For those of you who are looking for the slides…look no further!

All Kids Are Smart-Creating Balance 2012

Debrief to follow. After some sleep.

I actually began this post in early November, when I was feeling kind of sucky about my teaching. I wrote the following list.

Some Questions I Need to Remember to Ask Myself:

• How are students building their understanding of this concept?
• What is the context?
• When is the right time to remove the context?
• Do students know why we are practicing this skill?
• Do students understand how this connects to previous knowledge?
• Have I asked students to articulate these connections?

In the shower this morning, I was thinking about Big Questions. These are the Big Questions up on the walls in my classroom (note: I didn’t come up with these).

• What is mathematics?
• How does mathematics connect to the world around me?
• What is the pattern?
• How many ways can I represent it?
• How am I a mathematician?

I don’t feel like I use these questions very often. I don’t really refer back to them. I wanted to come up with something a little more personalized. So I did.

Big Questions (a work in progress):

• What story does the math tell?
• How could I represent this scenario in a different way? (& Which representation tells the story best?)
• What information do I need to solve this problem?
• What else can I figure out?

You can see these two lists are different, though there are certainly some common ideas in both (hello, multiple representations!). One of my goals in writing my own set of Big Questions is to create something from this year of teaching that I can bring to my future job(s) regardless of which grade level I’m teaching or what school I am at. I’ve been thinking about Big Questions for a while so it didn’t take me too long to come up with this list (and I didn’t waste too much water in the process).

What I like about both lists is that they are general enough to be used in any math class. I was trying to think about what big ideas and skills do I want students to take with them throughout their lives. And I think my list speaks to that idea.

While I’m in the swing of making lists I might as well make one for my new year’s resolutions. And while I’m at it, why not make two?

Personal Resolutions:

• Make a quilt.
• Start observing Meatless Mondays (or some other day of the week)
• Write something every day.
• Read 70+ books this year (I put this into the 2012 reading challenge on GoodReads).
• Bake bread regularly.

Professional Resolutions: 

• Be more consistent. [This is my always goal. I never do not have this goal. But in my mental space right now, I am thinking of being more consistent with my classroom routines like checking off homework and stuff like that. ]
• Give more presentations at conferences!

I think that about sums it up. Now that I’ve worn out the bulleted list button on my computer, I may have to relearn how to write in complete paragraphs. I do have one last goal though:

• Do not leave purse on plane. Again.

Lesson One: You can never have too many copies! [except, of course, for when you do...] 

I wasn’t expecting very many people to show up at my presentation. Well, I was wrong–there were people sitting on the floor. So, I didn’t have enough copies for everyone, which was a bummer. But people were really nice about sharing with the people next to them, and that led to (in many cases) a good buzz of collaboration, which may or may not have happened otherwise. Of course, most people would have preferred to have 2 copies–one to work on and another clean copy to take home with them. As someone who regularly kills trees with all of the printing and copying I do, I try to avoid dumping a big pile of extra handouts into the recycling. If I had been better organized, I could have gotten my materials onto the Asilomar CD so that people could have had it electronically.  I usually wind up chucking the Asilomar CD, which may be part of the reason I didn’t get my materials submitted by the deadline. I put everything up on my blog, which is sort of the same thing, but it takes an extra step to get into teachers’ hands.

Lesson Two: Do More Puzzles! 

I was happy to hear from people that they wanted to do more puzzles. More math is always a good thing in my playbook. In an earlier quasi-presentation, I did three different puzzles in 90 minutes and wound up feeling rushed. Much of that was due to the particular puzzles I chose, and in retrospect, I probably didn’t actually have 90 minutes at the PDO session. I realized mid-way through my Asilomar presentation that I had started out my pacing wrong and I was going to wind up with a big chunk of unfilled time. I had a quick pow-wow with Avery and decided on a plan, but still wound up being done 15 minutes early. And the last bit kind of dragged. The hardest part about adding in another puzzle will be deciding which one to use…

Lesson Three: I need an extra power cord.

I remembered my dongle, but didn’t have a power cord for my laptop. Someone told me that I could borrow his power cord for my session. *Ahem* However, that didn’t work out. Which was bad, because my laptop will go to sleep, regardless of setting preferences to “don’t sleep,” when it doesn’t have a power source. This was a pain in the ass, and made me look totally unprofessional. I’m not a professional, and this was my first attempt at a conference presentation, so I was okay with this. And my audience was very forgiving. But I’m for sure bringing my own power cord to NCTM in April.

Lesson Four: Giving a presentation is kind of like the first day of school.

Having only gone up and facilitated stuff like this in front of people who I actually know (and who know each other) I sorta forgot that people–even teachers–get shy and don’t want to talk in front of a group of strangers. As one person mentioned in their comments, “whole group reporting can take away momentum/energy.” There was a great sub-set of teachers who said some really interesting and valuable things, but many people didn’t want to speak and the room sounded full of crickets to me on a few memorable moments. Funny thing was that I had participated in a session several years ago that used much of the same format for the last part of my talk (i.e. I shamelessly stole this section of my presentation from that workshop) and it worked really well with that group. One challenge was we couldn’t really do a gallery walk, since the room was on the small side and filled with lots of people.

Lesson Five: I had a really great time!

I was nervous before-hand, especially at lunch right before my session. But after it was all over, I was so glad that I had done this. This was an experience that I learned a lot from. And giving a presentation to my teacher-peers made me feel like I’d grown a lot professionally. There aren’t all that many steps in the teacher professional growth path. Student teaching, teaching for real, and then what? You can do coaching, or go into administration, both of which usually involve leaving the classroom at least in part. This was a great way for me to see external evidence of the fact that I have progressed beyond “beginning teacher.” Well worth the butterflies in my stomach.

I’ve already started thinking about what to propose for next year…I guess I’m hooked

———————————————————————————

Most of my feedback highlighted the lessons I wrote about above. But there were a few that I’m still mulling over [included here so I don't forget 'em]:

• expand the idea of a proof to other classes and proof types [emphasis added by me 'cause this idea is great].
• want info about where to find materials.
• more focus on [how to?] transfer [from] puzzle to 2-column proof.
• more explanation of proofs in context of standards. basic proofs?
• would like some discussion on how to scaffold the “proof posters” for students.

I’m not sure what (if anything) I’ll do to address these comments when I give my talk again. As with all critique, some of it you use, some of it you don’t–but it all informs your process. The fact that I’m not sure yet where to go with these comments speaks to the value in getting feedback like this. These people got me thinking about my presentation and how I can make it better, and I’m still thinking about it a week later. Thank you for that!

First time being on stage (so to speak) at a math conference. I’m not ready to give the full post mortem, but I wanted to get my stuff up online for anyone who wants copies, or just to take a peek at what I did. Without further ado:

You can look at my prezi (and swoop through the slides as often as you want). You can even create & edit your own copy should you so desire.

Here are the two puzzles we worked on:

• Shikaku
• The Race

And a link to nikoli.com, one of my favorite puzzle sites. 

Tomorrow is the start of the CMC-North conference at Asilomar. If you’re going to be there, I hope to see you around. My talk, Beyond Sudoku, will be at Pacific Grove Middle School from 1:30 to 3:00 this Saturday. I am excited, but also a little nervous about my debut math conference performance. It should be fun.

Is it bad that I confessed to my tutee "this is why I hate properties" when talking about proving that -1*x=-x?—
Breedeen Murray (@btwnthenumbers) November 14, 2011

This is a slightly inaccurate depiction of what went down. In perfect honesty, I didn’t say that I hated properties; I said that I hated “these types of problems” i.e. algebraic properties style “proofs.” But that didn’t sound as snappy, so I changed it for the interwebs.

The thing is I love proofs. I was the totally nerdy freshman in high school who got jazzed about doing two-column geometry proofs. In hindsight, two-column proofs are the red-headed stepchild of real proofs, but, cut me some slack. I didn’t know any better at the time and it was my first real exposure to the idea of proving something rigorously.

You see, I am someone who loves being right. I can be the most bull-headed, stubborn pain in the you-know-what that you’ve ever met. In fact, I so dislike being wrong that I will do just about anything to avoid having to make a guess about something. Don’t  believe me? Just ask Avery. He’ll vouch for me.

Proofs are like manna from heaven for someone who loves to be right ALL THE TIME. They let you give the intellectual “up yours” to any doubters that might be lurking around every single time you write QED, or draw that little black square at the end of the paragraph.

So I love — and I do mean LOVE — proofs.

But I HATE the way we teach proof to students. It makes me die a little on the inside when I see kids having to prove that -1x=-x. Or that multiplication distributes across subtraction, just like it does across addition. Gasp!

The problem with these “proofs” (and I use that word with reluctance) is what I am going to refer to as the Duh Factor. No one doubts that either of these ideas is true. Not even for a second. Everyone knows they are true because they’ve been using these ideas for years by this point in their mathematical careers. You don’t get that smug satisfaction of flipping someone the mathematical bird by proving that -1x=-x. It’s an obvious, accepted fact.

No one cares.

Proofs are the persuasive writing of math. Writing a letter to someone to try to convince them of all the reasons why two-year-olds shouldn’t be taking the LSAT’s isn’t going to impress your English teacher. Why then are we making students do the intellectual equivalent in math?

If we want to amaze students with the inherent beauty, the power, the sheer coolness of math, we need to stop giving them problems with the Duh Factor and start giving them concepts to grapple with that truly stretch their thinking in new ways. That blow their friggin’ minds. Because what makes proofs truly powerful is their ability to prove that something which seems at first unbelievable is actually, unequivocally true.

Q.E.D.

The school I taught at last year, and the one I’m teaching at right now, are really a different environment. From the get-go I noticed that students really took comments to heart. They read them, they tried to understand what had happened with their test or quiz or other graded assessment. So, I feel like a lot of what I’m about to offer may be harder to implement in a setting where this isn’t the norm.

I also feel the need to qualify my description of these super-responsible students I’ve depicted. You do need to bring the level down a step or two for my current middle schoolers. They run the gamut from very responsible, perfectionistic, no I will not let you come in again to finish your test kids today to spacey, distracted, OMG! we have a test today?-what’s it on? kids. You know, regular middle school kids.

But part of the process of getting students to the point where they look at feedback and think about how to apply it is to give them opportunities to interact with feedback. Things like test corrections, or SBG reassessments, help students to see why reading comments and talking about them with their teachers is important. The process that I started using this year (stolen from my former co-teacher, now at-home-Mommy) is called a “recycle”. A recycle is different from test corrections I ways that I really like.

The format is that student fold a piece of paper along its vertical axis (i.e. a “hotdog” fold), or they just draw a line down the middle. The left-hand side is for students to correct all of the problems they made errors on in the quiz/test, and the right-hand side is for students to explain what kind of error they made and/or why they made that error. The second part is what I really like. Students have to really think about what kind of mistakes they are making. Are they careless errors? Are they big conceptual errors? Did they make a lot of errors involving negative signs? Did they not know the meaning of a word? As they do these recycles, students are involved in a high level of metacognition. They have to tease apart what and how they were thinking at the time they took the test and think about how that thinking has or might change now.

My eighth graders, who have been doing this process for over a year at this point, have a really good understanding of what kinds of errors they make and why. My seventh graders are still learning what makes a good recycle. Some of them continue to have trouble with the format. But they are getting there.

No matter where I wind up next school year, whether I wind up staying on at this school or continuing in my roving-teacher ways, I plan on bringing the recycle with me. After all, it’s good for the planet.

I’m trying to unpack just why that is. When I get together with other math teachers (or science teachers–Hi Jason!) I have plenty to say. I feel like an active participant in the conversations that are occurring. Why is it that I feel like I have nothing to say in the online conversations that are happening every day?

Last year I was trying out SBG and so I was thinking about that a lot. This year I am pushing myself in ways that lie outside of my daily practice. I am speaking at three different conferences, but in the classroom, I am not doing anything that is really new for me. Which is probably why I find myself logging on to my blog and then leaving without typing a word. However, that should change for the better in the next few weeks.

I will be giving my first talk in the beginning of December, so sometime in between now and then I will need to think through exactly what I plan on doing. And I would like to share what I do with those of you who won’t be at Asilomar this year.

And then in January, Geetha and I will be co-facilitating a workshop at the Creating Balance conference in SF. We are going to be talking about status in the math classroom. That one should have me thinking about all kinds of deep ideas.

And finally, I will be speaking at NCTM in Philly this April. The three-ring circus that NCTM can wind up being should be good for at least a post or five.

So, bear with me while I muddle through this bout of writer’s block (which, thankfully, hasn’t been hitting me with regards to my NaNoWriMo novel). I’ll come through it, keyboards a’blazing and knock your socks off. Just wait and see!

The goal of the course is pretty simple: we play puzzles and games. The challenging part is to 1) find games that can be learned and played in 40 minutes and 2) remember that I have rotation on Mondays and come up with something to do Sunday night. Yeah, I’m really proactive about this.

So far I’ve been doing this for about six weeks, give or take due to Monday holidays. This is the calendar of events so far:

Week One: Shikaku (four corners). This is a Japanese logic puzzle that I have written about previously. I like the premise of starting a puzzle by asking kids what the goal of the puzzle is. Went very well, except for one whiny kid who wanted to know–constantly!–when we would start playing games. I was able to use the SmartBoard to solve the online sample puzzles on Nikoli, and have kids come up to place their rectangles. Much fun was had by all.

Week Two: Nim and Tic-Tac-Grow. If you don’t know the rules of Nim, please don’t tell me about it because then I will have to stop being your friend. However if you’ve never heard of Tic-Tac-Grow, it’s because I made up the name though not the game itself. The rules are straightforward. You start off with a normal 3×3 tic-tac-toe board, but the goal is to get 4 x’s or o’s in a row. How is this possible? everyone will ask. Simple. After you place your x or o, you also place a square that somehow adjoins the grid. You can decide whether or not “adjoining” means on a side or if it also includes on a corner. This also went well, despite my use of interlocking centimeter cubes for Nim. Many were more interested in building little structures from the cubes instead of playing the game. I decided I was okay with that.

Week Three: MasterMind! In which we play a real, live, branded game. I taught them the rules by using a computer game online. Warning: most games you find through a Google search have been taken down due to copyright issues, but there are still one or two up and running. I also had three versions of the board game, which wasn’t quite enough for my group of ten. This turned out to be wonderful, since they had to play in groups of three (and one group of four). The groups of three were the best, with one person making the code and two people working together to break the code. It was great because they had to talk about what they were doing instead of just randomly guessing. I recommend the three person MasterMind game for all future MM endeavors.

Week Four: Bloxors. Super fun. I had to do basically nothing for this one. Just reserve some laptops and set up a bit.ly web address. They were off and running all by themselves. I told them to skip the tutorial, but I did tell them some of the tricks when they got to appropriate levels. Hint: the space bar comes in handy sometimes. I got my co-teacher (and apparently her husband too) hooked on this game.

Week Five: Set. Showed them the computer game individual version online at nytimes.com and then had them play with the actual card game. Had to move around and wrangle in kids who were grabbing at cards faster than their teammates could check them, but otherwise it went great.

And that’s it so far. Today, no Rotation since we have a Fall Holiday. Which is probably the reason I’ve actually written a new blog post.

We went back the day after we moved to clean the old apartment. As I was sweeping up the dust bunnies and clumps of cat hair I felt that sense of satisfied contentment that comes from seeing the results of your labor come to fruition. Without all of the furniture and such filling the space it’s much easier to see the change from dirty to clean, since everything is out in the open.

The act of sweeping up reminded me of my very first teaching job. I had finished up my student teaching and then stayed on for an extra week subbing for a colleague as a favor. Then I worked for the rest of the school year at a different high school covering for a woman who was on maternity leave. I was there for three of the longest, hardest months of my life.

One of the things that was really difficult for me was how much of a mess my students had created by the end of the school day. I believed that this was a reflection on my inability to control their behavior. Classroom management was certainly not my strongest suit at that time. But—of course—I was harder on myself than I needed to be.

The thing that saved my sanity in those months was that there was a broom in my classroom. At the end of a particularly rough day I would sweep up the wadded up paper balls and broken pencils and other detritus from the school day. The janitor would occasionally catch me in the act and chastise me. “You don’t need to do that! You have other things to do. I’ll take care of it.” And he would. The janitorial staff at the school was awesome. But I would continue to sweep up the mess. I didn’t do it because I felt like I had to. I did it because the act of sweeping was meditative for me. Seeing the dirty floor become clean, because of something that I had done made me feel calmer. It was the one thing I felt I had complete control over. It was the one activity that I did all day long that allowed me to see the results of my work.

Teaching, especially in the first few years, is such a difficult task to do day in and day out because the results of what you do aren’t clear and obvious. You have the same issues with Jimmy three months into school that you did three weeks in. Katy still gets upset whenever she makes a mistake. You realize after you collect a quiz that half of your students still have no idea how to add fractions even after you went over it with them for weeks.

The tricks that you pick up along the way, over the years, help you to gain the perspective to see and notice the changes that are occurring in your classroom. But in that first year you can’t see it. At least not on a short scale timeline. I remember looking back and reflecting at the end of my first (full) year of teaching and realizing that I had changed a lot, and my students had changed a lot. Had I been able to look ahead to that moment in my first few months of teaching that would have been really helpful. Because in that moment, every day, every week seemed the same as the one before. Only after the weeks turned into months was I able to recognize the results of my work.

There is a construction site near my old apartment which sat seemingly untouched for most of the time we lived there. Part of that was probably due to the economy, but a lot of it had to do with the way a structure is built. The ground gets leveled, the cement slab poured. And then the site just sits there for a long time while the cement dries and cures and the architects assess and make adjustments. This particular site had been lying dormant for months. I walked past it pretty much every day last spring and it always looked the same. But then, we came back from our summer trip and a building had sprouted up out of the ground. A really big building.

The foundation takes time to build and to make solid. Once that has happened the rest springs up quickly. But you can’t build a solid structure without a good foundation. It takes time and effort to make that foundation, and then the walls and the roof and everything else build off of the work that you’ve already done. It’s still hard work, but you can see the changes you’re making each day.

Becoming a teacher is a little like putting up a building. It takes a while to create your foundation. And it’s really difficult work. But once you have that in place, the rest becomes easier (I promise!). And then you can see the progress that you and your students are making much more clearly.