Thursday, November 13, 2014


Relearning Algebra with The Boy

The Boy is thirteen, and in the eighth grade.  He’s taking algebra, which is to say, we’re taking algebra.

Relearning algebra at age forty-six is a very different experience.  It’s not as intimidating as it was the first time around, if only because I remember getting past it before, and some of the logic seemed to stick. “Isolate the variable” is a life lesson masquerading as a mathematical technique.  I need some prompts as reminders, but so far they haven’t been too bad.  The notation is slightly odd -- why is the slope of a line abbreviated as “m”? -- but once I know that, it’s fine.

The first time around wasn’t like that.  I remember lots of daydreaming in class, which made it difficult to keep up with demonstrations on the chalkboard.  (It was even harder to catch up once I had missed a couple of steps.)  I didn’t see the relevance of any of it, and the logic behind it was often elusive.

The Boy reports that many of the same things are true for him, now.  

I can’t blame him, really.  Depending on how it’s taught, algebra can either be a really nifty bit of puzzle solving or a mystifying group of complicated processes with no obvious connection to each other.  And I”m sure that if I had to sit through an hour of it every morning, early, with a teenager’s body clock, I’d daydream, too.  

As the parent, I see it as my job to help TB move from “this is a random set of rules to memorize” to “here’s how it fits together.”  Once you have some sense of the connective tissue, it’s easier to reconstruct a rule that you’ve forgotten.

This week he had a big test, and some reason to be nervous about it, so we spent a couple of hours studying together.

The first thing I insisted on was turning off the computer.  I brought up several sheets of blank typing paper -- for younger readers, “typing” is the old-school version of printing -- and a pen.  I wanted us to have enough room to write nice and big.  I wanted to see each step as he did it, and I wanted him to see each step as I did it.  That means having plenty of white space.

There is no substitute for speaking math out loud, slowly, as you do it.  It’s not fast or pretty, but it forces a kind of clarity.

This is where generational parenting styles really show themselves.  We Gen X types were raised in what would now be called a “free-range” style, which meant that when it came to things like homework, we were on our own.  That could be very good or very bad.  The rules have changed since then; now, difficult homework is a group activity.  The key is in making sure that you’re clear on the difference between helping him understand, which is good, and doing it for him, which is not.  

The joy of helping with algebra homework is twofold.  It’s fun to devise word problems designed to make each other laugh.  And I still get a kick out of watching the lightbulb turn on when he gets it.  

If you had told me at age thirteen that I’d bond with my future son while helping him study for an algebra test, I would have laughed out loud.  Yet here we are.  If x equals spending time making The Boy laugh and helping him learn, then I’m happy to solve for it.  

I was going to say something about "better now than as a freshman in college" for him, then realized that you might now be qualified to do some tutoring for developmental math. Seriously. If you have a tutoring center, see if they will let you give it a try.

That technique of speaking math out loud is really powerful. The pros can get an entire class to do it.

Some approaches try to get them to write it out as a essay, like the Arabs did back in the beginning, but I find writing is too slow for most students. Algebra is, after all, just a shorthand for words. I've also noticed that many college students struggling with beginning algebra have the right instincts, that is, they say the right thing for the next step, but lack the confidence to follow through. Emphathy is key with them.
If you had told me at age sixteen that you’d bond with your future son while helping him study for an algebra test, I would have laughed out loud too.

If it helps, feel free to tell TB that I use algebra every single day. I think the only tools from math of that era that I don't use are synthetic division and the solve-by-hand square root algorithm.

Of course, xkcd has a relevant comic for your post.
If you want to turn the computer back on there is dragonbox 5+

I played it with my daughter who didn't know algebra and she couldn't quite make the connections between the game and real algebra (she was 10/11 yo). However, I actually thinks it makes more sense to play it as the same time as a person is learning algebra.

Slope is abbreviated as "m" because it makes perfect sense in German. This is true of most non-intuitive abbreviations in math, such as the double-struck Z for the integers. To be fair, sometimes it is yet some other language, but it seems like German is the culprit most often in middle/high school algebra. I wish textbooks would bring more of the history of math into things when they introduce the notation (both because it provides context and because it reminds students that someone had to figure this stuff out int he first place and the current state of math is cumulative effort on the part of many generations of people all over the world).

I'm glad we don't use "s" for slope, though, because s has a tendency to turn into a 5 if you're not careful and have handwriting like mine. Similarly, the only time I use cursive is when I'm using a letter like "b" (which turns into a 6) or "l" (which turns into a 1) in a math problem. I haven't found a good solution for "s" and "o" so I tend to avoid them as variable names.

The thing that helped me the most with algebra as a middle schooler was that I'd been writing computer programs for years, so I was able to transfer over some of my understanding of the concept of variable from there. This was less useful when I was just supposed to be finding some specific number to make a statement true, but it helped quite a bit with functions since I'd been writing functions in C for years by that point.
Slope is 'm' for the same reason there are 24 hours in a day. It has to be something, and once we all memorize it, it doesn't matter how arbitrary it is.

I mean, the history's fine -- it's fun to learn the history of timetelling, too. But some things are just arbitrary, because any answer is correct, as long as we all stick with it.

And as a small businessperson, I use algebra daily.

@Anonymous-- thanks for the Dragonbox 5+ recommendation-- DC1 loved it and finished it in two nights. We may have to upgrade to their larger version.
@Anonymous - Here's a cursive "S" that can be distinguished from "5". But I agree with you about the "O"; I tend to avoid it for the same reason you do.
I am frequently told by my students that they find it helpful to know why something has a particular name. It easier to learn if there is a context for it, a way to classify it or relate it to something you already know.

For example, I don't think we use m because the babylonians did. On the other hand, we use 12 hours and 60 minutes because of divisibility by integers (2,3, and 4, as well as 5 and 6 for 60) that led the babylonians to use that system for numbers. That is why there are 12 inches as well as 12 hours. Ever try dividing 10 exactly by 3?
No one knows why we use 'm' for slope.

The best we have, according to math historian Frederick Rickey is that it's not based on any historical reason (such as derivation from a French or German source). His hypothesis is that an influential algebra text from the US made that the choice for the parameter at one point and it just stuck.

That is... it appears to be arbitrary.

Some of my best adult students retraining to be math teachers come from a humanities background. The abstract proofs courses and conceptual understanding of math comes more naturally to them than for the traditional age preservice students. As for me, I am finding excitement in Macbeth and American History when I help my HS kid with his homework. Used to daydream in my own high school history and English courses.

Would just love to have folks with a humanities/ English background and an open mind to teach some of our Dev Math courses.
Good one and thanks a lot for sharing!
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