That Andrew Hacker would advocate ending the requirement to study algebra to get a four-year college degree is mildly surprising. There has been no hint of such anti-intellectualism in his many fine essays on demographics, race and the education system in the New York Review of Books and elsewhere throughout the years. On the other hand, he has not been afraid to express a controversial opinion, usually backed by a slew of empirical evidence.
That he would use cheap and transparent propaganda tricks to advocate anything, let alone the deep-sixing of algebra, as he does in his article in last Sunday’s New York Times opinion section, is both shameful and disappointing. The article makes a shambles out of truth by defining algebra by its hardest and most advanced features.
Hacker sprinkles his article with examples of “algebra” as proof that it’s just too hard for most kids:
- (x² + y²)² = (x² – y²)² + (2xy)²
- Vectorial angles and discontinuous functions
- Quadratic equations
- Fermat’s dilemma (I think he means Fermat’s Last Theorem)
Hacker is right to say that no one except engineers, scientists and the occasional financial analyst will need to know any of his examples, which are all very hard. But correct me if I’m wrong, these are all subjects for the second year of algebra (I think the first year includes some simple quadratics).
Let’s take a look at what else Hacker wants to keep children from learning (except the lucky few who will get technical degrees):
- X + 5 = 10
- 2X – 3 = 5
- .08x = 80
- a/b = c/d, so ad = bc
That’s all math from the first year of algebra and all necessary for most people in our technology-oriented society.
The uses for my first three examples come every time we buy anything, be it in a supermarket, department store, laundromat or stadium. These basics of algebra allow us to figure our taxes and balance our checkbook.
The last example is particularly noteworthy, because since I began working at my first job running a closed circuit television studio for a subsidiary of the old Ma Bell in Seattle and writing/directing such classics as “Safe Pole Climbing,” not a week has gone by when I have not needed this basic equation.
Here is a classic example: I am billing an employee’s time at $65 an hour and paying her a total compensation of $38,000, meaning I break even once she has billed 11 hours to clients every week. To what level do I have to raise her rate to get the same break-even point if I increase her total compensation to $45,000? In the basic equation a/b = c/d, so ad = bc: a is what she makes, b is her hourly billing rate and c is her new compensation.
Let’s plug it in:
$38,000 time d = $65 times $45,000
And now solve, using the simplest of algebra that is taught about a third of the way through the first year (and a calculator for the arithmetic!):
38,000d = 2,925,000
d = $76.97, which I would round up to $77/hour or down to $75/hour.
In one form or another, week after week for decades I have faced a problem that this equation helped me to solve—as a university instructor of foreign languages, as a television news writer and reporter, as a would-be Hollywood screenwriter, as a marketing manager, as a public relations executive.
Hacker draws a picture of algebra that has nothing to do with the real-world needs of people.
I won’t dwell on the fact that learning mathematics is good for young brains because it entails developing a new way of thinking—similar to studying Chinese or Spanish—since Hacker freely admits it himself and proposed an algebra-free math curriculum for the liberal arts type that focuses on finding the mathematical beauty in the visual arts, music and poetry.
I don’t think it’s unfair to ask college or even high school students to pass a first-year algebra class. The key word is “pass.” Getting a C because the last few weeks got a little rough is no shame. It just means that someone shouldn’t consider going into any science or technology career, as the kids best suited to those careers whiz through algebra, trigonometry, calculus and beyond. And it probably also means that you’ll have a deficit in one area when competing against those who excel in higher math courses in liberal arts fields such as writing, law, business administration, sales, human resources and even the visual and performing arts. For example, my understanding of physics, which hinges on an understanding of the rudiments of calculus, has helped me win the advertising and public relations work of many technology companies.
There are plenty of fields that don’t require that someone get through trigonometry, and many of them pay very well.
But the world has become too complicated for anyone who can’t figure out that two cans of beans that are $5.00 each cost $10.00 total. That’s 2X = ?, if X is $5. And that, Mr. Hacker, is algebra.
Let’s close with a slight subject change: Unfortunately, many non-college jobs pay very little money and much less than what they used to pay, which is why contemporary parents are in a panic to get their kids into the colleges associated with success in the high-paying fields. These parents would be better off campaigning for a higher minimum wage, laws that help unions organize and other laws that raise salaries so that one can attain and maintain a middle class lifestyle whether one is a Harvard-educated lawyer or a community college trained security guard.