The other day, I wrote about my university math students not knowing their times tables or how to add fractions. (By the way, you should go read the excellent comments to that one, which I will reply to eventually – where did all of my awesome commenters come from?) A few days earlier, Erin O’Connor, an English-prof-turned-high-school-English-teacher, posted an English teacher’s equivalent: grammatically ignorant English students. There are plenty of parallels:

Most high school students these days are not on the grammar curve at all. The parts of speech are largely mysterious to them; the rules of punctuation and agreement are likewise unfamiliar. Semi-colons, colons, and dashes do not come into play in their writing because they do not know what they are for…

Don’t get me wrong. Kids today are as smart, creative, and sharp as ever. Their grammar deficit is not their fault. They can’t be blamed for what they were never taught. It’s increasingly unfashionable to emphasize grammar and the rules of syntax in school, the reasons ranging from the hang-loose notion that the rules of usage are confining and binding and irrelevant anyway since language is a living, breathing thing, to the feel-good notion that grammar is boring and mind-numbing and kids will be turned off to reading and writing forever if they have to learn it.

The notion that “language is a living, breathing thing” doesn’t apply to math; math is seen as boring, and in need of sexing up (hence the skipping over the basics), and all of the people I know who love math and actually do see it as living and breathing are absolutely militant about making sure that the basics of math are taught. But just as the parts of speech are mysterious to Erin’s students, the whole *notion of quantitative data* is foreign to mine. Two of my commenters from the previous post confessed that they, too, never learned their times tables, but both are comfortable with math.

But I was appalled not at the fact that one of my students didn’t know off the top of her head that 3×8=24; rather, what appalled me was that she lacked the ability to figure out the value of 3×8. She left her calculator in her car, and therefore she would not know how to compute that quantity. She could not count groups of eight (or three) on her fingers. She could not make eight and eight and eight marks on a sheet of paper. Not only did she not know what 3×8 *was*, she did not know what 3×8 *meant*. And this is the real issue; students not getting the basic, basic aspects of what mathematics means.

Year after year, I’m reminded that my students, almost to the individual, are nigh incompetent when it comes to word problems. There’s this basic inability to translate quantitative data into useful equations. I’ve taken to reminding my students at the beginning of every section of word problems, “an equation is a relationship among quantities. So we need to figure out what quantities we’re interested in, and find relationships among them.”

I make a point of emphasizing this because, based on my students’ “solutions” to word problems on tests, their thought processes are something akin to the following:

Okay, let’s see, this question says that it takes me twice as long to get 25 km upstream, with a current of 3 km/h, as it does to get downstream. Okay, so I have a 25 in my question. And a 3. So I need an equation with both of those. How about…25+x=3? No, because 25 is

biggerthan 3. So – 3+x=25. No hold on, there’s something about “twice as long”, so…multiply something by 2? 2(3+x)=25? Yeah, let’s try this, that’ll work.

My students, almost to the individual, have little idea how to relate word problems to mathematical equations. The parts of math, in other words, are largely mysterious to my students, and it’s a crying shame that this is still the case in university.

[Timely update – Joanne Jacobs reports that LA schools are beginning to teach algebra in elementary school. The article is annoyingly contentless (what are these algebra games the kids are playing? Inquiring minds want to know), but dammit, it’s about time; I’ve been suggesting this for *years*. It’s completely ridiculous that every single first grader knows that two dogs plus three dogs equals five dogs, but then in seventh grade they’re completely perplexed to see that 2d+3d=5d.]