Hackery about educationPosted: July 31, 2012
I 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.