Let them make their own rules

Shamelessly stolen from a comment on Dan’s blog:

For things like exponent rules, students are expected to act like a computer programmer and be meticulous in how they work through the problems. Because exponents are just symbols to my students, sometimes they make up their own rules (as any teacher probably knows).

You may happily debate me about whether that second one will help or hurt – just seeing a fraction can make some kids freeze up. You may need to sneak them later in as a notational convenience instead. But what’s not up for debate is that finding patterns is like candy for kids – they are far less reluctant to do this than other types of math, especially if it’s just “guess the next number”. The barrier to entry on that is pretty low. Even if most of them don’t get it, they’ll be willing to guess, and enough kids will understand so that the others will want to know why (this is gold). Let the kids explain their rules.

Notice that we haven’t actually addressed exponents at all yet. we’ve just let them make rules for patterns. This is where you do the lazy math teacher thing – you just rewrite then numbers in exponent form under the patterns, and ask the kids to make the same predictions you did earlier.

After that, it’s a matter of formalizing the rules. Have the kids write up explanations, and then start throwing those explanations under the document camera, and let them debate. Let them decide the wording, let them argue about meaning. Let them do it with their neighbors, let them do it with the class. Let them make the rules.

Same idea for the other exponent rules. Throw this up on the screen:

Give them 3 minutes, and then start stealing student papers and throwing them under the camera. Get good answers, get bad answers. Let them debate whether the answer is fake or real. Use their answers to let them define the rules, both for what works, and what doesn’t work. This is probably more free wheeling and unstructured than the first, so don’t forget to constantly solicit why’s and whynot’s, and poll for who agrees and disagrees, and have them share with each other whenever you don’t get enough responses to the above.

If you’re careful, you’ll never explain a single rule to them.

They’ll make em up all on their own.

Worth noting: This is not a huge multimedia overhaul. I’m sure there are great real world problems you can involve in this. This is not THE optimal exponent lesson. This is just one option to get rid of the “explain then practice” model of teaching. If you get them thinking, it doesn’t have to be fancy.

Prominently Posting Standards

This is what I think of every time I hear an Administrator requiring that the current standard being taught be prominently displayed in the classroom:

It seems that everyone except people in education realizes that you don’t lead with your punchline.

Quick check for understanding.

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.).

Data! Testing! Gah!

So, part of what kills me about the whole testing debate is that even teachers seem to buy into the fact that the test itself is okay. They’ll present arguments like “You don’t know if the kid had a bad day” or “Who knows how well the questions are written”. But there’s never any decent questioning of the fact that the test can not, in fact, measure individual student achievement reliably. And I can’t seem to convince them that they’re missing the point.

I don’t seem to stop trying, however. Here’s my latest attempt:

Narrative vs Exposition

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.

Counting Days

I totally stole this from NASA:

(The black marbles are days to the CST – I hate how that’s become the focus of everything)

Math on web pages (Advancing Technology)

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!}

Aaaaand here we go, again.

I’ve not posted in a long time.

Years, at this point.

I want to talk about how my practice has improved, how I’m connecting better to kids, and how my lessons are kicking ass and taking names.

But that hasn’t been happening. I’ve been fighting a rearguard action, and it’s about as pretty as you expect those to be. There’s been a lot to whine about, but I’d be disgusted with myself for turning into one of those teachers.

So, nothing.

But, I can’t afford to stagnate as a teacher. Don’t want to, really. Too depressing.

One of the areas I need to improve on is using student work – using it for feedback, for examples, for having my students analyze what they are doing. Someone somewhere pointed at Math Mistakes. And I realized that, if nothing else, I could start collecting those examples, and putting them up here, with as much energy as I have time for. And that those will provide fodder for the online roadmap I’m trying to develop for my courses.

So, school starts next Tuesday. Lets see how this goes.

PS. Hey Sam – do I get to count as a new blog?

Letter to a New Teacher.

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.

Pseudolearning

I’m a little bit late jumping on the pseudoteaching meme. I’m wondering whether it’s the right thing to attack.

Look at that. I can’t tell if it’s wordle, or imitation wordle made by hand. But it’s front and center at our school lobby as “evidence of learning”. I can’t blame anyone for putting it there – it’s certainly more visually interesting than what I gather as evidence, and that space is supposed to be visually interesting.

But I also see people advocating twitter for communication. Or Powerpoints1 for final projects. Or any other number of things that seem to mostly look pretty, rather than cause a student to dig deep and struggle.

Our standards are so dense and thick that we are coerced into teaching them by rote – investigative lessons are mostly used to supplement the learning, rather than as the foundation of it.

The 1right3wrong tests we are judged on are yet another incentive eschew deep learning in favor of memorizing simple patterns. All of the pressures I see for how to teach seem to encourage flash over depth, and I’m not surprised that teaching at large is following along.

If things are to change, it needs to come from the motivations being given to us, and I for sure don’t see that happening any time soon.

1 Sure, Powerpoint can be effective. But I have a hard time believing that 5 slides with 18 words arranged as bullet points requires the same amount of thought and connection of concepts that a properly constructed 7 paragraph essay would.