In this clip, Linda Fisher, Carolyn Dobson, and Hillary Lewis-Wolfsen discuss how they anticipated the learning needs of the students in the classroom.
LINDA FISHER: When you guys were planning the lesson, how did you think about the learning needs of different students in the classroom, or how do you think the lesson will affect different students in the classroom? Students who had trouble with the task and students who sort of whipped right through all the questions?
HILLARY LEWIS-WOLFSEN: We will be addressing incorrect answers, and the students who’ve had trouble with a task, and I hope that they recognize some of their answers and are able to see where the logic doesn’t match and hopefully that helps push them, and help find where they can be successful, and where the correct answers are. Do you want to talk about the…?
CAROLYN DOBSON: When we first came at it, the concern was with the students who had not been successful. But in delivering the lesson, we found that it was so exciting for the children that already had answered it, they didn’t find it boring at all, because they were looking at it through different lenses and with a different perspectives. Seeing completely different ways of approaching the problem!
LINDA FISHER: I think there’s something about the way that you have posed the questions that makes everybody have to rethink whatever they had done originally. I think that rethinking is doing it. Somewhere, it seemed like you were talking about that students were maybe, like learning the process of developing a logical argument or justification…?
CAROLYN DOBSON: The kids were asking us for evidence, were asking us to show them why they’re thinking the way they’re thinking. I think one of the things that makes them reexamine is is that they don’t have their papers in front of them. Oftentimes we give the papers back and then start discussing them. In this case, they don’t have them. We’re just looking at the question all together, and re-remembering how it felt to do this problem. So they’re re-doing it without any work, in front of them.
LINDA FISHER: So I kind of think like, as I’ve observed the lesson now, a couple of times, kids are sort of like talking their way into understanding. So they may have solved it really fast, but they weren’t really sure about why, and this sort of helps to cement or solidify the types of thinking that they do so that they can remember it maybe for future problems.
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.