In which modernity is stupid

You may not be aware of this, if you’re not a math teacher or a middle school student: did you know you can just, like, Google any equation, and it will not only solve it for you but it’ll actually explain how to do it? I’ve talked about calculators here before, and my policy remains more or less the same: that I allow calculators on any assignment where calculation is not the point, because I don’t want a kid’s issues with basic multiplication to get in the way when they’re trying to internalize the Pythagorean theorem.

This one is … a bit more annoying. I mean, sure, it explains how to do the problem, which is an actual advantage over calculators– it’s not like the calculator is going to walk you through the multiplication algorithm or anything like that– but the Venn diagram of the types of kids who are going to Google equations rather than solving them and the types of kids who will read explanations is two completely separate circles. Also, I’m a little hamstrung right now by the fact that I need to present my assignments on computers; the easiest way to ensure that more of them do the work properly is to simply present the assignment on paper and restrict device use during those classes. I could also require them to give me answers as decimals, since Google always puts theirs as fractions, but that’s just going to add a different confounding factor to my grades, dragging down the kids who don’t know how to convert fractions to decimals and the kids who don’t read directions.

There is also the possibility of simply writing more complicated assignments than a list of fifteen equations to solve, of course; I could do word problems or any number of other things, but the problem is the specific skill I need them to have actually is solving equations. I need them to understand the logic of modifying both sides of an equation at once, the idea that constants and variables alike can be moved willy-nilly from one side of an equals sign to the other as needed, so long as you follow the rules properly … because if they don’t get this shit at this easily-Googlable level, life’s going to suddenly get much harder in high school when they hit equations that you can’t, at least yet, easily feed into Google. I think anything requiring a superscript or any actual math symbology might be a problem, for example, although I haven’t tried to test that.

I’m going to choose to ignore this particular problem, for the moment. There are ten instructional days of school left and I have two days of equations practice planned before we get back into systems, and I’ll make sure to write those assignments so that they’re not as easily Googled. Frankly, most of the kids who are cheating have grades so deep into failing territory that it barely even matters, so I’m not going to waste the energy necessary to stress about it other than maybe barking at them about it tomorrow. It will, children, actually hurt you much more than it will ever hurt me if you don’t get this stuff. You may think I’m training you to solve equations, which, true, you are unlikely to be presented with as an adult! However, mastering basic fucking logic is a life skill, as it turns out.

On calculators

20131025-172618.jpgA friend on Facebook just pointed me at this article from the Atlantic. Well, not me specifically, but… y’know. Entitled “The Great Forgetting,” the article discusses the ways in which computer automation of various tasks has affected the ability of us reg’lar folks to learn and remember how to do complicated tasks. The article begins by discussing a few recent plane crashes in which the autopilot failed and the pilot, panicking, did exactly the wrong thing and ended up crashing the plane.

What really caught my attention, though, was his comment that the article made an argument against use of calculators in math classes. I’m not convinced of that. I don’t doubt that the author’s basic premise is strong; automation has eroded our ability to do certain things. To pick a less important example, I used to have dozens of phone numbers memorized; nowadays I’m only able to recall my wife’s with difficulty, and I couldn’t tell you anyone else’s if my life depended on it. Now, of course, I’m certain I could recapture this ability; I simply haven’t bothered. The author also mentions things like mapreading; I’d be more inclined to buy that if I thought most people were ever able to read maps. Most people were never able to read maps.

(Similarly, spellcheck. No, spellcheck isn’t eroding our ability to write. Over all of human history, most people haven’t been able to spell or write worth shit. Spellcheck has manifestly not made this worse. What has happened is that the digital revolution has exposed us to much much much more of our fellow humans’ shitty attempts at writing. I can show you some documents in Biblical Hebrew with misspellings if you don’t believe me, and for those fuckers writing was their job.)

Another interesting example he brings up, albeit briefly, is surgeons using machines. I am not a doctor, obviously, and if I’m getting this wrong feel free to correct me, but I believe that most surgeries that are being done via computer nowadays are surgeries that are too goddamn complicated to be done by regular humans with our clumsy hands. My mother had surgery done on her lower spine a few years ago. The surgeon was startled at the extent of the damage, and likened fixing her back to peeling apart soaked sheets of wadded-up tissue paper. There is simply no fucking way that a doctor could have uncrushed her spinal nerves and delicately teased everything apart and put it back in the right place with our clumsy human monkey paws. The surgery didn’t replace human skill; the surgery enabled the human skill. Call me when we can’t set limbs because the computers do it better. (Which might actually be coming: I’ve seen a few articles on 3D-printed custom casts, which look like spiderwebs and are pretty freaking awesome.)

I would argue that, used properly, calculators are less like digital address books and more like surgical tools. I want my kids to be able to do math in their heads; you’re just going to have to take that on faith. I would much rather work with kids who don’t ever feel like they need calculators. But the simple fact is that (particularly in my special ed class, but not limited to them) I have a number of students– hell, probably most of them– who are uncomfortable, to put it mildly, with basic math facts. I have a few who do not appear to know they exist. In some cases, it’s probably because the kids are just lazy and/or disengaged from school. In several it’s because they have sub-60 IQ’s and are never going to be able to memorize basic math facts. It’s just not gonna happen.

Here’s when I allow calculator use in my class: whenever the calculation itself is not the point. If we are working on multiplying decimals, for example, I refuse them calculators. My more severe special ed kids will get cheat sheets for these, but no calculators. Any other time, though, when there’s process to be learned, I allow calculator use– because otherwise the calculation gets in the way and actually inhibits learning of the material I’m trying to teach.

A specific example, because we actually just finished this: the math my seventh graders were covering for the last few weeks involved similar triangles and metric and customary conversions of length, mass, and capacity. So, for example, I give you one triangle with legs that are 11 and 5 inches and a second where the long leg is 18 inches and I want to know the shorter leg, or I tell you that a given length is 12,203 feet and I want to know how many miles it is, rounded to, say, the nearest hundredth.

This is complicated math if you don’t know how to do it. It has the power to break their brains– even the smarter ones– early in the process before the methods involved really sink in, and if they are already struggling with basic facts it is manifestly impossible without a calculator. If you’re struggling with 5 x 7, you are never in a million years going to be able to divide 12,203 by 5,280. Even the kids who are good at math revolt at that kind of long division, with good reason: it’s a huge pain in the ass. It also introduces a whole bunch of new sources of error, all of which inhibit their ability to learn the actual material I want them to learn. I need them to learn how to set up equivalent fractions and figure out that 18 is (checks calculator) 11 x 1.63 repeating and that therefore you ought to multiply 5 by that same number to get the bottom leg, or that since you’re converting from a large unit to a small unit you need to divide and not multiply and then to (hopefully) remember or (acceptably) accurately look up that there are 5,280 feet in a mile and divide the two numbers in the right order– because that’s a mistake they make too, and if they divide 5,280 by 12,203 I need them to notice that the answer doesn’t look right and figure out why.

One check I’ve been using with similar triangles all week is to divide the long leg by the short leg of both triangles once they’ve got them figured out, and to make sure that they get the same number both times. The smarter kids took to this right away; the ones who are still struggling resist double-checking their work, but will when I remind them. This is already a fight, in other words– why would I make it twice as bad by insisting that they do both of those long division tasks manually? No way. They just won’t do it, and they’ll not be attending to their own precision with the rigor I need from them. Even with my brighter kids who might not need them, the sheer speed advantage calculators afford means that we can do more work with complicated mathematics than we might otherwise be able to if I had to wait for them to manually do every step of the problems.

In an ideal world, none of this is necessary, because my kids all love math and don’t have any preexisting disabilities (or just disinclinations) with math and I don’t ever have to worry about it. Or, in a slightly less ideal world, I have the time to work with these kids individually or in small groups and I can magically get them back on grade level by the end of the year. And I have some success stories in this regard– I can think of about half a dozen kids who were low but not necessarily special ed who were constantly insisting on calculators in sixth grade and now 25% of the way through seventh grade really don’t seem to need or want them anymore most of the time.

But for a lot– arguably too many– of my kids, and for millions of kids across the country, that’s not the case and it’s never going to be. I have to keep these kids on grade level as much as humanly possible. And regardless of whether I like it or not, that is just not possible without calculators.