I discovered recently that my calculus students do not know the meaning of the word “quorum.” Since a course in American government is a high school graduation requirement in most states (including here in Florida), I was taken aback.
How should I react? Should I take to the editorial pages of The New York Times, bemoaning the state of civics education? Should I call out political scientists and high school history teachers for their failures?
Surely you’d admonish me to calm down a bit and perhaps not venture into disciplines where I’m not an expert.
Yet Andrew Hacker, professor emeritus of political science at the City University of New York, recently took this exact approach to attack the teaching of algebra in American schools. He also wrote a book. And he’s done it before.
Nor is he alone. Novelist Nicholson Baker wrote a piece for Harper’s in 2013 that got the math community talking. The real target of Baker’s piece was the accountability movement and the associated standardized testing, but he chose mathematics as his straw man because it (a) is easy, and (b) will sell magazines. He manages to boil the modern course in Algebra II down to this:
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.
At least Baker is an entertaining writer.
Hacker makes many of the same points in his Times articles, decrying algebra as a high school graduation requirement that holds back far too many students from having a productive life. He argues instead for “numeracy” and suggests what such a course should contain. It’s mostly statistics and financial mathematics, and lessons in visualizing and analyzing data.
To fight off the counterassertion that it’s possible to learn this material in a high school advanced placement statistics course, Hacker comes up with lists of obscure terminology: “The A.P. [Statistics] syllabus is practically a research seminar for dissertation candidates. Some typical assignments: binomial random variables, least-square regression lines, pooled sample standard errors.”
It’s not just happening in math
Every subject in school has been broken down into a string of often unrelated facts or tasks, not just mathematics.
I recall an episode from my own son’s experience in ninth grade while taking “Honors Pre-AP English I” (yes, that’s the real name of the course, not some Orwellian nightmare). His teacher led the class through the “CD/CM method” of essay writing, which goes like this. Fill out a worksheet with the “funnel” (4-7 sentence introduction), the thesis statement, and then for each of three paragraphs create 11 (!) sentences – the topic sentence (fine) and then CD#1, CM#1, CD#2,CM#2,…,CD#5,CM#5. What is a CD, you ask? Concrete Detail. A CM? Comment, of course.
Now, this is really just a superextended outline for an essay, but my son was extremely frustrated by this, eventually exclaiming, “I just want to write the damn paper!”
Is this example from the humanities really any different from what Hacker and Baker complain about?
Hacker is not completely wrong, however. School mathematics has largely been drained of context and beauty. University mathematicians complain about this, too.
For example, my son has also brought home worksheets full of dozens of polynomials with the simple instruction: Factor. But why?
Light rays striking a parabolic mirror reflect to a common point called the focus (point F above). created in Geogebra by the author
There is no context given for why we care about polynomial equations, no discussion of why parabolas (graphs of quadratic equations) are useful things. Maybe we should explain that without parabolas, we wouldn’t have good headlights on our cars or all those pretty pictures of deep space from the Hubble telescope. But just as mathematicians would not argue for the elimination of English or civics from the high school curriculum, Hacker shouldn’t be arguing for the elimination of algebra.
Let’s be honest. Mostly because of the accountability movement and high-stakes testing, K-12 education suffers from these types of problems in every subject. Picking on math alone because it’s particularly vexing for some people is unsporting.
Of course, Hacker and Baker have proposals for how to fix this mess. The problem is that the major prerequisite for much of what Hacker proposes is, ironically, algebra. Not so much the grinding, symbol-driven form of algebra taught in school today, but algebra nonetheless. Reading bar graphs in the newspaper is a skill that we should expect high school graduates to be able to do, but nontrivial calculations with data require at least some facility with algebra. Hacker surely knows this, but it would undermine his argument to admit it.
He’s certainly not wrong that some students fall by the wayside, and the way we teach algebra and geometry in the middle grades is largely to blame. Stanford mathematician Keith Devlin wrote a wonderful response to Hacker’s recent piece, pointing out how his ideas may actually be correct but misguided:
Not only did that suggestion [the elimination of algebra from the high school curriculum] alienate accomplished scientists and engineers and a great many teachers – groups you’d want on your side if your goal is to change math education – it distracted attention from what was a very powerful argument for introducing the teaching of algebra into our schools, something I and many other mathematicians would enthusiastically support.
Unfortunately, Hacker undermines his credibility by stating falsehoods. For example, he claims “Coding is not based on mathematics … Most people who do coding, programming, software design, don’t do any mathematics at all.” It may be true that these individuals are not crunching numbers all day (that’s what software is for, of course), but the algorithmic processes underlying coding are the very essence of mathematics. To say otherwise is just delusional.
Hacker also asks, “Would you go to a mathematician to tell us what to do in Syria? It just defies comprehension.” Actually, it shouldn’t. The Central Intelligence Agency and other national security groups employ thousands of mathematicians to analyze data associated with foreign affairs, looking for patterns amid the chaos. So, Hacker is just plain wrong about some things, even if his overall idea has merit.
We’re all on the same team
You see, college math professors know there is a problem with K-12 mathematics. We see the results in our classrooms on campus. As much as Hacker would like to believe his ad hominem assertions about math faculties at high schools and colleges, we really just want our students well-prepared for the beautiful, fascinating and, yes, useful material we have to offer.
Algebra is a beautiful baby; it would be a shame to throw it out with some dirty bathwater.