Poopy Statistics

Most who read this blog know me as an English teacher. However, what some may not know is that I have taught at least one math course for all 9 years of my teaching career, including next year. In fact, I have taught every math course I am certified to teach: 6th, 7th, and 8th grade math, Pre-Algebra, Algebra I, Geometry, Algebra II, Trigonometry / Pre-Calculus, Calculus, and Statistics. I am even helping out with our AP Physics class next year, as it is a math-heavy course. I love math.

So math is where my mind was at when I came across this joke the other day (paraphrased):
“It’s skewed a bit by my first couple years, but I still poop my pants 22 times a year on average.”

I love this joke. I’m going to be 31 years old next month, and I probably poop my pants, on average, over 32 times a year.

The key, of course, is in the words “on average.” I’m definitely going to have my students calculate this for themselves next year in my stats course. Here’s what I did:

First, I needed an estimate of how many times I pooped my pants/diaper as an infant. Having a newborn of my own, I have a pretty good idea that this is way more than I thought humanly possible. A number my wife and I are often told is healthy is three times a day, at least for the first three months or so, when it begins to lessen. So for the first three months of my life, I probably pooped my pants about 90 times.

Fun fact: as I was typing that last sentence, my son pooped his pants.

Let’s be conservative with the rest of the poops. Maybe I pooped about once a day until I was 2, and then, like magic, I was potty-trained (crossing my fingers that this happens with my own son!). This gives us 730 pooped pants.

But let’s be honest. That number isn’t right. It’s probably actually over 1000 (I’m pretty sure my son is over 1000 already, and he’s not even 4 weeks old). So let’s just go ahead and settle on 1000 poops. It’s a nice number, easy to remember.

So I have pooped my pants 1000 times. Over 31 years of my life, that is — on average — over 32 times a year.

The reason I love this joke is because I can use it to help my students think about the measures of center, and which ones really make sense to use. Yes, I can say I still poop my pants, on average, 32 times a year, but that’s certainly not the case (I max out at like 25 or so, I swear). So which measure of center makes sense to use here? The mean (often called “the average”)? The median? The mode?

The default example for this seems to be income levels, with one worker making over a million dollars and everyone else making around $30,000. Trust me: that has no basis to our students. But tell them they poop their pants over 50 times a year, and I promise you you’ll have their attention.

And there’s even a bonus linear modeling question! If someone poops their pants an average of 22 times a year, and we assume they pooped 1000 times as an infant, how old are they likely to be? I’ll leave that one for you to work out on your own.

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On Those “Crazy” Math Problems

I know this has been a blog primarily from the perspective of an English teacher, but the fact is, of my 7 years teaching, 3 have been teaching English. All 7 have included teaching at least one math course. I’ve taught math at every level of my certification: from 6th grade to high school calculus, and everywhere in between. I’ve got some math chops; I just don’t often display them here.

But today. Today, I feel I must.

For, you see, math education in the United States is getting a pretty horrendous treatment right now, and today was the straw that broke the camel’s back.

It’s been tough to go too far without running into someone slamming what they call Common Core Math. Elementary math problems are made to be jokes for how difficult they are. Stephen Colbert and Louis C.K. have weighed in, along with other videos and photographs that have gone viral.

Today, I came across this guy: https://www.youtube.com/watch?v=Ldyl_uYrojs

This seems pretty standard fare for the level of derision being cast upon problems just like this one. To sum up:

He asks a bunch of people who were educated in the same way he was (savvy readers will notice my lack of an appositive there; savvier readers will know what that means) to look at a problem that is being taught in a different way. He shows them the way they all learned it, and is excited because it’s quick. “Answer. DONE.” Because to him, and apparently to the others in the video (or at least the one he shows), the reason to do simple subtraction problems as an elementary student is to get the answer. The other way, which nobody in the video seems to understand, is messy and leads to people being confused and asking questions about it. Which is clearly not the reason simple subtraction problems are assigned.

Now, as it is mostly English-minded people who read this blog, let me ask you a question: why do you assign reading? Is it so students can finish the passage and then move on with their lives? Or would you hope they actually glean something from the reading they can apply to their lives? Would you hope they actually think reflectively on what they were doing?

Here’s the truth about that subtraction problem: the “old” way — the way everyone in the video was likely taught — was an algorithm. It wasn’t a “how do you solve this problem?” education. It was a “here’s how to solve this problem” education. The “old” way gave a tool to students to solve subtraction problems. So long as both numbers were positive and the answer was also positive. Which does sort of leave out half of the numbers that exist.

Anyway, the “old” way works in those cases. Anybody know why? Anybody who hasn’t studied math actually know why that algorithm works? And do you then also know when it doesn’t work? I hope so, but I doubt it.

The “new” way involves what people actually do: they count. We use what we call landmarks: numbers we are comfortable using. You need to find the difference between 12 and 32? Well, that means you need to know how far it is from 12 to 32. Adding 3 to 12 will get you to 15, which is a nicer number. I’m more comfortable with that number than 12. Then 5 more will take me to 20. I like that a lot. 10 more takes me to 30, which is really close to where I want to go. Now, I just need 2 more. Ahh. 32. There we go. We’ve landed. So, how far did I go?

Well, I went up 3, then 5, then 10, and then 2. So 3 + 5 + 10 + 2 = 20. 32 – 12 is 20.

Did that take a while? Yes. Did we get to the same answer? Yes.

Did a young elementary student learning about subtraction actually have to do some genuine thinking, reason through a problem and have an understanding of what it means to subtract as opposed to merely use an algorithm nobody will ever explain? You betcha.

The thing is, I would much rather have in my middle school math class a student who learned to subtract this way. Would you like to know why? He or she could actually subtract. And subtract anything. Because this method works with any numbers, in any order. Negatives, positives, zero — you name it, this reasoning works.

This week, I was teaching 2-step equations to my 6th graders. It’s a difficult concept, but they’re a really smart class, and I know they’d be able to handle it with a little guidance. Here’s what I didn’t anticipate: they can’t subtract. When they’re given two positive numbers, they’re just fine. But when it comes to negatives? They’re lost. They’re grabbing at straws: “if they’re both negative, it’s positive, right? Or is that just for multiplication?” They don’t know the rules because all they were ever given were the rules. They weren’t actually taught what it means to subtract. And so I find myself teaching this rather than the content I was hoping to cover with them.

If we want our students to pass Algebra II by the time they graduate high school (Michigan state requirement), we can’t be teaching them how to subtract in 6th grade. We need something that makes sense to them when they’re younger that they can use when they’re older. We need teachers to teach them these basic concepts in a way that gives conceptual understanding, and not just an algorithm they can use to poke fun at things that are different when they’re older.

English teachers, I know we have all kinds of gripes with the CCSS. But in math, they’re not all that bad. We can rally against the testing all day long, but the math standards have some merit to them. We need a lot of this reform in our elementary schools. Imagine that someone only ever knew about poetry that rhymed. That’s all they did in school, and they thought that’s all poetry was. They never had to worry about using poems in their life, because pffff who does that? But when their child brought home a poem they wrote that didn’t rhyme, they knew they had to take to the Internet to point out how terrible this was. Their child’s poem didn’t even rhyme! What kind of system is this?! They asked their friends who also had only learned about poetry that rhymed. Their friends were right there with them, livid with the way their children were being taught. HOW DARE THEY TEACH ABOUT POETRY THAT DOESN’T RHYME!

What would you say? Would you let them stomp all over your now robust use of poetry, which you studied for years? Or would you stand up and tell them to show you where their English education degree is?

Math education is being dragged through the mud. It does need a good washing. But please, don’t throw the baby out with the dirty bathwater. And if you don’t know what you’re talking about: please, please stop talking.