### Back to basics

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 3x8=24; rather, what appalled me was that she lacked the ability to figure out the value of 3x8. 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 3x8 *was*, she did not know what 3x8 *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.]

I think something cut this one off early at the end; I’m not used to seeing you end sentences with “this is” (without any punctuation, even).

Without going back to count the people claiming it, are you counting me as one of the people who claimed to never learn their times tables? Just for the record, that’s not actually what I claimed - I claimed that I never sat down and memorized them (though even that wasn’t due to lack of effort on the part of my parents and teachers). I learned them quickly enough as soon as I started having to use them for something other than timed drills, because I was actually using them for something (something interesting, even) for which they were a useful thing to know.

Of course, the problem with trying to apply this to your complaints is that not everybody seems to see “because it’s fun” as a good reason to do math.

But I was appalled not at the fact that one of my students didnâ€™t know off the top of her head that 3x8=24; rather, what appalled me was that she lacked the ability to figure out the value of 3x8.Yes, that would be the real problem. And I think it’s a problem of schools being insensitive to the need to motivate students, and to the idea that different people have different learning styles. Your student presumably went to elementary school and so presumably somebody tried to teach her the time tables. If she failed to learn how to multiple even by making groups of dots on paper, would

moretimes tables have helped her? I don’t think so. I don’t think you’re saying that that would have helped, either, but itiswhat the conservative back-to-basics-in-education people seem to be saying. And that’s unfortunately, because it’s easy to blame the problems with the educational system on “hippie liberals who don’t want to teach the 3 R’s” (paraphrasing here), or on lazy students who would rather play video games. It’s much harder to askwhythis particular kid’s teachers didn’t have the skills they needed in order to get the concept of multiplication across to herin particular.Oops, I had had this semi-post on draft mode for awhile, and meant to save it as private, but that didn’t work. Now that it’s been viewed, I’ve edited it so that it makes some more sense (though it’s still a bit scattered, which is why I put it on the back burner to begin with).

Kirsten (and I swear it’s just a matter of time before I get your name wrong, as I know tons of Kristins and Kristens and Kirstins and such, so apologies in advance) - yeah, what really floors me is that we apparently have a system of education in which it’s possible to not learn, some way or other, what 3x8 is. Not that the younguns haven’t been exposed to enough flashcards (I wasn’t) or seen enough dots on paper (I didn’t), but because their lives haven’t followed a path in which 3x8 was the sort of thing that they saw rather often and, that figuring was as natural as figuring out how to conjugate a simple verb.

An example of something that I think would be worlds more useful (and fun!) than flashcards and the like, is cooking or baking with every kid who’s old enough not to drink the measuring cup full of vegetable oil. I’d like to see a study done on

adultswho think that 1/3+1/2=2/5. Betcha hardly any of them, at the age of five or six, helped mom or dad baked a cake that called for a third of a cup of sugar and a half of a cup of flour.While grading graduate level homework assignments in a radio-engineering course, I came across large numbers of students who had serious problems using logarithmic quantities: dB, dBm, and dBW. These “units” have the lovely feature that, because they’re on a logarithmic scale, unit arithmetic looks a little odd. They’re related like this:

0 dBW = 0 dBm + 30 dB = 30 dBm = 1 W

Not knowing what dBm or dBW mean at the beginning of a radio systems class is understandable. Taking a little while to get used to handling the different feel of these units is also understandable. Handing in several assignments without deciding that it would be important to understand the units in which everything is specified gets to be questionable. A class full of graduated electrical engineers who don’t know when a quantity is unitless, a voltage, or a power is downright scary (and par for the course).