FRAN DICKINSON, 5TH/6TH GRADE

CATHY HUMPHREYS, 9TH/10TH GRADE

In the documented lessons of Fran Dickinson and Cathy Humphreys, several of the mathematical practice standards are evident within one lesson/ problem. Both teachers have established a rapport with their students and a set of norms for students to turn and talk to each other as they work together. We don’t expect teachers or students to immediately establish this climate on the first day of school, but even from the first day teachers can establish a context for students to engage in mathematical thinking in this way. Dickinson and Humphreys serve as facilitators in their lessons—they lay out the task, and then invite the students to dig into the problems.

In both classrooms, you can see that students are having conversations and are able to state their thoughts, and are also comfortable with making any uncertainty explicit. In Dickinson’s classroom, for example, he and his students use a hand signal to make any dissent, disagreement, consensus, and confusion explicit. In such a classroom, it’s okay to say what you think, and it’s also okay to disagree and change your mind. It’s important with mathematics for students to be able to say that they don’t necessarily agree and ex-plain why. Too often, students’ reaction to mathematical confusion is silence. We believe these classrooms demonstrate a way to honor the process of developing mathematical understanding in students. The students’ independence in their math work rests on a climate of acceptance and mathematical risk-taking