I Don't Do Sympathy

 

What's the deal with fractions? Say it like Seinfeld and it's kind of funny. Say it exasperated while shaking your head, as I usually do after class, and it's not really funny at all. Really? What's the deal with fractions? It's one of the things I'll never understand as a teacher. Let me explain, I've broken down things students do into two categories: things I understand and things I'll never understand. As you can probably expect, that first category grows ever smaller while the second increases without bound. Don't misunderstand me though, I'm not completely unreasonable, there's plenty in that first column. For example, I can totally understand why a student would have trouble with logarithms the first time they see them; after all they require a complete backwards thinking that we haven't quite felt since learning that division was the opposite of multiplication (which by the time you hit logs was a long long time before). There are plenty more, keeping integration rules straight, dealing with Z mod 2 the first time and learning that 1+1=0 there and so on. Though as time goes on I start to wonder if I'll ever be able to stop adding things to this second category. Things I'll never understand include: How can a student solve an equation with xs but give them the same equation with zs then they're lost? Why does a student, who made it all the way to calculus, need their calculator to find 5-0? And of course, fractions, fractions blow minds, and I'll never understand why.

At one time in my life I might've lumped problems with fractions into the things I understand category, but now it is near the top of all the student dumbery that completely baffles me. What is it that people don't like about fractions? Now again, I'm not being unreasonable, (arguable I know) I'm not complaining because students have a problem with something like

I can understand a student having trouble with this. In fact, I'd be damned before doing that monstrosity by hand. No, I'm talking about having trouble with something like

So many students see this and their minds turn to mush. Why? This is the pinnacle of simplicity. I promise you understand that statement. If you have a pie and you cut it in half and give one half to the homeless hacker stealing the internet from your front porch, how much of the pie do you have? Half. That's what the above says, if you have one of something and take half of it away you are left with half. If you only have a third of a tank of gas left, you know that you only need two thirds to fill it up. In math terms

But there's some disconnect students have that I'm not understanding. Perhaps some of my readers can help me out here. What is it about fractions that makes you hate them so much? Not only do students hate fractions and are unable to do the simplest operations involving them, no that would be unfortunate but expected. No, what's worse is that they think it's ok that they don't know how to do something so basic.

My friend, let's call her Master J, had a student once who came by to get some help with trig, a class with lots of things that fall into my first category (things I can understand, if you remember). The problem broke down to basically finding something like 1/3 + 1/6. And so she asks the student "So what is 1/3 + 1/2?" and the student responds "I don't do fractions?" Excuse me? You don't do fractions? Well I don't pass snarky students that don't "do" fractions. And what the hell do you mean you don't do fractions? That's like telling your English teacher "Yeah, I don't do subject verb agreement." They'd look at you like you're an idiot. But nooo, when I look at a student like they're an idiot after they say something so retarded, I get called a grumpy math teacher that expects too much of his students. But I digress, Master J has some of the best student stories ever, I think mine are a bit too scared to try things like that with me, too bad really. The point I'm bouncing around here is that not knowing how to do fractions is one thing, but thinking that this deficiency is a-ok is completely unacceptable. Especially if you think it's one of the things you can choose not to do, and say so straight to your teacher's face. Not remembering how to do prime factor decompisitions might not hinder you in college algebra, not knowing how to do fractions will.

Here's why it's unacceptable. One, you've been learning fractions since around second grade. Think of other things you were taught in second grade. Are you expected to know these other things when you get to college? Yes, you're expected to know how to tell time, how to read a map, how to read a book, how to add and subtract numbers, ad infinitum. Why then, is it ok not to know shit about fractions when you get to college? Especially since, as with many math topics, you get retaught them pretty much every year.
I've already promised that you understand fractions, you do. I think it's just a problem of not taking the time to learn the little rules associated with them, and that's where most students falter; which is again unacceptable. Why?

I'll answer you by telling you a secret. It doesn't matter if you understand fractions at all, not one damn bit. This is the part where I'm going to sound like a terrible teacher, and I really don't care because it needs to be said, consider it tough love. There's been so much hoopla over students understanding. So much so, that entire classes have been restructured and new books have been adopted. What have we gained? Absolutely nothing is what. Guess what? Sometimes you wont understand what's being taught, it's fact. It has nothing to do with you as a student or how good your teacher is, it's not a judgment of either. There are some things you just wont understand your first time through, sorry, that's just how it is, and for different people it will be different things. But what can be done if you don't understand a topic in a class? Throw your hands up in futility and just miss that part of the test? Absolutely not! You merely employ one of the first learning skills you ever had, you MEMORIZE.

That's right kids, in this touchy-feely environment of students understanding math, the simple process of memorizing everything got lost in the shuffle. In fact, my first semester teaching I was told not to make my students memorize things, that the class should be based solely on their understanding of the material. Well that boys and girls is pure and unadulterated grade A bullshit. You've known how to memorize things since you learned the alphabet. Do you know the lord's prayer? I promise that's more complicated than memorizing the quadratic formula. Now before you start, let's say you don't understand fractions, what they are, what they mean, why they're important, or anything; but, you memorized the only two rules you need to know. That is, you've memorized

Guess what, you'll be able to do any fraction problem thrown at you. You don't really understand fractions, but you've memorized how to tackle them. Which is better? Most of  you might've said "understanding" before you actually thought about it. If you memorize a mathematical topic, and do enough problems, then the understanding will come with time. It will start to trickle into your brain as you do more and more problems. How do I know? I can't tell you how many times I've done this very thing myself. I've taken notes while not understanding a single word. I've memorized properties in order to do homework I didn't completely understand, to go on to ace tests on things I really knew nothing about. But as time went on and I did enough of them, the understanding finally came, it finally clicked. If I don't understand, my first instinct is to memorize, it hasn't let me down yet (my degrees don't lie).

Memorization is the easiest skill we have, mathematical concepts can be very hard to actually understand, but memorizing them is a piece of cake. But therein lies the problem, memorization might be easy, but it takes work, which is something college students refuse to do (another thing I won't ever understand). I think students feel like they should be able to just show up, halfway pay attention and be able to pass with an A. The moment they get a bad grade it's the teacher's fault. Learning math is not passive in any way, sorry, it is completely 100% active. You might understand everything in class, but come test time you can't work a single problem. It's because you haven't taken the time to practice, to do all the work required. Yet, someone who doesn't really understand what's going on but straight memorizes, and does all the homework, will usually get the grade. Concentrating on understanding is folly, because it gives the wrong impression: that you can just understand and get by, without putting forth any real effort. It's how we wish the world worked, but reality is much harsher, and pretending it isn't (even in a silly math class) doesn't do anyone any favors.

How did we get here? Wasn't I talking about fractions? Yeah, sorry, what I've basically said with these never ending paragraphs is that even if you don't understand fractions you still have no excuse. Just memorize the two rules I put up there. What else can you do to fractions besides add and multiply them? And I'll hit you if you say subtraction or division, those are just special cases of addition and multiplication anyway. Those are the only two rules you need to know. So memorize them and have confidence, now you can say "Yes, I do fractions!"