# Debrief - Part E

## debrief - part e

Expand +

Linda Fisher reflects on the kind of mathematical thinking she saw the students doing during the lesson and the depth of the mathematical arguments they made in the class discussion.

## debrief - part e

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

Next Up:   Debrief - Part F
Previous:  Debrief - Part D

LINDA FISHER: When I was looking at it, on the very first problem, remember I asked why they were going to spend so much time on the 6/9ths and the 2/3ds, because kids in that classroom did really well on that problem, but it sort of sets the stage for later. The two people I was observing both said, “Well, the 2/3ds has nothing to do with the picture. That doesn’t make sense at all.” And they just went to the reducing algorithm. Then, because there was extra time, they go “Oh well, it might.” And they started to see that relationship between it. But their first response was “That picture just doesn’t apply to the 2/3ds at all.” So that was really fun.

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.