Math Stories

For your kids:

Pick two numbers, randomly.

What is the probability that the product will be even?

(I suspect that this is one of those evaluating number sense questions that people would argue about forever on facebook if it showed up there.).

Prompt: Why did you name your blog what you did?

I was going to pass on this prompt, but I found out yesterday that I’m getting stulled this year, and realized that it is still an issue for me.

Lately, I’ve been hearing english teachers talk about a focus on exposition. And traditional teaching has always been about exposition: You stand up at the front of the room, and tell the kids how things are.

The thing is, exposition sucks.

It’s like reading an owners manual. My hollywood writer friends all know that exposition in a movie is a cheap hack – it’s much easier to have a character say someone is smart than it is to have that person actually demonstrate smartness. And it’s certainly not how we interact with other human beings. (Well, except for Twitter: “I just had a hamburger.” “I am at the airport.” Gah.)

We interact by telling stories. We build narratives. When we remember something, we remember it in the context of how we felt, who else was involved, and the tensions that escalated and were resolved. Sure, we can remember blunt facts too, but those take effort. They’re not spontaneous. And my poor little hormone addled 13 year olds don’t have the fortitude to do that for seven hours every day.

I don’t think this is news – it’s what’s behind the whole progressive education movement. It’s the difference between sages on stages and guides on the side. It’s what’s behind Dan’s dislike of textbooks. It’s even what’s behind the whole misguided Psuedocontext thing.

And that’s the trap – It is easy to think you’re creating engagement. It’s easy to think a kid should a question just because it peripherally relates something he likes.

But really, I’d rather have a good story about something I never knew I liked – something with tension, suspense, and satisfying resolution, than lame ad copy for my favorite thing in the world.

The last time I was evaluated, the AP told me the only way to teach was to make your objectives clear up front, and then explain them in a methodical manner. The lessons I submitted and demonstrated did anything but. He was happily surprised at both the engagement and the learning that happened. It’s now several years later, and I have a new administrator. This is the year I find out whether I’ve managed to build on this skill, or if I’ve gotten complacent and given in to the status quo.

I’m a luddite. When you, Mr Ed Tech advocate, come up with new stuff to try to impress me, it usually doesn’t.

But, there’s more than edtech out there in the world. People have been doing crafty stuff. Stuff like MathJax. Available both as a wordpress plugin, or a one line script load at the beginning of any web page.

Which lets you do stuff like this¹: $$e^x = \sum\limits_{n=1}^\infty \frac{x^n}{x!}$$

Notice that it’s not a image – it’s cut and pastable. And it looks good, and matches the fonts you’re using. Sure, you need to learn latex, but that’ll probably serve you well should you want to continue to create mathy type expressions in the future.

¹ What I actually typed in: e^x = \sum\limits_{n=1}^\infty \frac{x^n}{x!}

I was recently connected (via email) by a friend to a new teacher who is struggling.

I’m never quite sure what to say. For what it’s worth, here was my response:

> stress and anger management.

Heh. That seemed to define my first year.

The crappy thing about teaching is that (I’m convinced) no one knows how to teach how to do it. For all the talk of “education”, the people who are supposed masters are basically throwing us inn the deep end of the pond, and seeing who stays afloat.

That being said, here are a couple of ideas that stuck with me from my first year:

- You are responsible for the kids in your classroom. If they’re not learning, its your fault. Sure, it’s easy to blame parents or gangs or whatever else, but the truth of it is that for most of those kids, there is a teacher somewhere on that campus who’s made them want to learn. Be like those teachers, not the ones who constantly complain about the kids. This sucks to hear, but I’ve seen too many teachers with good potential get ruined because they couldn’t believe that changing what they did would change the kids.

- Observe observe observe. Use your conference period. Find out who’s good at classroom management, and go watch them teach. If you don’t see them in the first week of school, you won’t see how they got there. But you will see that it’s possible. (To which – every new teacher should be required to watch the 5 best classroom managers on campus for the first week of school, lesson planning be damned.)

- Only change one thing at a time. If you feel out of control, accept most of it for what it is, and only work on changing one thing about yourself at a time. The first thing I worked on was not answering a kid who just yelled at me – I had to teach myself to wait for them to raise their hand. I had post it notes reminding me of that everywhere. The kids laughed at me, didn’t change much, but eventually learned that they had to respond to me rather than the other way around.

- Make your expectations clear, in excruciating detail. Repeatedly. I spend about a week at the beginning of the year teaching them (as opposed to just telling them) my expectations. And still, every day, I need to remind my 5th period what they’re supposed to do before the tardy bell rings. Every week when I give a test, I go over the 3 rules. Even then, I’ll have a kid who starts talking before the test was completely over. But it happens rarely. If a kid ever does something I don’t want them to do, and I haven’t taught them about that, I take it as my fault. Sure it seems like they should know how to do some stuff as a student, but the reality is that they want to know that you know how they’re supposed to act before they’re willing to put in the effort.

Prevention is worth tons of cure, and I haven’t so much learned to manage my anger as find ways to prevent things that might make me angry from happening. I spent a full month of seven hour days during the summer after my first year making a list of things the kids did that drove me nuts, and then coming up with alternate behaviors to teach them, and then lessons to teach those things. Eventually, I got good at catching the precursors to those things as well as communicating those expectations, to the point where I can substitute a class from hell and have them eating out of my hand in 5 minutes.

That’s down the road, though. right now, pick one thing about yourself to change, and start practicing it.

And remember to get enough sleep.

I did some more thinking after my Point Loan post the other day:

• This probably a direct result of my Dan style SBG: even though the grade is an aggregation of a number of different scores, I see it as so representative of a students skills that I am loathe to twitch it a little bit for fear of losing its fidelity. This is a huge change from where I was a couple of years ago.

• This attitude seems to reflect itself in my students. I can’t remember the last time a student complained about the grade that I “gave” them. It’s all about what grade they got.

• Out of all of my qualified students, only one took me up on the offer. The other dozen or so decided that they’d take what they deserved, and keep their threshold for next semester just a little bit lower. Rather than seeing this as a wasted effort, I see it as a validation and reinforcement of how I want them to see their efforts.