In this clip, Linda Fisher invites the observing teachers to share their insights into the re-engagement lesson. Each teacher was asked to observe a pair of students in the fifth grade classroom during the Public Lesson.

5th Grade Math - Proportions & Ratios*Hillary Lewis-Wolfsen, Forest Park Elementary School, Fremont Unified School District, Fremont, California*

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LINDA FISHER: I’d now like to open it up to observers, if you want to comment on some of the mathematics that you saw, or some aspects of the lesson that you found interesting…

TEACHER 1: What I noticed that I really liked about the process was that when you put the problems up on the board, the different solutions, and they weren’t quite accurate, and the kids could look at them, and they started thinking about them. They could see where the person who did that problem got their answer, or could have misunderstood what it was asking. They could walk through, or talk through it and say, “Okay, that’s how the got there.” The one with one cream, two chocolate, for example. The one you showed where there were 9 creams and 18 chocolates. I think it was the boys in the back right corner were saying, “They misunderstood the problem. They were thinking 9, they were taking the 9 and thinking they had to times that by the 1 and by the 2. That’s how they came up with it. But they weren’t thinking about, or they didn’t catch the ‘in all’, so what they needed to see was there were 9 cups in all, and then go and figure out from there.” I really liked that they could take those problems, or answers that you posed to them. They could see where another student could have misinterpreted the problem, or where they went wrong. Or maybe not “wrong”, but off the wrong track.

TEACHER 2: And I like the process of reengagement because it gives them a chance, just like we were able to have a chance to be exposed to the methods and the problems and kind of have a rough idea of what to expect. Like today, to give them a chance to work it out without any prior knowledge of all the different methods of solving a problem, let them work it out the way they want to work it out, and then be exposed to how other people work it out. Then also to have the chance to work it out again, to see how other people got their reasoning. That further increases their understanding, and increases their logic. That communication, I think, is very important because especially in math, I don’t think we’re encouraging our students often enough to communicate with our words – written or verbally – about how we solve our problems. I think that just helps pull in those struggling students, and helps encourage those stronger students. What one student may be struggling with, he may be strong in maybe drawing something, or working it out with manipulatives. To give them the opportunity just further encourages them in terms of furthering their mathematical understanding. Also, it furthers the teacher’s understanding, in terms of “What does this student need, and how does this student learn, and how can I further support them?” Because if we’re just expected to have the students work it out with the algorithm, I think we’re losing a lot of students. And I think we’re cheating them. So I think this process is amazing, and I think that having them go back and correct their work is just a great thing for them, with the correcting pens. And even encouraging them, “See how many ways you can get the correct answer. Or see how many ways you can figure out how they got the wrong answer.” It just furthers their understanding. I think that’s great.

JEAN LIU: I think this method is great for teachers, because when a child comes up with something completely new that I haven’t even, you know, I didn’t even think about. I noticed Hillary was clicking too, like “Okay! All right!” Usually, at that “clicking” moment for me, I have the child come up and teach. So they’re teaching the class a new method, and reaching to kids that I don’t reach to. I find that often in this class.

HILLARY LEWIS-WOLFSEN: The observing teachers were all from our school, Forest Park. They represented grades 1-6, as well as both administrators and a long-term substitute (who was hired on full time for our site the following school year). This was the first lesson study experience for most of the people there. As a result of this experience, we have a lesson study team based at Forest Park this year.

LINDA FISHER: In my years teaching mathematics, I've learned that kids need to have their misconceptions confronted head-on. With re-engagement, we thought, let’s take that and pose them as dilemmas for kids to think about – get them talking about why some of these common things don’t make sense. That way, we can bring a focus on the mathematics and the concept, rather than solely on the solution and the answer.

When I work with teachers, they want to know what to do in terms of remediation. Teachers usually confront student mistakes by going back to a clean slate and start at ground zero. But there’s something profoundly different about reteaching than teaching it for the first time. When you go back to do a re-teaching leson, you don’t want to start as if people have never learned things. You want to get students to let go of why what they’re doing doesn’t work. Teachers need to find a way in to facilitating the conversation, to helping students see why what they’re doing doesn’t work. That’s one kind of reengagement: having kids reach the conclusions.

One of the critical things is that kids have a lot of mathematical ideas that teachers don’t see. My “hidden” agenda is to get teachers to be able to read student work and make sense of what they’re not understanding. Everyone with the wrong answer doesn’t need the same kind of help. In learning to classify student errors, we want teachers to tease out what are the different kinds of help, and why are they different, because they’re based on different mathematical ideas.