![]() And you could feel interested in helping that person revise. You might feel validated, as if, “Oh, this person thinks in ways that are similar to me.” You could feel challenged. But if you are listening in whatever moment, you're benefiting because you're thinking about what they said, you may get a new perspective on how to think about an idea that you hadn't thought about before. Hopefully multiple people are asked to share and there's a conversation about that person's thinking, so who’s the speaker and who's the listener should start shifting pretty quickly. And the class is going to try and make sense out of what they shared, so then they have that experience of their ideas being taken seriously in the community. Every time we're being asked to articulate our thinking we make new connections or crystallize our ideas just by trying to put them into words or trying to put them into writing. Jansen: The speaker is benefiting in a few ways. How does this benefit both the speaker and the listener? Your book takes us inside some classrooms to show how teachers facilitate students sharing solution strategies before they've refined them. They're really rooted in the ideas of complex instruction. And those ideas are not new for rough draft math. So there are all kinds of ways that the students can then contribute to help the whole class learn more that's not about getting an answer correct quickly. You can write an explanation that makes more sense to the class than what the teacher's explanation communicated. You can represent somebody else's thinking in a new way, like a drawing or a graph. You can notice how two people's ideas are related, and then you're making a new connection. Jansen: You can ask a question about someone else's thinking, and it could help the whole class learn something more. ![]() What are some other ways of being smart in math that can be highlighted via rough draft thinking? You alluded to how speed is often seen as the marker of math success. My ideas have value.” Everyone feels included in that kind of environment. My thinking actually matters in that space. Ultimately, after that initial shift, people do start to get more excited, like, “Wow, my ideas actually matter. So initially it's hard, but in the bigger picture, it's more liberating for all the students because they can start to see how they're contributing to their colleagues’ learning in a lot of different ways. Not just getting a correct answer quickly. Jansen: Really it opens up what it means to be good at math. How does it also benefit students who get the correct answer the first time? It might be more intuitive the ways that this approach can benefit students who struggle with math. And there's going to be something that we can learn from anyone's idea. And the job of a student in the classroom is different. If we shift our role as a teacher from an evaluator to more of someone that's making sense out of ideas along with people, that's a very different way of interacting. Instead, discussions can be a place where we're all learning together from what anyone shares. It’s more of an evaluation space in that moment. ![]() “Correct.” “Not correct.” And it's in public, in front of everyone. Jansen: When I think about math class being a place for performance, I think about the experiences that we may have had when we're asked to talk about our thinking and we find it as if we're being judged. You wrote that it is your dream for mathematics classrooms to shift from places of performance to places of exploration. In part two, learn some strategies for how to foster rough draft talk and how to structure revisions in math classrooms. Jansen is the author of Rough Draft Math: Revising to Learn, published this year by Stenhouse. In this Q&A, Amanda Jansen, a University of Delaware math education researcher, discusses how framing math as a shared exploration, rather than a set of right or wrong steps, enables more students to develop math competence and confidence. This is the first article in a two-part series about rough draft math, a concept that applies a process from language arts - creating, discussing and revising rough drafts - to math classrooms.
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