Rough Draft Math
There’s a better way for students to learn math, says UD professor Amanda Jansen
Do you remember what it was like to learn math? How challenging it was to find solutions to problems that you didn’t understand? The dread of wrong answers?
Before joining the University of Delaware’s School of Education, Professor Amanda Jansen was a junior high mathematics teacher, and she had these conversations with students all the time. Math should prompt interesting questions, she says, but when students constantly feel pressured to get the “correct” answer, it becomes difficult to view perplexity as a valuable part of the learning experience—as the kind of creative thinking that makes math interesting.
“Most of us have experienced mathematics classrooms where the ‘smart’ students were those who arrived at the correct answers quickly,” Jansen wrote in her new book, Rough Draft Math: Revising to Learn. “Everyone wants to feel smart, and no one wants to feel embarrassed for being wrong.”
Rather than having students internalize that feeling of uncertainty, Jansen argues for a new kind of mathematics instructional approach that emphasizes problem solving as an iterative process, similar to using rough drafts in language arts classrooms.
“Rough draft thinking happens when students share their unfinished, in-progress ideas and remain open to revising those ideas,” Jansen said. In contrast to “final draft” talk, which is presentational and performative, “rough draft” talk is exploratory and uncertain, encouraging students to follow their intellectual curiosity, to take risks and revise their ideas even if they got the “correct” answer on the first try.
What is Rough Draft Thinking?
When it comes to rough draft thinking, answers matter less than process. Sharing unfinished “drafts” and revising emerging ideas provide opportunities for students to change their approach to solving a problem or explaining a solution.
“Learning is messy business. When we learn, we actively work to make sense of an idea that does not make sense to us yet,” said Jansen, who began the research for Rough Draft Math in 2016 during a state-wide study group for middle and high school math teachers in Delaware. From there, the project snowballed, ultimately collecting data from 18 teachers in 16 schools, including 15 teachers in Delaware.
“As more teachers learned about the ideas, more teachers invited me into their classrooms or contacted me to share how they used rough drafts in their classroom,” Jansen said.
One of those teachers is Brandy Cooper, who teaches sixth-grade math at Milford Central Academy and co-wrote the article “Rough-Draft Talk in Mathematics Classrooms” with Jansen and Delaware middle school teachers Stefanie Vascellaro and Philip Wandless, published in Mathematics Teaching in the Middle School in 2016. The goal of rough draft thinking, Cooper said, is for students to feel comfortable sharing their unfinished ideas.
“When a student shares an answer, we take time to think through it together,” says Cooper. “I feel this creates a more curious culture in my classroom.”
| Photos by Kathy F. Atkinson