Hackery about education
Posted: July 31, 2012 Filed under: Uncategorized 5 CommentsI must admit that Andrew Hacker has been a byword for fatuousness to me for quite some time. His latest, however, is especially meretricious because it plays directly into what so many people desperately want to believe–that ignorance of algebra is AOK, so we shouldn’t bother trying to teach it. Apparently, algebra drives people to drop out of high school and fail competency tests, and these are Bad Things we can avoid by no longer teaching or testing it. (Next up–placing the thermometer in an ice bucket to cure your fever.)
Hacker’s most superficially compelling argument is that almost no workers use algebra in their day-to-day work, including a large number of people working in technical fields. (In a parody of Deweyism, he does want students to learn “citizen statistics” and “quantitative literacy” so they can understand how the Consumer Price Index is put together, although how you can understand a weighted average without understanding algebra is beyond me.) In case someone brings this job-relevance argument up at a party, here are some quick responses:
1. Jobs don’t require algebra largely because there aren’t very many people who are good at it. If no one could read, jobs wouldn’t require literacy, either, but there would be a significant productivity loss in many cases.
2. In the novel and movie The Caine Mutiny, the intellectual (though evil) character points out that in the Navy “everything was designed by geniuses to be run by idiots.” We could equally say that in the modern world everything is designed by people who know algebra to be used by people who don’t. The fewer people who know algebra, the more unnecessarily elitist that world will be.
a) It’s almost impossible to understand financial relationships without being able to manipulate algebraic formulae. You can plug and chug different numerical values into a calculator or spreadsheet formula, but you’ll have no idea about the sensitivity of results nor will you be able to check or modify the formulae.
b) Probability and statistics are doable, in a very limited and rote way, using prepared templates, for people who don’t know algebra. Anything beyond that, though, is impossible to figure out if you can’t manipulate the symbols properly. Would you trust someone to run a regression or interpret its results if they didn’t know in their bones what a coefficient represented, much less a log-linear relationship?
c) Some functional relationships can be grasped by drawing graphs without algebraic manipulation. If you need more than two dimensions or want to prove which way the curves have to move when you change assumptions, though, you’re going to have to be able to do some algebra.
d) Lots of non-STEM jobs involve spreadsheet formulas of various kinds. Media planning, job-cost estimation, tax planning, budgeting, etc. are common sorts of work for “office” employees. The people who use these spreadsheets probably could get by without algebra, but anyone who wants to write one is going to be at a big disadvantage without it.
3. It indeed would be a lot easier for people to learn algebra if it were contextualized better by being tied to applied topics in other subjects. But that approach would result in algebra becoming a more important step along the way to passing science, economics, and other courses rather than a less important part. Moreover, some of it requires rote memorization just as does learning the multiplication tables or irregular verbs in a foreign language. It will not always be fun, but some necessary things just aren’t fun.
4. Last I checked, very few jobs require writing or reading Elizabethan English, knowing about Reconstruction, drawing or painting, worrying about environmental issues, knowing the parts of a frog or flower, or understanding why potassium burns when placed in water. I bet I could reduce dropouts and improve test performance by removing those topics from the curriculum and who’d know the difference? Voc-ed uber alles!
5. Hacker’s earlier work questioned the cost/benefit ratio of college. If my hypothesis about the higher education market is correct, then Hacker’s suggestion to stop teaching algebra in high school would fuel the very phenomenon he decries.
StrategyProfs.net 
The Hacker article was one of the saddest articles that I have ever read. Where is his sense of competition and lust for knowledge? It’s like saying, “if shooting three pointers from the arc on a basketball court is too difficult, then make layups worth 3-points since it will be better for the player’s spirit.” In fact, this type of thinking will make the U.S. job markets much less competitive, which in turn will make offshoring for talent more attractive (than it is currently) and with that goes all of our hope for future competitiveness of this country.
The bigger question is, why is Algebra such a problem in the U.S.? In fact, it seems like anything that requires mental rigor or is remotely abstract is completely unattractive and deemed useless in this country. Why? When I was growing up, my friends and I would dream of being astronauts, doctors, and scientists. Today kids want to be Kobe Bryant and Lebron James. Is the entertainment industry to blame? Is it parents? Is it teachers? Is it capitalism?
Though I have my own theories, the one thing that is important here (which Hacker clearly missed – either intentionally or naively) is that we are not asking the right questions.
Mathematics is the most beautiful discovery of mankind (though some believe that mathematics is invented – I don’t) and diluting it any more that we already do in our schools is, in my opinion, a crime. The facts are (as professor Postrel points out), without mathematics you can NOT learn some of the most fundamental things we need in life today to function. From finance to chemistry.
Instead of not teaching it as “Hacker the Clown” suggests, why don’t we incentivize students by offering more credits for math (or more generally STEM) classes. So if you take more of these classes (and pass, of course), you can graduate earlier. Perhaps, aligning incentives (what kid doesn’t want to do less schooling), getting parents involved (which may include offering math illiterate parents classed in mathematics), and having higher standard for teachers is a more honorable and effective approach to the U.S. math epidemic.
The dispute as to whether mathematics is discovered or invented has its roots in antiquity. In fact, those who take the position that mathematics is simply discovered are called (slightly derogatorily) Platonists.
I’m well aware of that…I have my own argument as to why Platonic philosophy better aligns with my notion of mathematics, but that would be outside the scope of this discussion. I do, however, appreciate your wisdom.
I’m all for encouraging students to study all kinds of knowledge, but why do we push students to learn things that do not mesh with their abilities when it only wastes their time?
I mention this because I have found by experience that no amount of effort will enable me to do algebra. Algebra simply doesn’t work for me. I still understand most math and the sciences, perhaps because I am extremely strong in geometry. More to the point, beyond enough algebra to understand I would never understand it, I wasted a good deal of time and energy that would have been better directed elsewhere.
Or in other words: maybe we should offer algebra to high school students, but not make it a requirement for those students who are never going to be able to make use of it anyways? Maybe we should do that with all the subjects? In fact, maybe school shouldn’t be mandatory at all – after all, the literacy rate was higher when school was NOT mandatory.
I am more than sympathetic to arguments against excessive coercion and homogenization in education. I would have been very happy not to have grades when I was in school.
As educational advice, however, I would recommend trying hard to learn algebra at an early age. If a student can’t do it at all, even when properly taught, that’s one thing. But just writing it off as a luxury for a small number of techies, as a default position, is a terrible idea.