Here fellow colleague Patty Ferrant and I (Antoinette Villarin) share our lesson with our math coach Suzanne McSpadden. Our discussions include the objectives, process, and reasoning for how we approached area and perimeter.
We discuss why we chose the lesson, how we designed it, and what big ideas would be addressed in the lesson. We then share the design of our lesson, which Suzanne parallels to a MARS task. Our lesson includes entry-level discussions with the class about area and perimeter, a main activity addressing the core mathematics behind these concepts, and a ramp-up challenge for students who were ready to move on. In this discussion, Patty and I want to emphasize our goals of justification, discourse, and making connections between the procedural skill and the big ideas.
7th Grade Math - Area and Perimeter
LINDA FISHER: Hi, Hillary and Carolyn, I’m really excited to get to observe your lesson today. I understand you’re going to be doing something on a protocol called “re- engagement.” Could you tell me a little bit about what that means to you?
HILLARY LEWIS-WOLFSEN: Well, um, we’re going to do a lesson: the class has already taken an assessment and we’re going to go back to that assessment and have them think about the problems again.
CAROLYN DOBSON: We’re going to have them look at some of the other responses to the problem that the different classmates have had, so that they can understand different approaches to the problem, and therefore get a broader view of all the mathematics involved in the problem.
LINDA FISHER: Why do you think that it’s really important to go back and re-discuss a task after you’ve already given it to the class?
HILLARY LEWIS-WOLFSEN: Well, for the students who didn’t do it all correctly and still need to learn from it, that gives them more time to understand that items they didn’t understand the first time around, and for the students who did do well, they will get a chance to think about other ways of solving the problem and to push themselves a little bit further.
CAROLYN DOBSON: Once they’ve done a task, they’re familiar with it. So when they go back, sometimes, I know that I’m amazed to find out how much more there is to get out of a task, just by rethinking it, and thinking about it more deeply!
LINDA FISHER: Can you tell us a little bit about the process of how you chose your questions or your problems that you’re going to present to the students today?
CAROLYN DOBSON: We looked back at some of the student work, and we saw where some of the students were having some difficulties. We saw what we thought was interesting mathematically in those difficulties, and we wanted to get them to confront what didn’t make sense, and really think it through. Think about why it did and why it didn’t.
LINDA FISHER: What are you hoping that students will get out of today’s lesson?
HILLARY LEWIS-WOLFSEN: I’m hoping that it will further their understanding – that they will each learn a little bit more about the problems than they had done the first time around.
CAROLYN DOBSON: They should discover that it’s so much fun doing this kind of mathematics, the logic of the thinking, it’s pure fun! There’s no right and wrong, except in the mathematics itself!
LINDA FISHER: I know when you guys were planning the lesson, you had a really large discussion about how to introduce the lesson. Can you rethink what some of your logic was, about how you were going to introduce the lesson?
HILLARY LEWIS-WOLFSEN: I’m trying to remember… (laughter)
LINDA FISHER: You know, like how were you going to present the problem originally, why you wanted to look at this thinking again?
HILLARY LEWIS-WOLFSEN: Was that with the… we decided to start with the first problem on the assessment, is that what you were thinking?
CAROLYN DOBSON: Are you trying to think about what order we wanted to have? (03:44)
LINDA FISHER: I think it was like you wanted to pose the questions to students in a way that would get them excited about rethinking those particular tasks?
CAROLYN DOBSON: That’s right. You know, when you come back, the idea was, you come back and it was so interesting—we got so many different responses from these different
I learned early in my teaching career that post-reflection is an important part of the process. It wasn't until much later that I realized that pre-reflection is just as important. This includes having a learning goal for the lesson and envisioning what the lesson might look like before jumping in the classroom. From this footage of our pre-lesson conversation, I am reminded of the value of internalizing a lesson before teaching it. Sharing it with others definitely helps with this process.
I remember in this first video, the three of us discussing what we were planning to do in the lesson. Patty and I were sharing with Suzanne our objective and how we were hoping to begin. Here, sharing the lesson with others and articulating our ideas helped us envision what it would look like. Through articulation and the collaboration that came with this process, we prepared ourselves pretty much for teaching it. We were able to run through what was going to happen, and justify each step with an objective. In turn, the lesson became meaningful for everyone involved. Both teachers and observers could see that planning a lesson was a process where reflection at the beginning was just as important as reflection at the end.