Lesson

# Clip 11/13: Graphing Quadratics Lesson - Part 11

## Overview

Cabana meets with a group of students and gives them evaluative feedback about the strength and robustness of their approaches to solving the problems. He challenges them to write down the necessary steps, excluding those they can accomplish through mental math.

## Teacher Commentary

Maria, the first student with whom I interact, is definitely much more bilingual than most kids. I think she was a ninth grader. Maira, who's in the red, with the white hair band, is older, I think she was a junior, and Alejandro was also older, so therefore more recent immigrants.

I remember that Maria was a quietly confident learner who doesn't impose herself on the group, and doesn't often ask questions of the group, but is willing to share her thinking (complete or incomplete) with everybody, so she creates a calm atmosphere within her team.

It felt like a really difficult team to manage, in retrospect. I felt like I needed to make sure that Maria understands, because she's got to be the one facilitating the conversation, no matter what, which I hesitate to do. I don't really want to think about the designated "teacher" in the group. But in this particular group, given the dynamics of the other three kids, I don't think they're going to have an easy conversation as a foursome. So Maria can facilitate it, but I'm not sure that as much learning would happen as needs to happen.

I think that's part of my mindset in circulating to teams, trying to attend to which student is doing the facilitating and what does that sound like. Are they just saying like "first you do this and then you do that?" Or are they giving reasons and are they putting questions in the middle or just making statements?

Then as I talk to both groups simultaneously, it's getting close to the end of the hour and they're both stuck in the same kind of place. I wanted to try to get them "unstuck" together, so that they get far enough that we can have a productive conversation the next day.

As teachers move toward the end of an instructional period, most of the time we're used to doing that by pulling the whole class together and doing a quick lecture or something that might feel like Socratic dialogue, but I try to not do that. Instead I'm trying to keep things focused within the group conversation and in this case my compromise is to try to pull two groups together.

I realized from the conversations with the other two groups, that kids were stuck on finding the coordinates of the vertex in a way that I maybe couldn't necessarily anticipate. I wanted to push them towards that, because otherwise they won't have a complete graph of the parabola. What I want the next day is the whole picture, everything you need to do to have an "A+" sketch of a parabola.

That includes not just procedural fluency but being able to give reasons along the way, and insight into strategic choices about which form of the equation, and how do you find the middle number. I had in my head the big picture of what we'll need to discuss the next day.

There's always this balance between pushing kids faster than they are going themselves, but I feel like in this clip I'm short-cutting paths a little bit of what I'm thinking their questions might be based on the other two groups. That way, they get far enough today that the next day's work won't feel like someone is presenting information that they haven't thought about themselves already.