It all started when I was reading the Michigan State chapter of How To Build a Better Teacher on my way to work and I started getting all excited. Since it was about my Alma Mater, and talked about the elementary school near my brother’s apartment, it was as if the fight song was playing in my head the whole time. By the end of the Chapter, I was excited about really tearing into a problem with a class discussion. Excited might not even be strong enough. I was ready to run through a pedagogical wall. When I was back at Michigan State we saw some of the footage of Magdalene Lampert and thought about how I always wanted to have a class discussion that could function like that, and assumed I’d have figure out in maybe my first 10 weeks of teaching. The truth is, while I’m starting my 10th year, I still feel that I have a long way to go.
Why haven’t I got the class discussion figured out? It’s rough having long deep conversations about math in my school, for the littany of reasons that one would expect (large classes, complex content, pacing concerns, classroom management, for starters), but in all honesty it’s probably me. It’s probably that I just get satisfied too easily, and don’t try to push it.
But today’s class could be different for three reasons.
1) I have small classes. My class is only partially full because I’m holding spots for the kids who are going to be transfering from their school in a few weeks. We always save spots for kids who report to their school in september and then decide to leave in october, and this year we are setting those students up with spaces in set aside classes. Since I have a small group, and I have less pressure, it has led me to try more of this “Become a different teacher” Goal that Ihave for the year.
2) The content is perfect. Today’s lesson was talking about representation, and connections, and how they should be represented in a math project. In all honesty we could have done whatever I want because I don’t have to dig in to the course until October’s influx of new Students. This lesson today was designed to get students comfortable with the NCTM process standards, so they can understand how they will get graded.
3) I started slow, but I am going to finish fast. I was as pumped about it as Apollos Hester, and the motivation was going to take me over the top. Today is the day. We are having the discussion.
We started the class talking about estimation as we always have, then we focused on two problems.
The first was a “5th test” problem, where there had been 4 test previously and what would need to be scored on the 5th in order to reach a certain average. The 4 tests were 98, 96, 97, and 89, and they needed to find out what score the 5th one should be in order to get a 95. What students got stuck on was the fact that the 4 tests actually averaged out to 95 on their own. It was strange how much of the class was confused because the number 95 was the same number they were starting with, and the same number they needed. All of a sudden, we were doing it, we were having a conversation about what this means, and it was pretty natural. The students understood that if a test lower than 95 was scored, and a test higher than 95 was scored, it would lower and raise the average, so it followed that the number 95 would be the only one to maintain the average on the final test. I guided them through this proof, and it wound up the students all writing my logic as the explanation for the problem.
The conversation about the first problem didn’t lead to the rich mathematical discussion that I wanted, but I still had the Skittle problem. Roger has 2520 skittles, how many would he get if he had to divide them among 2, 3, 4, 5, 6 or more people. There was too much here to not have all the students get engaged, and we can have the students develop the function during the conversation. We are DOING this!
The class worked silently at first, and I circulated to gather the students’ various responses. The goal of this problem was to think about representation, and we had talked earlier about how graphs, tables and equations were all great representation, so I took note of these things as they popped up around the room. One student tried graphing, so I had him make a neater graph on graph paper to show up under the document camera. Another girl who said she hates math on the first day made a table out to 10, so I had her write it up on the board. I was setting the stage for a pretty dope conversation.
We got started. I asked kids “What are the ways they could represent this?” The table was already up there, everyone agreed with the numbers, the graph was an obvious choice, and I put the student’s graph on the document camera. We had a diversion about the graph, where asked them about what they thought the graph would do, and I put a couple of extra points on Walters graph that we knew from Janice’s table. Seemed like a good time to talk about asymptotic behavior.
Then I asked if anyone had represented it as an equation. Shaking heads. I asked everyone to think quietly about an equation and then we were going to construct the equation based on each others thinking. I was amped. After 5 minutes I wrote everyone’s equation on the board. I asked Janice, she said “S = 2520 + P.” This seemed like addition infatuation, when people think it should be addition just because. We could totally break down why that operation isn’t important. I didn’t say any of this, I just quietly moved on to the next student. Roger, gave me “S/P = X.” This seems like we could quickly touch on which variables are important here, and what variables even mean. Next, Clyde said he didn’t know, and Walter said “S = x.”
Is it weird that I was excited about having a bunch of “wrong” answers on the board? I was about to launch into one of those conversations about math where the kids talk about what they were thinking, and defend their points against what other kids proposed, and develop conjectures when all of a sudden Clyde says:
“Is it s = 2520/p?”
And my response was:
“Oh, That’s right.”
WHY DID I SAY THAT!!?!?!?!!!????? The blood left my face as the impact of that statement reverberated through the class. My reflexive affirming of Clyde’s statement triggered a cascade of verbatim copying across the class. Once they all had the “Answer,” I might as well have been teaching Charlie Brown, as the rest of the students begin focusing on packing their bags. Before I had time to recover, Walter reminded that class had already ended, and filed out of class with rest of class past the board full of answers that I had accidentally confirmed as “wrong”. Everyone filed past me as I lamented another opportunity lost. Hopefully they still learned something. I guess I still have a lot of learning to do, and a lot of bad habits to break.
Have you found ways to improve in this area?