Is Algebra Necessary? – Seriously, is that even a question?

Andrew Hacker, political scientist extraordinaire, seems used to making waves about the utility of math education. I originally saw his 2012 New York Times piece (‘Is Algebra Necessary?‘) a few years ago and did not think too much of it, apart from spurring myself to furiously critique everything that was wrong and idiotic but it was never published. Now, it seems that his deep concern over math education has created an urge to write a book about the very topic, creatively titled The Math Myth: And Other STEM Delusions. I’m not sure whose advise it was (or lack therefore) to make such a grammatically spurious title (colons don’t just suddenly become semicolons after all), but I am sure that it fits with his overall approach to anything with applied intellect (it is so very hard to think).

The entire hype – with even Scientific American getting in on the action – has made me re-evaluate my original critique. No doubt, from the sounds of the groans of all those mathematicians who have read it, the book is simply an extended version of the original New York Times piece (even the cover is identical!). Although, at $16.95 for 240 pages worth of extended rant I would seriously question the notion that the book could even slightly increase your utility function, even if it did produce some schadenfreude  with regards to said author’s abilities (grammatical or otherwise).

Anyway, here is my original piece, faithfully reproduced:

Teachers lie when they say there is no such thing as a stupid question, as I soon found out with the lackadaisical title of Andrew Hackers “opinion” piece for the New York Times: Is Algebra Necessary?. Yes, he was being serious. It’s not just the title that makes one roll on the floor in a fit of laughter; the author seems quite intent on contradicting himself, stringing non-sequitur sentences together, and just generally showing extreme ignorance. He makes some very amusing statements, of which I will kindly share the most uproarious.

  1. “But the more I examine them [the defences of Algebra], the clearer it seems that they are largely or wholly wrong — unsupported by research or evidence, or based on wishful logic.”

It is a little unclear why he should mention research or evidence; surely if one has done some research it would at least include evidence? It seems the author is a tad overzealous in applying the set of three rule in writing, and also seems to have forgotten to mention said research (or evidence) that has so enlightened him.

  1. “Making mathematics mandatory prevents us from discovering and developing young talent. In the interest of maintaining rigor, we’re actually depleting our pool of brainpower. I say this as a writer and social scientist whose work relies heavily on the use of numbers. My aim is not to spare students from a difficult subject, but to call attention to the real problems we are causing by misdirecting precious resources.”

I don’t need to make a comment for this one.

  1. “Even well-endowed schools have otherwise talented students who are impeded by algebra, to say nothing of calculus and trigonometry.”

Uh…this one actually makes one speechless. It seems that Mr. Hacker quite convinces himself that one could actually do without calculus and trigonometry. Wait, it gets better.

  1. “It’s true that students in Finland, South Korea and Canada score better on mathematics tests. But it’s their perseverance, not their classroom algebra, that fits them for demanding jobs.”

What Mr. Hacker is probably referencing is the PISA (Programme for International School Assessment) table which assess fifteen year olds performance in maths, reading, and scientific literacy. The United States currently (as of 2009) performs below the OECD average for maths (see for details). So, the cure for such poor performance, coming from the richest country in the world, is to set the bar lower? It gets worse.

  1. “Of course, people should learn basic numerical skills: decimals, ratios and estimating, sharpened by a good grounding in arithmetic.”

Shouldn’t that be the basic minimum requirement?  He might change his mind once he realizes that calculators exist.

  1. “Ours is fast becoming a statistical age, which raises the bar for informed citizenship. What is needed is not textbook formulas but greater understanding of where various numbers come from, and what they actually convey.”

Mr. Hacker doesn’t seem to quite grasp that statistics is more than the regurgitation of shiny percentages, you actually need…algebra. Plus calculus. It seems his second statement has turned into a kind of art appreciation for mathematics (wait, does that even make any sense?). In fact, in order to show that two plus two is four and not five you need some sharp maths.

  1. “What of the claim that mathematics sharpens our minds and makes us more intellectually adept as individuals and a citizen body? It’s true that mathematics requires mental exertion. But there’s no evidence that being able to prove (x² + y²)² = (x² – y²)² + (2xy)² leads to more credible political opinions or social analysis.”

It just makes you competent.

  1. “Many of those who struggled through a traditional math regimen feel that doing so annealed their character. This may or may not speak to the fact that institutions and occupations often install prerequisites just to look rigorous — hardly a rational justification for maintaining so many mathematics mandates.”

The definition of annealed according to Oxford Dictionaries is to: “heat (metal or glass) and allow it to cool slowly, in order to remove internal stress and toughen it.” That sounds like a good thing.

  1. “I hope that mathematics departments can also create courses in the history and philosophy of their discipline, as well as its applications in early cultures.”

Right, we can start with the Indians who first developed the concept of the zero, but that would require knowing algebra. Uh…well, then we could learn about the Greek mathematicians such as Pythagoras, which would require trigonometry. Maybe we just skip him and go onto Euclid; oh, that would mean studying geometry. Let’s just forget the Greeks and move onto more modern times- Gauss, no; Euler, no. Isaac Newton? The understanding of calculus is required. I rest my case.

  1. “Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions.”

There is a funny story about long division; long multiplication and long division are impossible to do without the concept of a zero. It simply doesn’t work when using Roman numerals.  So, in the end, it rests on algebra.

There you have it; the ten most idiotic phrases Andrew Hacker made in a single article. Certainly when he mentioned that he was in the “social sciences” I thought he was maybe a sociologist or a psychologist, however it turns out that he is a ‘political scientist’. He also seems determined to butcher the English language; one thinks when he might decide that grammar is now defunct, or that studying Shakespeare is a waste of time. He punctuates his writing with annoyingly short sentences, inserts commas so haphazardly that one assumes he blind folded himself before adding them, and makes the most unimpassioned arguments. Is there any other way to say “I’ve found myself moving toward the strong view that we shouldn’t [teach Algebra]” without causing someone to wonder how this movement takes place? Could he not have written: My ideas on this subject have progressed to the degree whereby I firmly believe that it need not be taught? Not that I think he is right, I’m just playing Devil’s advocate.



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