## Friday, December 19, 2014

### Math Is Dumb (and Why)

Okay, so to be fair to math, it's not math that is stupid. I mean, math is just math, after all. Math, regular math like addition/subtraction, multiplication/division, algebra, doesn't change. 2+2 will always be 4. Always. The quadratic formula will ALWAYS be the quadratic formula:
Am I giving anyone flashbacks? Or nightmares? Or flashbacks to nightmares?

So it's not math that's the problem; it's the people who write and/or produce textbooks.

There's been stuff in the news recently about how some school districts have been offering classes for parents who need help with their math skills in relation to the new common core math standards. Every one of the news stories I have heard or read make it sound like there is some issue with these adults. They're having to go back to school because they're just dumb. Smart parents don't need help with the math. I don't think this is necessarily the case.

Granted, I don't think a lot of adults have retained much of their high school math and, really, that's okay, because you don't need, in general, much math to get by on. Heck, if you have any kind of cell phone or tablet (and who doesn't? I mean, even I have a Kindle at this point), you can get free calculator apps and stuff, so all you need to know is when to add or subtract or whatever, not actually be able to do it. But I don't think the issue with the new common core stuff is lack of ability or knowledge; I think it's because it's full of made up crap that didn't exist thirty years ago.

And, yes, I mean made up crap because, as I said, basic math doesn't change. There is nothing new to add to it, because, guess what, 2 + 2 = 4! Period (okay, exclamation point). End of story.

So, a few weeks ago, my daughter asked me to help her with her math. This not an uncommon occurrence, nor has it been an uncommon occurrence with any of my kids. I mean, I have spent time teaching both algebra and calculus so getting asked to help with BASIC MATHEMATICS should not be an issue, right? RIGHT? Except what she said was, "Hey, Dad, I need help with this neutral table."
...

...

...

Neutral table? What the heck? I'd never heard of a neutral table. Which is kind of what I said except it went more like:
"What are you talking about? There's no such thing as a neutral table."
"Well, I have to do one for my homework."
Great, my kid had to do some thing that wasn't even real for homework. So I had to take her math book and figure out what the heck she was talking about because, guess what, neutral tables are SO made up that you can't conveniently find them online.

Are any of you wondering, now, what a neutral table is? Well, I'll show you.
Pretend you need to figure out the answer to 7-3 and you can't work that out in your head and you don't have any fingers. Guess what! You can use a neutral table! It looks something like this

+ + + + + + +
-  -  -

only with a box drawn around it. You match the +s to the -s and remove all of those pairs. Whatever you have left is the answer to your problem, so the answer to this one is 4+s. The problem here is that doing it like this does not address something like 7 - (-3), because you still have to know to make that into 7 + 3. To be fair to my daughter, the problem she needed help with was slightly more complicated although not much more. My question was, "Why aren't you just using a number line?"
Remember those?
That, actually, is still my question. And she didn't have an answer for it.

But I actually know the answer. It's an answer I don't much like.
You can't sell new textbooks without "new" math in them. There's no incentive without new material, after all, other than to just replace books that are falling apart, but how often do schools really need to do that? Judging by the texts I used when I was in school, not more than once a decade at best. But if there's new material... Well, that changes things, so you have to make up brand new "math" to convince schools to re-invest in new texts.

The problem is that it's not really math. I'm sorry (okay, I'm really not); neutral tables are not math. There should not be a section in a math book about how to use neutral tables. They are not a THING. At best, they are an example of a thing, a way of showing a kid who isn't getting adding and subtracting a way to figure it out. So, maybe, you give this info to teachers of 1st and 2nd graders (to the teacher) as a way to explain adding and subtracting, but it does not belong in a 6th grade math text as a THING that you need to know how to use to algebra.

Neutral tables are not the only thing my kids have asked me about that didn't exist in math a couple of decades ago; they are just the most inane thing they have asked me about. And they are inane. It's a waste of teaching, a waste of class time, a waste of brain space. And, now, it's a waste of my own brain space just knowing that these things exist.

Seriously, that our education system is tied up with textbook publishers is one of the reasons that our education system is suffering so much. The education system should not be allowed to become like the military, paying for gold-plated toilet seats and the like. But, again, the education system and what's wrong with it is another topic entirely.

1. Never heard of a neutral table either. I do remember the number line, as we used it to understand negative numbers.
I remember trying to learn some 'new math' in grade school, in part due to a new way to do division (which was quickly abandoned) and trying to switch to metric (which was also quickly abandoned.)

1. Alex: Metric stayed around for a while. We spent several years working with metrics and, because of it, it has become standard in science-related topics, now, I believe.

2. And this is why I will likely be homeschooling my (future) children... and also why I should probably start haunting all the local used curriculum hang outs so I can get 'older' math textbooks before they're all gone.

1. I home schooled my daughter and it was the best thing I ever did. She's on full scholarship at Uni now. She's bored out of her mind because they're teaching at a level that is too low for her.

2. Rebekah: Or just get workbooks and don't bother with texts at all?

Anne: I breezed through Calculus in college because of the teacher I had in high school. Actually, there wasn't much in college that I hadn't already done at a higher level in high school but, then, my high school wasn't really typical.

3. They keep calling these ridiculous changes the "new math". And you're right, it's not new.

Back in my day there were no calculators, they hadn't been invented. I was horrified to find out that my kids were allowed to use them in class.

1. Anne: I'm still ambivalent about calculators. On the one hand, they're like wikipedia, which I am all for. Why bother to enforce memorization of facts that can easily be looked up, now. On the other, I still think it's a good idea to know some of the basic skills we're turning over to machines. But maybe it's not? I mean, why should I bother to work out some cumbersome long division problem when my calculator can just tell me the answer?

4. I've never heard of a number line. I guess what they teach changes a lot.

I'm not sure if it's a waste of teaching. Most people don't use anything but the most basic forms of math, so if you're going to teach beyond that, there has to be a purpose. And I think that purpose is how to solve problems in different ways, like by calculator or some weird system. It's a good idea to stretch the mind by learning new approaches.

That being said, yes, the education system is totally broken and textbooks publishers are a cancer in that system. I think in order to effect real change, it's going to have to be at both the local level and the national level, and the former is going to be totally hindered by the latter's insistence on state exams.

1. Jeanne: You didn't have number lines? That's just... weird.
And, by the way, the neutral tables are for teaching -basic- math, because negative numbers are basic math.

5. That's ridiculous. A neutral table--bah, humbug!

Love,
Janie

1. Janie: I agree!

6. I've never gotten along with math. We've agreed to remain distant acquaintances.

7. As long as you don't make it mad. You never want to make math mad.

8. You sound a lot like me talking about everything.

I'm kind of with you, a bit? First my complaint: I don't like homework. I've come to realize how dumb it is. When you give homework, you take a kid who doesn't know this stuff, and say "Go work it out and teach yourself." If he can't teach himself (few can) he has to ask for help -- from parents. I have a poli sci and law degree. WHAT I KNOW FROM MATH? And also, what do I know about teaching?

So homework delegates an important function -- teaching -- to thousands of unqualified, untested, possibly unmotivated people. Homework should end. (I note that homework also disadvantages kids whose parents work longer hours, or who have less educated parents, making it a trap for poorer/less educated families.)

Anyway: About all this different math. I agree with you that they shouldn't just invent new things to sell textbooks. But as I have been working with Mr Bunches this year on his math (because I am apparently an adjunct teacher to our school district thanks to homework) I've noticed the many many different ways the present information, some of which are new to me. (Number Triangles or something like that baffled me). But Mr Bunches in particular has a really hard time with abstract concepts like math, and seeing things several different ways seems to really help him. So if number lines work for me and you but neutral tables help teach the concepts to someone else and Mr Bunches needs Number Triangles, I don't think that's such a bad thing.

I struggled with math all my life, until one day I thought "Math is just a different language. It's like Spanish or computer programming. It's just a way to SAY things." I know that's not 100% accurate but that thinking was a breakthrough for me and I now understand math a lot better.

So new concepts to sell new textbooks, I'm with you it's stupid. But if they're actually helping kids understand hard concepts and get a love of math, I'm okay with that.

1. Briane: I don't have an issue with having a variety of paths to teach kids to get to the same goal. I do that a lot when I'm teaching (and I have been a math teacher and know that you often have to have many different examples so that everyone will get it). The problem, though, is that neutral tables are not a goal; they are a path. The goal is adding with negative numbers. Now, first, adding and subtracting is not a skill that should be being taught in 6th grade to begin with and, actually, it wasn't being taught. The neutral tables were being taught as if they were a thing all unto themselves, like finding the area of your living room or the volume of a fish tank. You don't take the path and make it the goal.

And, yes, on the homework. Study after study has shown that disadvantaged kids struggle more with homework and fall even farther behind in homework-heavy environments.
But, you know, do it harder and faster and maybe something will change.

9. I think we mostly agree; I don't know about neutral tables in particular but I'd rather have you teaching my kids than a lot of others.

10. Briane: If it wasn't my own kids, I'd rather have me teaching them than a lot of others, too.