# TRACY BARE - METZGER FELLOWSHIP ESSAY

**LUNCH AT THE MATH BUFFET**

Welcome to my classroom--a weird, oblong, 1970’s concrete box at the Pierce School. We are in the midst of a POWFest. This week, self-selected groups of kids are working on an array of challenging math problems--one problem might take a group a class period or more. There are all kinds of problems in the packet, of varying levels of difficulty, but none of them are easy or routine. Students choose which problems to attempt--it is a math buffet. The expectation? Students do the hardest problems they can, as many as they can.

I am not in the front of the room. In fact, I perhaps appear to be doing not much of anything as I talk to kids.

A student named Cassie calls me over.

“Do you think I can do this one?”

"Why don’t you try and see. I bet you can do something with that.”

She tries and struggles for a while. She loudly announces, “I hate this!” Then quietly and less emphatically, “Do I stink at math? I do, don’t I?” She asks me this question regularly when pushed out of her comfort zone.

“Of course not,” I always say. “You can do this. Don’t psych yourself out. To see a pattern, it is helpful to organize your information.”

Another girl at Cassie’s table has an idea about what they should try. They put their heads down and keep working. A while later, they figure it out. They leap out of their chairs, shout and high five each other. They’ve worked through Part 1 and call me over to show me their system. They both feel very proud.

This is the best thing that happens in my classroom--students working together and thinking hard, everybody being challenged at their own level. It’s taken me a long time to get here.

Prior to my arrival in 1999, Pierce had 8th Grade math classes that were tracked into four levels. The previous spring, after the class sections had been constructed, the vice-principal had decided to end tracking. The previous math teacher quit in protest. For various reasons, the kids were left in tracked groupings, but the parents had been notified that I, the new teacher, would teach everyone the same material at the same pace, every day. Needless to say, this did not work well. I taught in a very traditional way--each day I explained that day’s math, conveniently chunked by the textbook, then went through a few examples on an overhead projector, then assigned homework practice. I went over questions about the assignments the next day. In retrospect, this sounds awful, although perhaps I had a certain new teacher enthusiasm that made it bearable.

My one-size-fits-all teacher-centered instruction was too difficult and fast for some sections, too easy and slow for others. That winter a tall, skinny and outspoken student named Natasha said to me, “You know Ms. Bare, a lot of words and a whole lot of numbers come out of your mouth, but I don’t understand a thing that you say.”

Middle-schoolers make pronouncements like this all the time, but this one stuck with me. Natasha was in the lowest of my four sections, and I expect what she said was true--what I was conveying was making no sense at all to many of those kids.

My second and third years teaching are a bit of blur; I had two small children and my mother was dying of lung cancer. As I recall, I taught the same way, but to heterogeneous classes. I worried about students like Natasha, who just could not access the Algebra I curriculum. I thought I knew the answer--go back to tracking. After all, the tracked classes at my junior high worked fine for me. It never occurred to me that I had always been in the top track and that I had no personal experience with a low track class. I asked my principal if we could try one, and she agreed.

The next year, I got my low-level tracked class of 7th graders. My principal even assigned two teachers to this class so students could get more attention. My co-teacher Amy and I were set up for success. Well, not so much, as it turned out. This was, in fact, a phenomenally bad idea on my part.

Even with two teachers, our co-taught class was a disaster, because few of the students had the mindset and habits to be successful. The students weren’t just poor math students; they were poor students generally. These students were only 12 years old and had already concluded, to use Cassie’s words, that they “stank at math” and it wasn’t worth trying anymore. And looking around, they saw no one who thought any differently. In particular, the students refused to listen to any full class instruction. In retrospect, I think they figured they wouldn’t understand what was being said anyway--after all words and numbers were coming out of our mouths--so they decided to wait until they could ask their own questions individually. If you put yourself in their shoes, this makes a certain amount of sense, but it doesn’t work in a classroom with a full complement of kids. On many days the absurdity of our co-taught class left Amy and me certain that we were being filmed for an episode of “Candid Camera”. It would have been funny if it hadn’t been so frustratingly sad. I had learned the hard way that tracking students was not the answer.

A bit shell-shocked from the co-taught class, we asked for the class to be disbanded for 8th grade. It was clear that the kids were much better off that way. In subsequent years, my classes were always heterogeneous. I began to do what I could to differentiate, often giving students a choice of a few worksheets of varying difficulties. I learned from colleagues about labeling assignments “Circle, Square, Diamond”--shorthand for easier, medium and harder based on the symbols used on ski slopes. I started assigning more thought-provoking Problems of the Week (POWs), which were also circle/square/diamond. This amounted to a sort of a math menu--pick the chicken, salmon or roast beef as you please. It was better than my prior system of serving everyone chicken whether they liked it or not. But there were still problems. Kids got stuck at a level and couldn’t get out of it. Also, there are far more than three types of kids in any classroom. Some kids started telling me the square was too easy but the diamond was too hard--didn’t I have something in between? Students didn’t want a menu; they wanted a buffet.

The real turning point was when I agreed to switch to teaching both math and science. This made me quite nervous at the time. I could answer just about any question in math class, but in science, how could anyone possibly know everything a student could ask about the universe or chemistry or the weather? What I realized while being bombarded with astronomy questions to which I did not know the answers was that it was okay not to know all the facts, because the most important things in science are the processes and concepts. One can look up facts, and I certainly did, but it is much more important to learn to think deeply about the framework in which those facts make sense.

Math seems different to most people, but I now realize that it isn’t. The math equivalent of science facts is a variety of procedures, such as solving for x or finding the point where two lines cross. Math classes have been tracked in the past, I think, because math class was about procedures, and it is undeniable that some students can master procedures much, much faster than others. But why would a person teach a class that was all about procedures? That is like teaching a class in painting techniques while never letting students actually paint a picture. In my view, that never made sense, but certainly serves no purpose in the 21st century, when computers can implement a rote procedure thousands of times faster than any human. Students need a certain level of procedural fluency, but mostly they need to learn to use math to think quantitatively and analytically about the world. Everyone can learn to be a better thinker, and students can and should learn to do that together, by working on their own thinking while observing and helping others who are grappling with similar ideas.

So, now, whenever I can, I operate a math buffet. I don’t talk much in class except when there is critical information that I need to impart to everyone in the room. I spend a great deal of time finding and writing problems to stock my buffet. This is a very long-term project that I work on for a few weeks each July while my daughters are at sleep-away camp. In class, I help kids and push them to try new things. Problems contain some guidance, like “Diamond” or “Circles Skip” or “Squares try, but it is okay if you can’t”. Students take this to heart. They say things like, “I’m a square/diamond,” or, “I think I can do this, I’m a circle plus,” or, “I was at my grandma’s late, so I don’t think I’m up for the diamond today. Okay, Ms. Bare?”

Remember Cassie and the POWFest? I love to see kids with that kind of pride and intellectual satisfaction. In a tracked class, I expect that Cassie would never have been asked to do a problem like that--I am certain that chaos would have ensued if we had ever attempted such a thing in our co-taught class. Cassie also wouldn’t have been in the same level as her friend. She wouldn’t have had peers around her who were modeling perseverance and other excellent problem solving behaviors. Conversely, her peers would not have learned to explain their thoughts--an obviously important life skill. Cassie would have just been told she was having the chicken for lunch every day whether she liked it or not. That is not the right thing to do in public education, at least in the realm of my experience with middle school math and science. Cassie should not be stuck having chicken for lunch every day. That is how one creates life-long chicken haters--and we already have quite a lot of those in America. If we want Cassie to grow as a thinker, we need to offer her rich choices and push her to continue to put new things on her plate.

*Tracy Bare teaches 8 ^{th} grade math and science at Pierce School.*