Tuesday, November 17, 2009
I gave them almost no direction at all, just showed them a couple of small starts that I'd made and they went nuts. I should have brought my camera. It was awesome! They worked so well together, building stuff, talking about what the building blocks were (these dangly things, not fully formed cubes) and didn't eat anything or poke each other at all.
Once they were supposed to start actually counting stuff, finding patterns and rules, the whole thing deteriorated. I left class feeling sort of defeated but determined, sure that I should feel some sense of accomplishment. After all: trying something new, messy, unpredictable. That's success right there, in a way.
So next, I'm trying to figure out how to get it to feel like that more often, how to connect the work they do in their minds to the work they do with their hands. How to get them to really bite into the concept of the variable, which was my motivation to do the lesson in the first place.
Also, what to do tomorrow. Ah.
Wednesday, November 11, 2009
Yesterday proved to be on the difficult side. The kids had had a rough morning (last day of the quarter, NYPD metal detector surprise that morning, typical season affective disorder type blues) and weren't getting quiet. After a couple of minutes of reiterating instructions, and individually trying to help kids focus, Phil went around with big blue paper tape, drew smiling mouths, some with tongues out, and gave it to kids to tape their mouths closed, which they all wanted to do.
This looked ridiculous to anyone who came in at that moment. Comical, maybe even inappropriate. But the thing is, Phil could have yelled, made the kids feel bad, expressed his frustration, disappointment, he could have sent kids outside, called home, whatever. Instead kids were "smilingly" (both on the tape and underneath) trying to be quieter than their neighbor. They ate it up.
The tape didn't exactly turn our kids into models of focus and undivided attention. But kids got some individual attention, which they seemed to need, they got a structural intervention to help them follow instructions and get quiet, and the room stayed positive and focused on the math.
I realized after I watched it happen that this kind of thing is something they didn't teach me in grad school. I've never even (consciously) heard anybody talk about it before. But it seems like a vital part of that magic that good teachers have: to be able to keep the forward momentum, the mathematical focus, the positive energy, in the face of whatever the kids throw at us. It can be so easy to take a momentary failure personally, to get frustrated, feel like the kids aren't listening, whatever. Or just to run out of ideas. What Phil did in that moment was magic because he didn't drop the expectation: the kids were still supposed to be quiet. But he didn't get nego either, on them or himself. He gave them a new reason to follow directions, perhaps clarifying the directions for some kids in the process, and then back to the math.
Phil transformed what could have been a power struggle into a collaboration. He turned what could have been rule-following into a game. He was able to honor the kids, acknowledge their state and their need, give them total respect, and still help them transition and move forward towards our mathy goals. It was beautiful.
The whole thing took maybe 60 seconds. It wasn't such a big part of classtime. But I think it's those moments, the decisions we teachers make in those moments, that set the tone and culture of the class. We are in this together. We teachers aren't going to pull the authority card just because we can. We want to have fun with you while we work. For me, cultivating this feeling in the classroom is the best leverage I've got, for getting a class working, and it's way more fun to be in a room where that's the vibe.
I love teaching with Phil. May you all be so lucky in your teaching collaborations.
My whole class is (ideally) based on group work. My students should nearly always be talking to each other, comparing answers, helping when someone needs help, asking questions when they're confused, helping each other stay on task, etc. Sometimes this is natural, and mostly I see that this is how kids want to do math. Some training is helpful though.
While doing the row game yesterday with order of operations and signed arithmetic, I heard the best conversations I've heard in my new 9th grade classes. I witnessed serious debate, authentic and sustained engagement, passionate investment in each other's work, and evidence of a compelling motivation to deeply look at one another's work, since they hadn't themselves already done one another's problems.
Simple to create and direct, this activity is going to change my class. THANK YOU KATE!
Kate's current post is also beautiful and I'm going to use it in class imminently. I'm excited about the accessibility of the visuals and the ease with which I think kids can interpret and make meaning of them.
While I'm thanking Kate, I should also say that she is the reason I know about blogging in the first place, and the primary support for me starting this here blog, which I'm so glad I did.
Sunday, November 8, 2009
"Educational Revolutionary Mathematics"
That felt like the arising of my own personal cheerleading team.
That was also about three weeks ago.
Since then, I've been negotiating parent teacher conferences, failed experiments in the classroom, incorporating a student teacher (my first), dealing with longer darker evenings, the storming phase of group dynamics, and my own personal dramas around all of the above. Truth is it's felt like such a hard couple of weeks that I didn't want to look at the reality of it in my own head, much less write about it to anybody else. However, I did learn some things.
Highlights that I'll share:
If I feel disrespected, discouraged, frustrated, like a failure...
it's worth considering how my students are feeling. Because they are probably feeling a bunch of those things, and I want to be conscious and sensitive to how I respond to such volatile and hot emotions. Also because I feel immediately compassionate for them in a way that I struggle to feel for myself, and that's a useful button to push in me.
Because when I'm feeling pissed off at myself or them or the situation or whatever, I get distracted by all those feelings and forget to actually look at what's happening, pay attention to the math and the kids who are learning (or struggling to learn it). But once I hit my compassion button, and start looking out for my kids' feelings, then I'm paying attention again, and it's just a problem solving activity, rather than an ego trip or an identity crisis.
I can't be sure, but I think it's safe to guess that I'm not the only teacher who takes stuff personally when they shouldn't, and for all of you out there, I just want to offer this:
Whatever your worst feelings, your students' are worse. Focus on that and it's easier (for me) to let go of my own head trip and get back to thinking about something I can actually do something about (tomorrow, or right now) rather than impossibly fretting about the past.
I want to be your cheerleader now, assure you that somehow it's all about the process, all about showing up and doing your best and working hard and enjoying it as much as possible and in fact doing whatever you need to do so that the hard work feels good. Remember to sleep enough. Remember to eat three square meals every day. Remember to love yourself. Remember to tell them how awesome they are, whenever they are. Look for those moments so you can jump up and down and cheerlead them. We all need it, eh?
Hope your last three weeks have been fantastic. Hope that your Mondays are awesome.
I wanted to share another few excerpts from Larry. He gave a talk last Tuesday at the NY Math Circle's PD for Middle School Teachers, and I was impressed again by how he asks questions to extend thinking about a problem, offer more entry points, and deepens my interest. He does it so quickly, I can't help but get interested and then my mind is thinking about 10 different but connected things at once, and whatever I get into relates to the bigger picture, and it's like magic differentiated instruction and guided inquiry. It's really awesome. We did a bunch of problems, and here are three that I wrote down his questions for:
Show that the sum of two odd numbers is an even number.
What is an odd number?
What is an even number?
Is 4 even?
Is 0 even?
Are there any even primes?
What’s the next even prime?
Are all prime #s greater than 2 odd?
Are all #s greater than 2 prime?
Is -4 even?
Is -6 even? Why?
So now, what is an odd number?
Is every even a multiple of 4?
Show that no perfect sq ends in 3.
Do you believe it?
Do any end in 6?
Did you know that every sq ends in 6 iff the number’s 10s digit must be odd?
Would anyone like to see a proof of that? Good! Go do it.
(I was curious to observe here that every sq is
- a multiple of 5
- one less than a multiple of 5
- one more than a multiple of 5)
Show that x2 – y2 = 2 has no solutions in integers
Translate this into words.
Say this in words: x2 + y2
(x + y)2
x2 + 5x + 6 = (x + 2)(x + 3) Find the value of x that makes this false.
Factor it using diff of squares: (x + y)(x – y) = 2
Note: remember given info
Integers factors must be 2 & 1
“I wanna savor that for a minute. To some people that sounds trivial, but to me it sounds profound. Never dismiss the obvious as being trivial. Even if it’s obvious it may be very very important.”
x + y = 2 and x – y = 1 (or other way around)
“Do something, do anything, and if it doesn’t work, SO WHAT?”