How counting collections of objects helps elementary-age children develop number sense and number relations. The authors provide evidence that counting collections offers multiple entry points for children at different places on the counting trajectory. The teacher's role is one of noticing, questioning, and extending what children naturally do, moving them to more sophisticated strategies as children count, organize, and record their collections. Includes multiple examples of student work.

Description of a year-long professional development project involving the integration of problem solving into the third-grade mathematics curriculum and implications for learning and teaching elementary mathematics.

An elementary school principal, a former high school mathematics teacher, uses the geoboard in her work with a group of fifth-grade students. As the investigation of polygons progresses from symmetry to area to perimeter, hands-on applications of advanced mathematics topics such as the Pythagorean theorem and square roots emerge.