After the lesson, Tracy shares with her colleagues feelings about how the lesson played out. She and math coach Leslie Thornley discuss the rationale for the selection of additional posters that were not explored.
2nd Grade Math - Word Problem Clues
Tracy Lewis, Anna Yates Elementary School, Emery Unified School District, Emeryville, California
TRACY LEWIS: Ahh. Do I get to start?
LESLIE THORNLEY: You can...if you want to start now, we'll let you talk and then we're going to take a look and spend a few minutes together looking at the student work.
TRACY LEWIS: Um, how do...let me just tell you how I felt like it went. Um, some things were good, some things were not so good. Um, I see this is a completely different lesson than the previous, than the lesson that was actually planned. Um, I felt like I ran out of time. Um, I was kind of upset I wasn't able to get or process through more of the posters so students could see the different ways to answer things. Um, things that I felt like went well was their level of participation and their wanting, some of them or most of them to either share their thinking, stretch themselves and some of the students' willingness to say, "I am lost right here," or "I'm stuck right here." Um, because that gives me a better window into what I need to work on with direct instruction. Um, I was really happy to see how much they talk to each other about their own work and the comfort level that has come up. Because in the beginning of the year some of them would not discuss their work, especially if they saw any kind of mark, or after they noticed "Oh wow, the right answer is 82 and I don't have 82 on my paper. I'm not going to say anything." Now they're more willing to talk about it. So I feel like I'm making progress but this is a very different lesson because I do want them to go beyond, um, pictures, numbers, and words, and actually start looking at how those things work together; and actually taking apart a word problem, which is a completely a different lesson, different re-engagement lesson.
LESLIE THORNLEY: So why don't you talk a little bit about the work samples in the ones you got to and the ones you didn't. And why we initially selected these even though we didn't get to them.
TRACY LEWIS: Okay. So this, okay, you saw these two. This one was selected... Can we turn the heater off?
ANTHONY ROGERS: Yes.
TRACY LEWIS: You turned it off? This one was selected because of, well this is a traditional algorithm but also the words "I added 36 but I know you could not just write twelve..."
LESLIE THORNLEY: Sorry, let's get Camille to turn the heater off.
TRACY LESIS: Okay. There we go. Um, but also a lot or not a lot, a few of my students are using a number line and so when they use a number line to add on, which is another strategy for subtracting, um, "I counted by ones on the number line. I started with 59 so I said one." So she looked at the number line and said, "59, hmm, one. Whenever I get to another number, I started at the right number. So 59..." Now she's telling us why she picked 59. "59 became one and so on and so one it went." She came up with 31 which is really, really close. She started with her number line 59, 60 and you see she goes all the way up to 72. And I'm assuming she got tired so dot, dot, dot because she needs to get to 92. This becomes 1, 2, 3. This is her difference up here which is one strategy for finding out the correct answer. The only problem is when we get into right here; something happened to 64 and 65. And so this would've been good for the students to see as another strategy or how to verbalize a strategy that they might be using because some of them did actually use the strategy, but on their paper they didn't explain it this way. So that's why this poster was chosen.
This one was chosen because this student actually decided to use the base ten blocks and actually showed an appropriate way of the difference, or they're showing how they got the difference. Here's the 92 and they're x'ing things out; they regroup these and marked these off. Here is the answer of what's left, 34 as opposed to this. Usually in 2nd grade when we do number talks or things like that, they are still here, you know. And they stay here for awhile counting on the fingers and then they go to counting, you know, 1, 2, 3. At least this has been my observation. And then somewhere along the line they start looking at groups of things which makes better sense of the algorithm. I noticed that before Deron saw this as 28, 92, and 58 and he thought all these numbers were being added together, which was a big red flag for me about how you use the words, and are these words describing this picture or are these words describing how this person added the numbers up. Because some of them are a little confused or is a little fuzzy about how things are added up. That's why those posters were actually chosen.
LESLIE THORNLEY: And this one here is actually a work sample from another school. These are from Tracy's classes, these were student work but we felt that this was a um, a correct example of a strategy that we saw the kids using on their papers. A lot of the kids were tempting to use base ten blocks and draw pictures of it but their mathematics was incorrect, and so we thought this was a strong example of a successful attempt. And that's why Ellen was chosen.
The students took this lesson down a different path than originally planned. The beauty in this is that as a teacher I could clearly see where student misconceptions were. One problem presented several different needs.