In a recent study, researchers at the University of Delaware interviewed dozens of K–12 educators to identify actionable strategies for implementing “rough draft thinking” in their mathematics teaching. Rough Daft Math (RDM) is a teaching framework where “a teacher invites students to share their in-progress thinking and provides opportunities for students to revise their thinking," according to Amanda Jansen, lead researcher, professor at the University of Delaware, and author of the book Rough Draft Math: Revising to Relearn. “Talking and writing about unfinished ideas is vital to learning mathematics, but most students only speak up when they think they have the right answer,” said Jansen. “As part of the rough draft framework, a class of students becomes an equitable and inclusive community of thinkers, one where students feel safe to engage in discourse while developing mathematical competency and confidence.”
In the study, Jansen and her colleagues focused on discovering what teachers intended to do when implementing RDM, including what is important to them (salient) and what they identify as possible to implement (feasible) in their classrooms. They found that the two most salient and feasible variations included (1) incorporating the concept of revising in math learning and (2) selecting math tasks that invite the practices of drafting and revising.
For example, for revising, one teacher reported that the students who folded a paper in half and used one side for “first thinking” and the other for “next thinking” were suddenly OK with “everything being messy and not erasing it.” Another teacher told her students to avoid erasing and use a different color when making changes which allowed students to see the evolution of their own thinking and normalize the practice of making continuous improvements.
For math tasks that invite drafting, one teacher presented students with a photo of different colored candies, with a simple prompt: “Contemplate then calculate - how many?” Rather than expecting to find one correct answer, the students were open to discussing a variety of ways of seeing math in the image including fractions, multiplication, repeated addition and even geometry.
By harnessing the power of rough drafts, the math teachers’ role can shift from evaluating to facilitating collaboration between students. And when students share their ‘in-progress thinking” and then reflect on their work, they become more effective and confident problem-solvers, according to researchers.
StepUp Note
Neuroscience research shows us the very important role of anticipation in the process of learning. This research shows how “ambitious teaching” helps children to share their thought processes as they work through math problems. The children anticipate possible solutions, then use their problem-solving data to think of even better solutions. StepUp exercises give children the opportunity to experience this same trial-and-error learning process. Day by day, they become more able to coordinate more details of the movement rhythms of each exercise.
Note by Nancy W Rowe, MS, CCC/A
Full research in Journal of Mathematics Teacher Education