Wrong Answer: The Case Against Algebra II

In the September 2013 issue of Harpers Magazine, by author Nicholson Baker.  For the complete article go here.  Yellow highlights our own.

In 1545, Girolamo Cardano, a doctor, a wearer of magical amulets, and a compulsive gambler, published a math book in Latin called Ars Magna. The “great art” of the title was algebra. When Cardano was done, he knew he had come up with something huge and powerful and timeless; on the last page was the declaration, WRITTEN IN FIVE YEARS, MAY IT LAST AS MANY THOUSANDS. The equations in Ars Magna looked very different from the ones we are familiar with — here, for instance, is how Cardano wrote the solution to x3 + 6x = 20:

Rv: cu. : R108 p : 10m : Rv :cu. R108m : 10

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.

That’s what’s so amazing and mysterious about the mathematical universe. It doesn’t go out of date. It’s bigger than history. It offers seemingly superhuman powers of interlinkage. It’s true. Mathematics, said a professor named James Byrnie Shaw in 1918, is a kind of ancient sequoia of knowledge, rooted in the labors and learning of the dead:

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.

And:

Imagine for a moment that you are a high school student, halfway through a required Algebra II class. It’s a Monday, and this week, it seems, you’re moving into something called “rational functions.” (Last week was a strenuous forced march through logarithms.) You’re sleepy, bored, and discouraged. There’s an inspiring poster on the wall — it shows a photograph of Einstein in a sweater, saying, “Do not worry about your difficulties in mathematics; I can assure you that mine are still greater.” The word ASYMPTOTE is on the whiteboard, and below it, QUIZ THURSDAY! The teacher is hardworking, jokey, smart, exhausted — she knows most of the kids in her class don’t want to be there. 

You look down at your textbook, which is published by Pearson. It’s very new and very heavy. It’s called Algebra 2 Common Core. 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. The gecko robot has green compound eyes and is held together with shiny chrome screws. It has a gold jaw and splayed gold toenails. Perhaps you like the idea of robotic geckos, and you might expect, reasonably, that there would be something about the mathematics either of geckos or of robots somewhere in this book. There isn’t.

There is, however, at the beginning of Chapter 8 (“Rational Functions”), an interesting high-speed photograph of a basilisk lizard, also known as a Jesus Christ lizard, that is dashing on tiptoe across the surface of a body of water. A facing caption says:

Rational functions help explain how surface tension allows some animals to tread across a pond’s surface. How can you graph rational functions and solve rational equations? You will learn how in this chapter.

But again you discover, to your disappointment, that the lizard image is just a bit of bait-and-switch. 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. They’re not like water striders; they’re much too heavy. 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. If basilisk lizards had to rely instead on equations of surface tension they would sink immediately, as many algebra students do.

So no lizards, no geckos, no robots. Here’s what you actually learn about rational functions in Chapter 8 of Pearson’s Algebra 2 Common Core:

A rational function is a function that you can write in the form f(x) = , where P(x) and Q(x) are polynomial functions. The domain of f(x) is all real numbers except those for which Q(x) = 0.

Not only that, a rational function can be continuous or discontinuous, and a continuous rational function is one that, if you graph it, “has no jumps, breaks, or holes.” No holes? We’ll see about that. 

And: 

Algebra 2 Common Core is, in other words, a typical, old-fashioned algebra textbook. 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.