tant dimensions, with further research and development of component features of particular interest.

Algebra is crucial to the development of mathematical proficiency because it functions as the language system for ideas about quantity and space and is foundational for much other mathematics. However, there is currently little agreement regarding the content that should be included in the algebra curriculum or the instructional approach that is most effective.

We propose four initiatives aimed at improving algebra learning and instruction:

1. research and development on alternative approaches in the teaching and learning of algebra, with controlled experimentation at the level of particular program features, with a companion effort to extend existing curricula in promising directions;

2. research on the knowledge of mathematics needed to teach algebra effectively at different grade levels and research and development on effective teacher education interventions;

3. research and development of algebra assessments for the range of grade levels and the range of assessment purposes; and

4. study of students’ algebra proficiency over time with the introduction of algebra as a K-12 topic.

The existing knowledge base in physics education is relatively advanced. It includes the development and testing of exemplary instructional programs, with outcomes that suggest the possibility of a much deeper conceptual understanding of the subject, and by a broader range of students than are typically successful at physics today. We propose three initiatives designed to take research-based knowledge into the classroom: