Principals weigh proven professional development strategies to help teachers implement new reform ideas.

A second/third-grade class develops spatial sense as they subdivide and change squares to create different shapes. The language of geometry: square, trapezoid, hexagon, etc., grows naturally from their explorations. NCTM standards: geometry and spacial sense, communication, reasoning.

This lesson helps fourth-graders develop number sense by exploring magnitudes of large numbers (the number of listings in the phone book) and reasonableness of estimates. Students mark their estimates on a number line and justify their estimates verbally and in writing. NCTM standards: estimation, number sense and numeration, problem solving, connections.

Third-graders use problem-solving approaches--such as role playing or drawing pictures—to investigate and understand division. They make connections to everyday life and use calculators as they determine unit costs for two different boxes of cereal. NCTM Standards: concepts of whole number operation, fractions and decimals, problem solving, communication.

Alice in Wonderland is the focus of a lesson on algebra and functions for a tenth-grade class.

Discover the role that communication plays in your teaching and in your students’ learning. Topics covered include effective questioning, helping students understand and use precise language, and using writing assignments and presentations to help students clarify and deepen their thinking. The session also includes content and activities designed to help you better assess your personal formal and informal mathematical communication.

In this session, Cynthia Stone will provide teachers with a range of hands-on experiences that they can immediately use in the classroom so that students can begin to build conceptual understandings in measurement. These activities will develop four concepts: making comparison between objects by matching; comparing objects with nonstandard units; comparing objects with standard units; and choosing suitable units for specific measurements. The session will also address how teachers will know when students "understand", and what is acceptable evidence of understanding..

One of the strands of the Rutgers long-term study was to find out how useful ideas spread through a community of learners and evolve over time. Here, the focus is in on the teacher's role in fostering thoughtful mathematics.