master abstract algebraic techniques that they find meaningless.

I asked Wiener, who taught journalism after switching over from math in the 1960s, about the plan to impose stringent Common Core math standards on all students in all states.

I would respectfully suggest that Arne Duncan and Bill and Melinda Gates and all the Standardistas at Achieve take a few days to read these three short books, plus an amazing cri de coeur by Paul Lockhart called A Mathematician’s Lament.

Their endlessly repeated defense of Algebra II is derived from an obvious statistical tautology: people who take Algebra II are more likely to go to college, since Algebra II is, after all, a college requirement.

In their eagerness to impose “reasoning skills” on young people, they have in fact succumbed to an old bit of illogic: the post hoc ergo propter hoc fallacy of misplaced causation.

In their eagerness to impose “reasoning skills” on young people, they have in fact succumbed to an old bit of illogic: the post hoc ergo propter hoc fallacy of misplaced causation.

In 1907, education laws changed in Chicago, more or less in concert with changes happening across the country.

He rejected the notion — still held by many then and now — that a child’s mind is like an underdeveloped quadriceps muscle, to be strengthened by the more or less arbitrary tasks of classical-grammar parsing and vigorous mathematical squat thrusting.

He rejected the notion — still held by many then and now — that a child’s mind is like an underdeveloped quadriceps muscle, to be strengthened by the more or less arbitrary tasks of classical-grammar parsing and vigorous mathematical squat thrusting.

He rejected the notion — still held by many then and now — that a child’s mind is like an underdeveloped quadriceps muscle, to be strengthened by the more or less arbitrary tasks of classical-grammar parsing and vigorous mathematical squat thrusting.

The mind which has been molded to the method of mathematics will use that method in mathematics, and in thinking allied to mathematics, alone.

The mathematician himself behaves in about the same manner as other mortals in a social or a political situation, but he reacts more efficiently in a certain type of scientific situation than does he who is devoid of mathematical training.

“School administrators and school patrons,” he wrote in 1921, “have come to the conclusion that algebra and geometry as traditionally taught in the high schools are intolerable failures.”

McAndrew, like Morrison, had taught algebra and geometry, and he could discern (as he told an audience of teachers in 1908) no correspondence between these high school subjects and “the educative processes of real life.”

These assaults on the algebraic citadel alarmed the traditionalists, chief among them a high school math teacher named C. M. Austin, founder of the Men’s Mathematics Club of Chicago.

In the early 1920s, Austin, lamenting that “high school mathematics courses have been assailed on every hand,” launched a counterattack by organizing the National Council of Teachers of Mathematics — the same group that Arne Duncan addressed in 2011.

Its appointed task was to make the case for required math and stop the spread of freethinking, Deweyite, student-friendly doctrines.

Ohio was among the first states to remove the math requirement from high school, in 1921, declaring that “it is not fair to impose a study upon a pupil on the contingency that he may some day utilize it in a practical way when the indications all point in the opposite direction.”

“If the mathematics enthusiasts would study the failure rates of mathematics throughout the junior- and senior-high-school period,” he said, “they might be aghast at the death and destruction that prescribed and even recommended mathematics scatter in their trains.”

“If the mathematics enthusiasts would study the failure rates of mathematics throughout the junior- and senior-high-school period,” he said, “they might be aghast at the death and destruction that prescribed and even recommended mathematics scatter in their trains.”

The most widely read denunciation of required algebra came that same year, from a syndicated advice columnist named Arthur Dean.

I cannot see that algebra contributes one iota to a young person’s health or one grain of inspiration to his spirit.

One mother sent a dissenting note in favor of algebra.

So pervasive and forceful were the arguments by Dean, Cox, McAndrew, and others against required high school math that Eric Bell, a mathematician and science-fiction writer, maintained in 1937 that the entire discipline was under siege: “Are not mathematicians and teachers of mathematics in liberal America today facing the bitterest struggle for their continued existence in the history of our Republic?”

So pervasive and forceful were the arguments by Dean, Cox, McAndrew, and others against required high school math that Eric Bell, a mathematician and science-fiction writer, maintained in 1937 that the entire discipline was under siege: “Are not mathematicians and teachers of mathematics in liberal America today facing the bitterest struggle for their continued existence in the history of our Republic?”

Mathematics was, Bell said, “fighting a desperate rear-guard action to ward off annihilation.”

There may have been fewer math teachers employed in public high schools as a consequence of the removal of the algebra requirement, but those who fancied math were working hard at it and doing it well, and the sciences that relied on applied-math proficiencies were making discoveries by the boatload.

By 1950, at a time when only a quarter of American high school students were taking algebra, the nation’s technological prowess was the envy of the planet.

As the curtain rose on the baby boom era — the purported golden age of American education, when high school was really high school and girls wore cardigans and boys wore narrow ties and everyone aspired to work for Ford and AT&T, when Dictaphones were king and food engineers gave us mashed-potato flakes, when GM was designing the Chevy small-block V-8 engine, when missile silos held freshly minted hydrogen bombs and Admiral Hyman Rickover’s nuclear-powered submarines patrolled the waves — only a

Admiral Rickover, in his popular 1959 book Education and Freedom, fretted over the “Russian success in combining mass education with highest-quality education for large numbers of her children.”

We got Neil Armstrong to the moon, a feat that required huge supercooled tanks of liquid algebra, yet still the grim duelists banged their spoons on the pot lid of unprecedented crisis.

By lowering our standards, the report said, America had been “committing an act of unthinking, unilateral educational disarmament.”