A serious question

When was the last time you had to do long division?

Let me take a second and define my terms here– by “do long division,” what I mean is that you had to solve a division problem that you were unable to do in your head, where a quick estimation wasn’t acceptable, and where calculators of any kind were not available– like, you actually had to take out a pen or pencil and a piece of paper and actually use the algorithm to work the problem out to get an answer. Bonus points if you weren’t able to end with a remainder and actually had to solve the division out to decimals.

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.

Arithmetical exegesis

20131011-180914.jpg
This one’s interesting. Same kid as last time; he’s actually got it together a little bit more at the moment, most likely because I glued myself to his side the second he got to the board and coached him through when he needed it. The problem in question is 8 5/12 + 11 1/4; note a few things:

1) Correctly adds eight and eleven to get nineteen. This represents progress!
2) Recognizes that 1/4 needs to be converted to twelfths in order to add the two fractions, and– amazingly, to my mind– that he needs to multiply the numerator AND denominator by three to achieve this, and then does so correctly;
3) Successfully adds five twelfths and three twelfths to get eight twelfths.
4) Spells “mark” as “mork.” Can’t win ’em all.

Then an interesting thing happened. I asked him if he needed to do anything with 8/12 and after thinking for a second he came up with the word “reduce.” However, despite having just multiplied three and four to get twelve, he absolutely could not figure out that he needed to divide by four, nor could he successfully divide either eight or twelve by four. Note on the far left of the picture, where he’s tried to divide it, figured out that four goes into eight twice, written the eight underneath the other eight without actually putting a “2” at the top of the problem, subtracted eight from eight to get zero– and then informed me that eight divided by four was zero.

(gets interrupted by customers, promptly makes a subtraction mistake while redeeming tickets)

Harder to read is at the bottom of the picture where he tries to divide twelve by four. He first thinks the answer is two (but doesn’t write it up again) then borrows from the ten digit so that he can make the ones digit… twelve, again, which is where I stopped him and pointed out that he’d already gotten that answer by multiplying.

Note also the rogue seven near the last division part. I don’t know why that’s there, but it’s intentional; he said “seven” when he wrote it.

Clearly we need to work on long division a bit. It’ll be interesting to see how many other issues that ends up clearing up.

On being smart

photo

One of the things that’s really hitting me with my Algebra kids this year is just how unused they are to having to work in class.  These kids are smart, right?  And they’re used to being the smart kids, and with only a couple of exceptions they’re used to thinking of themselves as smart kids; it’s part of their self-identity; something they’re proud of.

Smart kids are supposed to get stuff.  School’s not supposed to be hard for smart kids.

Literally the first thing I said to these kids when they walked into my room on the first day of school was “Welcome to high school.”  I’m walking a fine line here; I’m trying to push them as far and as fast as I can without breaking any of them, and it’s an interesting and delicate dance to be involved in.  I’m thinking about this because I graded a mid-chapter quiz today, and I’m trying to figure out what to do with the kids who didn’t do well– some of them are clearly smart kids (remember, I’ve had everyone in this group before except for about three of them) who are so unused to having to ask questions in class that I think they’re actually ashamed to have to do so.  I gotta work on that.  By and large, considering the volume of stuff I threw at them in the last three weeks, they did well.  It’s just the handful that didn’t that I need to figure out how to handle.

Getting a new student on Monday.  I can pronounce neither of her names, and I only know she’s a she because I looked her up. My wild-ass guess is that she’s Kenyan.  This should be interesting.  (Kenyans speak, what, English and Swahili?  With maybe French as a distant third?  Hopefully there’s not a language issue.)


So, yeah.  Smart kids.  Then there’s whatever is going on in that picture there, which I took in my classroom on Friday after a student volunteered to do that problem on the board.  Now, this is my special ed group– don’t get me wrong, I’m not in any way trying to make fun of this kid, just to give you an idea of the range of abilities I see throughout the day, because after this kid leaves my room I get the Algebra kids, a group that contains a kid who got a perfect score on his math ISTEP last year.  I was trying to demonstrate the various algebraic principles; the problem on the other side of the one on the board is 4x(6×5) and the idea is that they’re supposed to notice that both equal 120 regardless of where the parentheses are.  Note that this does not represent multiple attempts to solve the problem.  He did the green part first, where rather than multiplying four by six (or adding it six times, which would have been fine) he raised four to the fourth power.  Then he switched to a blue marker, getting into an argument over whether it was “his” marker in the process, added six to itself four times and got 24.  What caused him to privilege the 24 over the 32, I’m not sure, although this kid is prone to giving me multiple choice answers on assignments– he’ll literally write “3 or 30 or 4 or 17” next to a problem.  The blue squiggle next to the 2 under the actual problem is supposed to be a 4; there are also huge handwriting issues.

Then he switched to a red marker and tried to multiply 24 by 5.  Note that he’s first tried to add it, but only four times, and that the presence of a tens digit has utterly confounded him– he’s added the two pairs of fours to get two eights, then added those and gotten six instead of sixteen.  This isn’t forgetting to add a digit; I was standing behind him watching this performance and he actually said “four plus four is six” while he was writing.  He then turned around and told me that the answer was six, at which point I took this picture, erased the whole mess, and walked through everything with him.

I do this often, by the way– letting a kid dig himself into a hole can frequently be useful because it gives me insight into how they handle mathematics.  Unfortunately, for the second time this year, I’m looking at this and getting the “holy shit, I can’t fix this” vibe that I get from writing sometimes.  The kid can’t handle basic multiplication on his own, and even with other adults in the room I can’t get around to them often enough to help him with everything he needs help with.  Luckily, he has involved parents; I can’t imagine what he’d be like otherwise, as this is what he is like with help at home.

I’ll figure it out– I’ll figure him out, I always do– but Christ, do I have a headache right now.