Poincaré Courses

The heart of the Institute is a sequence of three graduate-level online courses, supplemented by face-to-face sessions, designed to meet the needs of middle school mathematics teachers. The courses focus on the mathematics of functions as it relates to topics in the mathematics curriculum, applications to science and real life situations, analysis of lessons, and analysis of students’ ways of thinking and learning. Activities are designed to drawn on the perspectives of teachers of various grade levels and assignments are designed to be both challenging and accessible to participating teachers.

The course structure features a highly interactive approach. By actively carrying out and discussing their own mathematical investigations, formulating conjectures, and checking their validity and generality, teachers will gain fluency with ideas that appear in a variety of situations and representations. At the same time, they will learn about relevant research findings in mathematics learning and teaching and will conduct teaching and learning investigations related to particular mathematics topics.

Each course is organized into four units of three weeks each. In the first week of each unit, the notes, videos, software demonstrations, and problems to be discussed and solved focus on the interweaving of mathematical content and student learning. During the second week the materials address more complex mathematics content. In the third week teachers analyze videotaped classroom lessons and results of interviews they conduct with their own students’ initial and evolving understandings of mathematics topics. Each course ends with the interactive planning, implementation, videotape, and analysis of a classroom learning activity by each teacher. Teachers post drafts of their work online, discuss their drafts with other members of their online groups, and post final versions of their answers to assignments by given deadlines.

Teachers receive graduate credits from Tufts University for each of the three courses.