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For the geometry teachers.

This is awesome. I’m not sure if you plan a lesson around it, or just have kids fill extra time with it.

It could be bigger than Oregon Trail.

The value of substituting

I’ve been teaching for a while now. A lot of the bloggers who were around back when have moved on to bigger things than being in the classroom. I, apparently, have gone the other direction.

The school I had taught at for the past 4 years shrunk their enrollment precipitously. Some combination of demographics, charter schools, the school choice act and the fact that we had no academies or magnets made it difficult to attract students to replace those who might go elsewhere.

As a result, I was displaced. district wide, I was one of many hundreds. It was a hell of a job market to be in. I have done my time at poorly managed schools, and had no interest in returning to a high stress position where I would have to assume the responsibilities of my peers in addition to my own.

So, after very few acceptable (and apparently just pro forma) bites on my resume, I decided to spend this year as a pool teacher. Really, that means being a sub with fewer privileges.

Subs are very near the bottom of a totem pole at the school. It is not a position that garners a lot of innate respect. This can be demoralizing. It can also be very educational.

You do not have a lot of the usual disciplinary support. You don’t have the chance to establish practice routines. You do not get to plan interesting and engaging lessons. For a while, you don’t even know what to expect for the day when you wake up in the morning1.

But you also get a lot:

  • You get to practice your first impressions.
  • You get immediate feedback on how clearly you set expectations
  • You get to see the benefits of teaching in a structured environment (if the teacher you’re subbing for has one)
  • You get to see how much kids desire structure (if they don’t)
  • You get to practice developing curiosity with very limited materials.
  • The bar for failure is low – you can step out of your comfort zone, and even the most abject failures will have no repercussions past the end of the day.

In essence, being a sub means that your teaching practices are put under the microscope, and you get to tweak and modify and analyze far more than you do when you settle into your routine in a classroom.

You also get to see a plethora of administrative styles. If the school board really wanted to know how schools were doing, they’d do weekly polls of the substitutes – Stepping in as a sub tells you much more about the school culture than any dog and pony show ever would.

As a bonus, I’ve made good connections at schools that I like – I’ve had three requests for resumes even before the job application process begins. This is a very different situation from a year ago.

1 I had the good luck to spend most of the substituting time this year in long term positions – I effectively got to borrow a class to teach for several months while the regular teacher is out on maternity or medical leave)

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).

If you know they’re going to make their own rules, then make that your lesson. Start with this as your warm up:


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.

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.).

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?