… Revise Solutions: My Favorite Rough Draft ![]() Taking moments to talk about talking is important, but it is even more important to give students firsthand experience engaging in rough draft talk and to name and label those rough draft moments. She shifted back and forth with students from rough draft to more formal language to begin refining their rough draft talk, but then affirmed that the rough draft language of “a weird rectangle” was a useful way to get started talking about the shape. But there was a moment that Christine did not necessarily anticipate, which was rough draft talk around how Jason named the shape he saw in the diagram. This sort of exploratory talk invites multiple ways of seeing mathematical relationships. The first was the moment the teacher intended, which was when students shared multiple ways of seeing how to chunk the diagram to count the total. There were multiple moments when students engaged in rough draft sharing during this Number Talk. ![]() Then she asked, “So what can we call that shape?” Jason replied, “A weird rectangle thing.” Calista said, “It’s a parallelogram.” Another student shouted out, “It’s a thingy!” Christine said, “Calista is telling us that it’s a parallelogram.” Then she went on to say, “Yeah, we could describe it either way, but if we call it a parallelogram, that’s using more precise language that we can all visualize.” Michael Reitemeyer, the math coach in Christine’s district, was also in the room and asked, “So is it okay during rough draft talk to maybe call it a weird rectangle?” Christine turned to her students and said, “What do we think, as a class?” Students said, yes, so she said “Sure, we can accept it. Students brainstormed names for the shape, saying things like pentagon, parallelogram, rhombus, or “I can’t remember.” Christine identified the terms that students used and asked them to describe what they are (e.g., “What’s a pentagon?”). To me this looks like a diamond.Ĭhristine: Jason’s saying he sees a shape, is this what you’re showing? What shape is that? (Christine drew in lines as seen in Figure 2.6). So there were six and then I made them into one sideways diamond. Jason: So I saw these three and then these three. ![]() Another student came up to the front of the room and gestured to indicate diagonal lines: The second student saw the three on top, the three on the bottom, and the two in the middle. The first student saw a set of five, as if it was a side of dice, plus three more. They all reported seeing eight dots.įigure 2.5 Dot Pattern for Christine’s Number TalkĬhristine then invited students to share: “Can anybody be brave enough to share and justify why they think there’s eight dots up there?” A number of students went up to the whiteboard to draw how they grouped and chunked the diagram to count. A student asked, “A strategy is a different way of counting?” Christine said, “Exactly.” After flashing up the image of the dots (Figure 2.5), Christine then collected answers-how many dots students saw. Try and see how you can figure out how many are up there without counting one by one.Ĭhristine also introduced hand signals for Number Talks, specifically putting a number of fingers at your chest to indicate how many strategies you have. After talking with her students about rough draft thinking, Christine engaged her students in a Number Talk about ways to visualize chunking a set of dots to make the set easier to count.Ĭhristine: I want you in your mind to be thinking about how many dots there are.Ĭhristine: Yeah, you’re going to see that some patterns might remind you of dominoes. By trying out rough draft talk, they learn to believe in its usefulness through reflecting on their experience. … It is helpful, then, for students to engage in rough draft talk soon after defining it with them. She starts her school year by talking with her students about the role of rough drafts in learning. This post uses classroom examples to show some of the ways teachers can foster rough draft talk and set up students to revise their solutions.īy Amanda Jansen Talking about Rough Draft Talk: Christine’s ClassroomĬhristine Hubbard teaches seventh-grade at Meredith Middle School in Middletown, Delaware. In the first post, University of Delaware professor Amanda Jansen discusses how framing math as a shared exploration enables more students to develop math competence and confidence. This is the second article in a two-part series about rough draft math. ![]() Excerpted from Rough Draft Math: Revising to Learn by Amanda Jansen, copyright © 2020, reproduced with permission of Stenhouse Publishers.
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