Part of me thought I would get to the Park City Math Institute and be blogging up a storm. I would sit down each night, twitching with excitement, ready to blog about all the ideas and problems and conversations I would be having.
And I am aflutter with excitement about this program.
But the problem is that I’m spending all day talking about math and teaching, and thinking and thinking and thinking, and I don’t have the motivation at the end of the day to organize my thoughts.
This is problematic. Because my memory:elephant’s memory::pebble:mountain.
So tonight I’m just going to jot down a few ideas/observations/thoughts that don’t fit into the larger posts I feel compelled to write on (a) lesson study, (b) math talk, and (c) PCMI-as-a-learning-community [1].
0. There’s a really personable, funny person at PCMI who writes a blog that I’ve been to a few times — but for some reason wasn’t in my reader. It’s awesome. From his about page: “I’m a recently tenured college professor teaching mathematics at a high school during my sabbatical leave. I’m blogging about my experiences mainly to record my successes, frustrations, thoughts and feelings.” The best part: it’s concrete and on the ground and honest. And being new to high school, he makes observations of things we don’t always notice — or that we’ve forgotten (example here). So go back through the archives and drink up! Adventures in Teaching
1. When kids are working in groups, and you want to start having them wind down without the time pressure, you ask them to hold up a 1, 2, or 3 fingers to represent how many more minutes they need. And to make sure everyone is participating, if they don’t need any more time, they hold up a fist.
2. If you’re having a problem with student attending class on time, on certain days you can give raffle tickets to students if they are in their seat before class starts. When class starts, you select a raffle ticket to win a prize. Sometimes the prizes can be lame, sometimes they should be good. (They do this with US — adults — to get to the morning session on time. It works for me.)
3. Watching videos of teachers is powerful. I would love to have DVDs of good teachers teaching. Nothing else – no text, no explanations, just the videos for me to watch and mull over.
4. A group of teachers from Seattle came for a week and presented the work they’re doing with “Complex Instruction.” Part of their work was building a supportive and hard-working community. No easy task. One of the things they do is video tape their lessons and have discussions about the tapes. When talking with one of ’em, he said that the teacher on the tapes of him was not anything like the teacher he thought he was. Powerful, and scary. I asked more about how they set up a safe space for teachers to look at the tapes, and feel supported, and not defensive, it was clear they had to do a lot of work beforehand to make sure that happened. There were stages. But what struck me the most was the norms they had when viewing the tapes. The teachers teaching weren’t individual teachers. They were any and all teachers. They said more than a few times that “it could be any of them.” To emphasize this, they only referred to the teacher as “Teacher” — not by the name of the specific teacher teaching. Everyone saw themselves as working almost as one collective, one Teacher, working towards improvement of practice through these videos and discussions. Just like we say how blogs and twitter have changed our lives when it comes to teaching, they say videos have done that. Scary, but I want to do something like this with a few teachers I feel safe with.
5. Teacher moves. This is a term I’ve picked up here. I generally hate jargon. I am a philistine. But I have come to really embrace it. Because it gives a name to something that we do all the time. We are confronted with a situation (whether it be academic, behavioral, social, blah blah blah) and we have about 2 seconds to decide how we’re going to deal with it. What I’m learning is that although we all have our own set of teacher moves — most that come naturally to us — we can work on expanding our repertoire and honing these teacher moves. How? First, by talking to (or reading blogs of!) other teachers — to see other teacher moves. Second, by thinking through hypothetical situations that might arise in the classroom and anticipating how you’re going to respond to them. For me, just giving these things a name — “teacher moves” — let’s us start having conversations about improvement.
It is letting me see the whole class as a set of discrete teacher moves. Moves I make consciously and unconsciously. But by starting to conceptualize my time in the classroom as a string of discrete teacher moves, I can start thinking about things in a somewhat more concrete way. It let’s me focus more on my actions.
6. In my classroom, as I suspect in most classrooms across the country, the teacher is the sole authority of knowledge. What’s right and what’s wrong. It makes sense, of course. But I’ve been learning that this setup might not be the only approach. One of the most important things to instill in our kids is confidence in their abilities, and the ability to take intellectual risks. The way most math classes are structured, well that’s not so conducive for risk taking. And the teacher is the arbiter of knowledge — that’s right, that’s wrong. Students look to what the teacher writes on the board and starts to believe that only the teacher can be a math authority. I have no problem with the teacher being a math authority. But I’m starting to realize that in my classes, I am the math authority. I want kids to be math authorities too, and to view each other as valuable sources of information. It might be something to think about. Because I suspect that getting at this is also getting at independent learners. And getting at math confidence.
7. Me at the 4th of July parade with a bunch of math nerds! “We love math, how about you?” was the final two lines of our chant.
There are more things, but I’m tired. Sorry it isn’t so coherent.
[1] If I don’t write about these in a reasonable amount of time, feel free to harass me.
Continuous Everywhere but Differentiable Nowhere 
Thanks for the post. Looking forward to a report about other things you learn there and maybe about how this program got it right.
I’m definitely going to post something about how PCMI got it right. At least for me. I can’t speak for all participants, but to date, I haven’t heard anyone saying it was a waste of 3 weeks. And for teachers who are on summer vacation, the majority of them who left the day after their school ended, that’s quite a testimony.
The idea about “teacher moves” make a lot of sense to me. Over the last two years I’ve been mentoring the trainee teacher in the maths department. We talk about planning out how they will respond to types of behaviour and how to carry themselves. Then I get them to write the phrases they can use on mini-index cards (and read them into the mirror if necessary!). For example, words of praise they would like to use more naturally, or a standard response to off-task behaviour. It would be great to compare with my colleagues what teacher moves they use regularly.
I wonder if we can’t start compiling a list of em somewhere. Now that I’m going to be more conscientious about teacher moves, I might start blogging about the ones that I use well, or the ones that I use that don’t work well. (And if I can suss out why.) But that will have to wait until school starts, I suppose.
Realizing that you don’t have to be the sole mathematical authority in the classroom is powerful. You will be amazed at the observations made and risks taken once your kids come to the same realization. It takes a lot of work to get there. I’ve found that for it to happen in my classroom, I have to work to establish that culture from day one.
It can be frustrating for the students at first. It so goes against everything they’ve learned about what it means to learn and do math. But they can unlearn and learn.
Thanks for writing up your experiences there – it sounds like a wonderful learning adventure. I can’t wait to read more.
Can you write something about how you establish the norms/culture early on in the year?
An excellent post, Sam, and I’m looking forward to your other insights. You explore some very complex concepts in ways that seem so simple:
Re: Maths Authority. I have realised long ago that many students in my classes can be valid sources of Math knowledge. It’s relatively easy to tap into on a small scale this with certain kinds of group work. I’ve found it harder to use an individual’s knowledge in classwide situations that don’t make the student in question feel unconfortable about being an authority. The other kids take a while to trust another students authority too. I read an awesome blog post last week which I can’t find now about doing a review in the lesson-after-an-assessment (normally a dull lesson) that is run by students who are authorities. I’m really keen to try it now.
Keep up the good work. Even posting these tiny snippets of thoughts is enough to get discussion rolling on lots of topics in the twittoblogoverse.
Love the tessellation. Being the authority in the class is something I struggle with all the time too and I also am beginning to figure out that it is a disservice to the kids when they look at me as being the all-knowing one and they are simply there as recipients of knowledge as opposed to co-collaborators of the synthesis of knowledge. It is something that I hopefully will address with my colleagues in the fall. Kids need to create their own knowledge but often I feel, with high stakes testing involved, that I must give them the information rather than them discovering it themselves to cover my own butt at the end of the year.
So would a “Teacher Moves” wiki do the trick?
I suspect the answer is no, the more I think about it. Wikis are hard to get off the ground unless there is a core group of people willing to devote a lot of time to making it useful/somewhat comprehensive.
An alternative would be to have it slowly grow on the Math Teacher Wiki (http://msmathwiki.pbworks.com/) which is awesome. I think if you started a page called “Teacher Moves” and then defined what you meant by them… if they were generalizable, it could be really useful.
So start it up! FIRE IT UP!
When I was on a math trip that left me similarly exhausted and buzzing with things that were worth remembering, I just stayed up way too late and did a memory dump. I remember writing “If I had more time, I’d write less” but I just didn’t have the time and energy to process and refine anything.
Maybe that approach will work for you — just blog, dump some undigested ideas out there, and later on reading what you wrote will help with the memory thing.