Monday, October 29, 2018

NOW That's What I Call High Quality Math Engagement

As a reflective educator who is constantly trying to prevent his ego from overwhelming his sense of skill, it's important that I recognize that the biggest flaw in my I'm A Creative Teacher shtick is my math instruction. I'm not a bad math teacher, but I'm also not coming up with all kinds of fancy ways to teach it that are crazy engaging and nifty like I am for the more language arts-based subjects. My math instruction is effective, but more workmanlike. As such, my goal for improvement the last few years has been math instruction. When I go to a conference I always choose at least one math-centric session in the hopes that I'll grab up something good. The last time that happened was at iPDX when I saw one half of the Classroom Chef team, Matt Vaudrey, run a wonderful session on discourse.

It's happening again.

At the end of the school year last year my principal sent an email to the 4th and 5th teams asking us if we'd like to participate in a summer math training. I agreed and spent three days in a library at a nearby elementary school getting some strong math discourse knowledge dropped on me. Also a lot of binders that should be Google Drive folders. Which...whatever. That's my hang up. Then I went away and set up my classroom, trying to remember all the stuff I learned and find ways to implement it.

But that was not all. Oh no, that was not all.

What's you biggest complaint after a professional development, dear reader? Clarification- After a good professional development. If you're anything like me (and if you are, congratulations on being so attractive, smart, and modest) the thing you think most at the end of a big PD is, "That was great, but one shot isn't really enough. Regular refreshers and supplemental trainings would really help this be usable." Friends, be careful what you wish for.

I'm not complaining. Not really. But that summer math training came in a package that included regular trainings/math studio days during the school year. I didn't realize this. It might have been in the initial email I skimmed. Either way, I'm having to take one or two sub days a quarter to go to a school, meet with the trainer and my group from the summer, get trained up, and watch some sample lessons in a math studio class. Yes, I can see you in the back with your hand up- A math studio is a specific class in our district that has been earmarked as the one where the teacher will specifically be using these strategies and when we have a training we will also observe her class being taught. So it's both classroom and practical. Really, it's everything you'd want out of a training, save for the sub day thing. But if it makes me a better math teacher it's worth the time this year.

And it's paying off.

I tell you all that as a preface because it's important to me that we see the value in trainings like this, and it's important to me that cool ideas that aren't my ideas are not passed off as such. We're all stealing. Trust me, I try to let you know when something works that I've thought of whole cloth. Or I will as soon as that happens. I 100% stole this project from the math studio class and modified it to suit where my fourth graders were at.

There should be number block representations in that last column, dunno what the computer did with them.
We were working on addition and subtraction, along with place value and representing numbers. This was a few weeks ago, for those of you overlaying your math pacing guide with the time of year. I'm not that far behind. I created the above four by five grid of math problems represented in the traditional way, as word problems, in expanded form, as place value charts, and in number blocks (not pictured because of some weird computer glitch). Also, for those of you looking closely, there are one or two mistakes in there. Total accident, but they actually played into what happened next so I'm ok with my mistakes.

I printed sixteen copies of this sheet, one on each color of paper I could dig up in the copy room. So 16 copies because a) that creates groups of two students, mostly, and b) I was shocked I could find 16 different colors of paper in the copy room so I went with it. Then I cut the little squares out, paper clipped each color together in no particular order, and put the paper clipped squares into envelopes. This took longer than I'd prefer, but sometimes you gotta suffer for your art and all that inspiring meme-fodder. Then it got fun.

I love presenting projects to my students like this- I had them partner up. Then I held an envelope up without speaking for long enough that they were salivating at the thought of what might be in there. It works, it's all in the presentation. And I proclaimed, "Within these envelopes are small squares! These squares are related in some way! Your job is to organize them! This i all the direction I will give you! Tallest person from each group, come to be and receive your envelope!" I love giving non-specific directions. 

Students immediately started pulling all the cards out and doing that thing students do- Not being thoughtful or organized at all in their initial look at the cards. Just flipping them over at random. Pushing them around. Going much too fast. Slowly most pairs reached the same conclusion and hands waved, "We're done!" What do you think they had done, dear reader? Did they grid it out? Of course not. They made five piles. A pile for each different kind of problem. When three groups did the same, which I'm totally going to pretend to have expected, I stopped the whole class. "I see lots of you organizing the cards into similar piles. Yes, that's organizing them. No, that's not what I want. Keep trying."

SO MUCH math discourse, my friends. It started naturally. They had to have it. They had to start talking to each other about what they were seeing. "Oh wait, this one equals 1,349! I saw a thousands block...look! These are the same. No, see, because blah blah blah." Some groups got it faster than others, of course. Some floundered. To those I suggested maybe a short walk around the classroom would be in order. Not to steal ideas, of course. Just to see. 

Soon a group was done. Almost. "Mr Robertson, we've still got all these blank ones." 

"Hmmm," I say. "Interesting. Blank ones you say? Do you think those are in there on accident?"

"" the students reply. They know me by now. They know the class mantra this year is, "Everything Has A Reason."

"Hmmmm," I say again, nodding and pulling at my chin. "I wonder why they're there. Good luck." Then I walk away, mentally rubbing my hands together like a Bond villain right after the world's greatest super spy stumbled into my trap again. And I listen with my Teacher Ears for the, "Ohhh! Look look look! This row is missing that kind of problem! And this row...OH! OH! Mr Robertson! We figured it out!"

Bwahahaha. I love teaching without saying anything. 

Once enough groups had figured it out Phase Two went into effect. The groups had to pair up with another finished group. Then switch sides. Group A looks at Group B's card grid, and Group B looks at Group A's. Then Group B has to explain to Group A what they see Group A did. Group A has to listen without interrupting, then they are allowed to ask clarifying questions. Then it reverses. In the parlance of the internet- Much discourse. So math. Very disequilibrium. Such thinkings. 

To be clear, this whole process took the entire math block, just over an hour. And some partnerships didn't finish. But they still got to talk to another group and see what was done. 

The kids loved it so much, and I was so blown away by how well it worked, that I determined I would do it again. So last week I built one for multiplication. You can see that below.

Again, no idea why the graphic representation isn't loading, but trust me, it's cool.
This one was greeted by cheers from my kids. Yes, I said it. They were so pumped. I wish I could be all chest poundy about this, but all I'm doing is finding something that worked once and hoping it'll work again. The only credit I take it seeing that it was a good idea, modifying it, and then chasing the dragon a second time. 

This time, just because I like playing with fire, I invited my principal in. She wanted to see what I was learning from the training, and she never gets invited into classrooms. She's always got to schedule something for an observation or whatever. But she's got the soul of a classroom teacher still, so it's fun to ask her to come in. 

It went even better the second time! They knew the trick going in this time, so everything went much quicker as far as grouping the cards, even with it being multiplication and my making some of the relationships between cards a little more unclear. Instead of making them group up, though, I used what seems to be every teacher on social media's tool de jure, The Grid of Flipping. (I swear, if you even think Fl!pGr!d on twitter their social media team will smell it and send you a dozen Stepford-like helpful tweets. I'm good, back off.) I set up a grid, set the video time limit at five minutes, and had the kids explain their thinking to the camera on their Chromebooks. Then they needed to watch at least two other explanations and reply to those with sentences like, "I like that you", "It's interesting that you", "When you did x I was y." 

At the end of all that we talked about the habits of mind and the habits of math discourse that we used during the game (I called it a game, a rose by any other name can still trick students into thinking it's a game), which was also valuable. Kids talking about when they used reasoning, when they used mistakes and perseverance, when they used modeling, and so forth. I am not too modest to say that my principal was blown away. She praised my kids for their work and their thought, she gave me some nice pats on the head, and my kids were jazzed.

So much so that at the end one girl raised her hand and asked if we were going to do it again when we finished division. I told her I was thinking about it but that I was also thinking, now that they seem to be experts at it, what if I gave them twenty blank squares and they had to set the whole thing up? Friends, remember, this is a math lesson. It's a heavy lift math lesson. There's a lot of cognitive load happening. It's not easy. And what I'm proposing is even more difficult than I think they expect. But they were so high on math at that moment they cheered the idea. I'm not making that up, I wouldn't lie to you. I would tell you if a collective groan went up, but it didn't. 

I laughed at/with them and told them, "I'm so excited that you are so excited about this. I'm also so excited that you all decided to react like that while the principal was in the room, so that's for that."

I love getting deeper into mathematical discourse and finding creative ways to increase the cognitive load my kids are carrying, while also making them more independent and helping them see themselves as mathematicians. 

If you have any questions about the projects I wrote about here, math studio, ideas to make my math instruction better, or anything else, please leave a comment, shoot me an email at theweirdteacher@gmail, or send me a tweet at @TheWeirdTeacher.

If you like this post and the other posts on this blog you should know I’ve written three books about teaching- He’s the Weird TeacherTHE Teaching Text (You’re Welcome), and the just released A Classroom Of One. I’ve also written one novel- The Unforgiving Road. You should check them out, I’m even better in long form. I’m also on the tweets @TheWeirdTeacher.


  1. Love this! Stealing and trying to create one for rounding and comparing decimals!