Saturday, 18th of February, 2006

If you read the science blogs at all you may have come across this by now. A couple of days ago Richard Cohen wrote a somewhat disingenuous article at the Washington Post called “What Is The Value of Algebra?”, in which he addressed high-school dropout Gabriela Ocampo, who gave up after apparently failing algebra six times — quite an achievement.
Choice quote:

Here’s the thing, Gabriela: You will never need to know algebra. I have never once used it and never once even rued that I could not use it.

Actually, choicer quote, the really bad shit:

Gabriela, sooner or later someone’s going to tell you that algebra teaches reasoning. This is a lie propagated by, among others, algebra teachers. Writing is the highest form of reasoning. This is a fact. Algebra is not. The proof of this, Gabriela, is all the people in my high school who were whizzes at math but did not know a thing about history and could not write a readable English sentence.

PZ Myers over at Pharyngula is furious and writes a beautiful piece tearing Cohen to shreds, and rightly so. Well… I was going to suggest that maybe he was overreacting a tad (despite the egregious second quote above, which I’ll get to in a minute) — after all, some people in some positions don’t need alegbra, and sure, you can get through life without having a clue about it (although more on this below). But here’s the pretty scary coda, added a day later from the LA Times:

“I don’t want to be there no more,” she said, her eyes watering from raw onions, shortly before she quit to enroll in a training program to become a medical assistant.

I’m sorry? Gabriela, not only can’t you pass algebra, but you don’t know English grammar, and without basic maths you want to be a fucking medical assistant?!!@!! I don’t know what to say.

More infuriating, though, are Cohen’s other two assertions, the second quote above. Firstly, his proof: ALL the maths whizzes had no idea about history, geography and writing English? Come off it! It’s not hard to point out a few maths whizzes who are perfectly rounded people and write beautiful English to boot — take Ian Stewart, for a start. Then, given that anyone who’s done any architecture, science (including medicine, nursing, pharmacy), computer science, web coding, and the list goes on, would have to have done reasonably well in high school algebra, suddenly we’re open to a huge list of individuals. Let’s just jot a few down: Doug Hofstadter, Daniel Dennett, Richard Dawkins, Greg Egan, Paul McAuley, Charles Stross, Alastair Reynolds, Cory Doctorow, PZ Myers, Chris Mooney… I mean you don’t have to agree or even like with what these people write to realise that they’re quite capable of writing, and — ooh — reasoning. Looks like I’ve refuted your argument, Mr Cohen — but you’d have to have a rudimentary grasp of logic to realise that, and logic, of course, is just a branch of algebra.

So. “Writing is the highest form of reasoning”? Huh? Should these people’s writing be counted as prior to their algebra skills in some way? — that’s a generous interpretation of Cohen’s argument. And it’s a good question; good writing skills are by no means equivalent to good algebra skills. But all that being able to grasp the basics of algebra means is being able to reason abstractly. High school algebra tends to involve on the one hand translating real world situations into abstract formulations, and on the other hand manipulating abstract formulations in order to derive new information. And that’s a skill that’s applicable all over the place — as suggested above, a paramedic is going to have to be able to think on the fly about, for instance, how much dosage of a drug to give to someone, based on various factors (patient’s weight, age & gender; length of time since trauma; etc). Anyone involved in public policy will have to be able to reason about abstracted qualities and quantities in order to make decisions that matter to all of us — and any member of the public who wants to understand matters of policy in order to make judgements about policies to vote for is going to need a bit of that ability too.

I’d hate to seem like a killjoy here (or, as thesaurus.com suggests, a fussbudget - cute!), so let me remind you here that I’m a musician, as well as a comics devotee and an avid reader. By no means do I think that numbers and formulas are all that life’s about. But abstract reasoning runs too deep to be dismissed as unnecessary for practically anyone wanting to engage in the world, and I think Richard Cohen is seriously deluding himself if he thinks he’s never used those skills in his adult life.

Abstract reasoning is integral to music-making and fine art too — I’m by no means the only person I know even from my single university year who was deeply involved in music at the same time as majoring (well, co-majoring) in maths. My other major? Philosophy. Look — I can string a sentence together in English! Pretty good for a maths geek, hey?

That said, should algebra be compulsory (and this is the issue, from Cohen’s article: “the L.A. school district now requires all students to pass a year of algebra and a year of geometry in order to graduate”)? I’m not sure. In Australia (at least in New South Wales), the year after I did my HSC the Board of Studies decided to make it compulsory not only to do (and pass) English but to include the mark in your aggregate total. [Explanation for the puzzled: you can take more units than the 10 that count towards your final mark; for the last 14 years two of the 10 that count have had to be English.] On the face of it, this sounds fair enough — we want our university students to be able to string words together in the official language of this country. The trouble is, English for the HSC has nothing to do with learning to reason, or learning anything about language (Linguistics? Grammar? What’s that? Phonetics? As if! How about History of English? Unlikely!) It’s just literature studies — learning lots of quotes from texts, and worse, these days, regurgitating some half-understood bits of po-mo literary theory. How schoolkids are meant to grasp post-colonial theory or Marxist interpretations of Shakespeare without any historical context is beyond me (and beyond them, and beyond their teachers…)
In that context, I’m strongly against English being compulsory; I did badly in it because I hated learning quotes from texts, and didn’t like most of the texts we studied, and frankly had philosophical positions that ran counter to the conclusions my teachers wanted me to draw from them. First year in Uni, I was getting distinctions and higher in my philosophy essays, so it’s not like my English skills were lacking.

That’s just me, but it does make one pause to think, briefly, about whether a kid who’s just no good at algebra is still smart enough to be allowed to pass their matriculation. But I’m not really sure it’s a valid one. In my case, had English been compulsory, I would’ve made sure I did well enough, one way or other. And I’m sorry, Gabriela, but if you really tried, and tried, to pass that algebra subject, six times in six semesters, and you still failed, then maybe your place is behind the counter at that Subway branch, and you might just have to give up the dreams of becoming a medical assistant. Or you’re just going to have to try a whole lot harder.

Notes: i) “Try a lot harder”: Lest I seem too unfair here, a) I know, Gabriela can still achieve much more than being a fast-food salesperson; but b) I’m serious about trying a lot harder. Most people who can’t pass high school maths are just deathly afraid of it. Getting over one’s fear (and therefore one’s hatred) of maths goes a long way towards managing to at least scrape through. And finding a sympathetic someone to tutor one, face to face, is going to help a lot too.

ii) Oh that’s right! I knew I wanted to comment on something else. Lest we think Cohen’s just got an axe to grind and isn’t himself particularly ignorant, consider this:

You will never need to know — never mind want to know — how many boys it will take to mow a lawn if one of them quits halfway and two more show up later — or something like that. Most of math can now be done by a computer or a calculator. On the other hand, no computer can write a column or even a thank-you note — or reason even a little bit.

This is an incredibly foolish statement. You don’t even have to generalise the problem in the first sentence to deny it — the sort of logistics required here come up in all sorts of jobs; if you want to avoid having to think about such problems, then throw away your ambitions of responsible employment.
How about computers and calculators, then? Here, especially, Cohen is leading his audience up the garden path. Anyone who wants to write a computer program, or understand a script they want to put in a webpage, will have to have a solid understanding of algebra, but you don’t need to go for such a (relatively) esoteric example: anyone who wants to put together an Excel (or substitute your favourite program) spreadsheet needs to have a basic understanding of algebra in order to work out the formulas to relate sets of cells to other cells.
You don’t need algebra because computers can do it all now? Talk about topsy-turvy! Computers are no better at solving high school algebra problems than they are at writing opinion pieces for the Washington Post — the problem’s the same; computers can’t (yet) comprehend the abstract concepts because so much social context is required. But a smart person can use them to do wonderful things, as long as they’ve mastered abstract reasoning themselves. The sort of reasoning that Cohen wants isn’t an indivisible thing that’s based entirely in writing skills; it’s a hybrid, requiring vast general knowledge from experience, plus the skills of abstract reasoning — logic/algebra — and communication — “writing”, I guess, however exactly we define that. However we define it, we’re not going to be able to separate logic from it if we want it to be the “highest form of reasoning” (or, hey, any form of reasoning).

iii) Addendum: Janet at Adventures in Ethics and Science puts the blame fairly and squarely on the teachers, and it’s hard to disagree.

4 Responses to “On Algebra”

1. Tim says:
   February 19th, 2006 at 10:40 am

   It comes down to the devaluing of education in society in general; Nelson’s university reforms, for example, are geared to making university a place of vocational training rather than a place where knowledge and learning is valued above everything else.

   I can’t imagine that she’d be able to get through that many university courses without algebra. The point of learning is not whether you need to know something in your daily life, though - I don’t think I’ve ever directly used my knowledge of ancient history in daily life - but that knowledge in general enriches you - like you say, if you have no concept of algebra, you have no concept of logic, whereas knowledge of history makes you see society in a different way.

   Knowledge of the canon of English literature is important too; taught well, you can learn a lot from Shakespeare. I agree that there should be more emphasis on English skills as opposed to literature - certainly the quality of undergraduate essays I’ve read recently is quite shocking. But there are benefits in English essays - the high distinctions you got at university were partly due to learning how to write essays in English, I’m sure - any English teacher worth their salt would have grounded you in the technique of writing, the logic and structure and rhetoric.

   As to whether it should be compulsory, I suspect that both it and maths should be compulsory - maths was effectively compulsory at my (selective) high school, by the way, and at many others - because I believe that people should have a rounded education, even if they wish to specialise.

   tim.

2. Peter says:
   February 19th, 2006 at 4:02 pm

   Thanks for that, Tim! Educational as vocational training is a sad, sad thing. There’ll still be people like you & me who choose their subjects entirely because they’re interesting, and get themselves a rounded education out of it, but it’s hardly something that’s encouraged these days.

   And due to having had a very good rounded education, I do have a good idea of history, and therefore a good context in which to understand my society. Indeed, regardless of how much I hated English at school (due in no small part to having abominably bad teachers all the way through high school), I know my Shakespeare, and know enough about the classics of the canon. I have to say, though, that I was doing well in philosophy at uni because of skills taught me by my mother (linguistics teacher @ UNSW) and in other subjects (music, French, Latin, etc) as well as my own reading of philosophy & science rather than from my English teachers. Sad, but somewhat true.

   I think you’re right that both should be compulsory, although whether the mark should have to count? Probably… it’s a tricky one. Making the mark count means making your performance in the subjects count as well as just ensuring you scraped a pass. I guess we should care about that. It’d be nice if we didn’t have to care so much about the minutiae of the marks anyway, but we have so many people trying to get into the Unis these days that I can’t see another way of doing things. Direct entrance exams held by the individual institutions?

3. Peter says:
   February 19th, 2006 at 4:09 pm

   I was going to say, also, that one of the reasons that students hate maths so much is that so many maths teachers are so dire. And the reason for that is that education is so undervalued in our society that becoming a teacher is what you do when you fail at everything else. Teaching should be one of the most desired vocations there is. It should stem from a love of interacting with young people, and from a passion for communicating ideas. Above all it should be about inspiring students to be interested in the subject, interested in learning.

   (I guess the other reason students hate maths is that it’s too much like hard work. And seems uncool. But inspired teaching is the answer to this too.)

4. Drinkwater says:
   March 17th, 2006 at 5:27 pm

   not to nitpick but Cohen is saying that there were many people at his school who could do math but not English, not that all of the kids who could do math couldn’t do English - he never says that the one implies the other. Nonetheless he should learn how to write a readable English sentence himself, else he’s even worse than those math whizzes he insults. And his standards of proof are far lower than anything in math or science - where’d he get them? Everything else he says is, of course, complete and total crap. You do have to feel sorry for the girl - though anyone who wants to become a medical assistant after failing Algebra 1 several times should seriously consider psychiatric help. Let’s just agree that Cohen is a nut job bullshitter and leave it at that.