In this clip, Linda Fisher asks Jean Liu, the classroom teacher, to reflect on the 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: So you know your kids better than anybody: what struck you as you watched the lesson unfold?

JEAN LIU: I think generally they are pretty engaged. So they are, the majority of them. But what really stood out was it brought out the strengths of the kids that sometimes don’t participate. So I would say, I assumed that the “higher” kids would be all over those problems, but it was generally sort of the middle range kids that spoke the most, and they were really engaged. They loved the manipulatives, so that was one of my surprises, was, “I can’t believe some of the kids who never—I’m going to have to pull out sticks to get them to talk!” They were so excited to contribute. Also, I noticed that there were so many—they really showed today the different range of thinking, the different ways of thinking. For example, the Valerie and Cindy problem, my boy who has attention problems, said, “It’s all messy! I don’t understand that one.” However, another student said, “I like the one that was on a diagonal.” So, it was the thought processes, how they think. I also noticed, when we went into the in-depth problem, we lost some of the lower, the weaker kids. But that brought up the higher thinkers, and they were having this discussion: “Oh, let me clarify!” That really, those are moments that really are strong in my class, because they have been together for a long time. That is what their strengths are. They like going into deeper thinking. This allowed them to show off. I think that’s…. yeah. I really enjoyed today. For me to sit back and see them, this is their strength, is the discussion, and showing that off to all of you. So thank you for coming!

COMMENTARY BY HILLARY LEWIS-WOLFSEN: After hearing Sabrina’s comment about who was participating and who was not, it got me wondering. Why were the higher students not speaking out as much as she’d expected? They’d understood the problems. I wonder if they were afraid to make a mistake on camera. I’ve noticed with some high achievers, they are afraid to make mistakes; they don’t take risks. We need to take risks and be willing to make mistakes. How else will we learn?

COMMENTARY BY 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.