Barbara Shreve and her coach Phil Tucher discuss the lesson outcomes. The coach facilitates the flow of the conversation. Initially it begins with both the coach and teacher listing highlights and questions they recall from the lesson. The discussion begins with the two taking turns sharing the highlights that they listed. The teacher is the first to share. The coach reinforces the highlight with specific examples he observed. The discussion continues with each sharing highlights, reflecting with regard to student learning and providing specific examples to corroborate the effect of the instruction. The coach suggests that they collectively examine student work to see how students were making sense of the mathematics. The act of looking at student work provokes further discussion. The teacher and coach share insight into student thinking, the progress they are making, and areas of struggle. The coach takes the opportunity to ask follow-up questions to help the teacher reflect about her practice and consider ext steps with the class.
PHIL TUCHER: Let's shift over to questions.
BARBARA SHREVE: Okay.
PHIL TUCHER: What do you have on your list?
BARBARA SHREVE: Um, well, the first piece that we talked about together with the three examples for solving the equation, which was a correct way to start, um, didn't go quite as I anticipated. It took a bit longer and it was a bit harder for kids to access than I had expected. Um...
PHIL TUCHER: What's your question about it?
BARBARA SHREVE: Um, I think I have a question in how I structured it, of how I kind of give them access to parsing through what those different things were, and was this the right way to start to move them into it and build their confidence. Um, I had moments where I wasn't sure what questions to ask to help them keep thinking. I felt like I had to insert more information and I'm not sure if there's another way around that. I just wasn't finding the questions in the moment or different ways to look at it. And I had a question of, is there a representation here that if they were able to look at it in a different way where these three are still fairly symbolic, if that would've been a different way to help them start accessing it?
PHIL TUCHER: So the "Who's Right?" the first one that didn't...the conversation didn't go the way you had expected you said. You're wondering about whether that's the right start, what information did they need, what information might have you provided as well, are there other representations besides these three that would've completed the picture for them. Let's look at that in a minute. What else were you...do you have anything else on your questions list?
BARBARA SHREVE: Um, overall on the lesson I think because this took a little bit longer, because they really had these quite deep conversations...they had deeper conversations or lengthier conversations about the matching that I had expected. They didn't get to the piece following that where they actually would've had to do some problems on their own. And they would've had answers and problems but actually had needed to do the work to see what went together. And so in terms of individual information that I have about where they are individually, and how they were making sense is really only from the pieces of their conversation that I was able to overhear, or the questions that I was able to ask them when I was at their groups. And so in that respect, I don't have as much information as I would like about their individual understanding. So I'm still wondering how well they'll be able to apply these ideas of first steps and what the answer should look like.
PHIL TUCHER: I thought about a similar question in terms of closure and I wondered, um, so the bell surprised you; slightly shorter day and not an issue at all except that being Friday wondering what can you do next time you see them that comes close to the wonderful way you started today. Here's where we were when we're last together, I wondered were there anything you could do for closure beyond the acknowledging that you did - the solid work, the good work is going to get you through when we meet next time, you'll be in a good place. Was there something that you could've done in terms of individual, or in terms of summary statement? Or similar kind of question. What else do you have?
BARBARA SHREVE: Um, I think by nature again, this day was really symbolic and as we're having conversations with the warm-ups and thinking about what is an x-intercept, I wondered if there were pieces where another representation or saying something graphically could've been brought in. I don't know if that's within this context or in the next step is definitely something I'm curious about.
PHIL TUCHER: You asked at the beginning whether or not students would be able make some generalization statements, "Oh, I get it. You use a generic rectangle when..." I want to ask...and If we have time, I'd like to look at "Did you hear those kinds of statements, if so what helped bring those to the surface? And if you didn't hear them, what do you think could happen differently so the kids would be asking those...making those generalization statements?"
BARBARA SHREVE: Okay.
PHIL TUCHER: Well that's more than enough.
BARBARA SHREVE: Do you want to dig into one of those?
PHIL TUCHER: Let's do that.
Phil begins the debrief with a very nice technique. He asks Barbara to take individual think time to write down some highlights and some questions. As Barbara makes her list. Phil also makes his two lists. Then Phil asks Barbara to start with her highlights. After Barbara finishes her first highlight, Phil reinforces how the lesson was successful by citing specific examples of how the students were engaged. Barbara also highlights how students persevered and were highly engaged in the lesson. She talks about how she hoped this would occur because the students were showing signs of acting more independent and improving their small group discussions, and this was new behavior that she hoped would continue to develop. Phil shares his highlights with Barbara about three boys that were working together in the back of the room. He discusses how the group really worked together problem solving in a safe environment. Phil points out that this collaboration was not an accident, implying the work that Barbara had done previously was bearing fruit. Sharing evidence and descriptions of students engaged or not engaged is a powerful technique a coach can use to surface issues and reinforce success. Barbara and Phil dialog about the successes of the group, then they shift to examining student work. Phil provides some topics that could be a lens for looking at student work (who’s right, access, right start, individual understanding, closure, graphic interpretations, and generalization statements). Barbara identifies a piece of work from a group to examine for individual understanding. The group work had limited evidence of erasures. Phil had observed the group and shares his thoughts. The act of sharing information about a set of students by both the teacher and coach can generate new insights, reinforce assumptions, or clarify issues that groups may be struggling with. These coaching conversations raise the level of awareness around issues of teaching and learning. Barbara realizes the sheets the students completed did not show enough of their thinking for her to do an adequate assessment of what they learned. She goes on to suggest that she should have stopped the class with a few minutes left in the period to do a journal write. This would have given her more information to assess their learning. Phil follows up on the idea and helps Barbara work through some journal sentence stems. Phil and Barbara also discuss closure ideas. Barbara reflects on where students were successful (factoring) and where they struggled (finding x-intercepts). She questions how she rolled out the lesson and wonders out loud whether, if she reverses the order the problems appear on the sheet, if that would have helped students see connections earlier. The last major topic of the coaching discussion moves to language issues in the lesson. The students in the class are often English learners and paying attention to language and vocabulary in the lesson is critical. Phil facilitates the discussion, poses some ideas and then lets Barbara discuss the ideas that make sense to her. In the final part of the debrief, the discussion circles back to the mathematics, and Phil asks Barbara to recall why she designed the lesson with a “who’s right” structure and a matching structure. Barbara reflects on the power of these structures. They allow students to work at a high cognitive level critiquing other students’ methods and procedures. They also promote multiple paths and multiple solutions for students to compare.