## The Poincare Institute: Nurturing Expertise in Mathematics Teaching and Learning

### Summary

The Poincare Institute aims to promote student learning of Middle School mathematics by developing teachers' expertise regarding (1) key mathematical objects related to algebra and the mathematics of functions; (2) representational systems for these objects (tables, number lines, graphs, written notation, and natural language); (3) modeling situations involving quantities and (4) classroom research about students' mathematical representations. Teachers (grades 5-9) from nine New England districts will engage in online courses as well as discussion forums in schools. Teacher and student progress will be evaluated on the basis of classroom discussions, interviews, and written assessments. Dependent measures of student success cover their mastery of mathematical objects and their properties (functions, equations, equivalence), algebra in modeling, and using and interpreting mathematical representations.