tending to instructional practice, students’ opportunities to learn, and implementation issues. In addition, based on what is known about teachers’ knowledge of whole numbers and operations for teaching, as well as about their learning, systematic variations could be designed to support the implementation of these different instructional approaches. For example, in one set of schools, a teacher specialist model might be deployed and, in others, teachers might engage in closely focused study of practice (instruction, student learning, mathematical tasks), coplanning and analyzing lessons across the year. In still others, teachers might be given time and be provided incentives to spend time planning with the ample teacher guides.

The work could be conducted in carefully controlled, longitudinal studies carried out in SERP field sites. Because SERP would have relationships established with a number of field sites and data collection efforts in those sites already under way, taking on a controlled experimental study of alternative curricula would be far less daunting a task than it would be for researchers working independently. Moreover, the concern for undertaking research that is maximally useful to educational practice and the ability to design and conduct—or oversee the conduct of—that research will be combined in a single organization. Such a situation does not now exist.

ALGEBRA

STUDENT KNOWLEDGE

Algebra, foundational to so much other mathematics, and so poorly learned in general, is an area in critical need of concentrated research and development. Algebra is crucial to the development of mathematical proficiency because it functions as the language system for ideas about quantity and space. Algebra moves attention from particular numerical relations and computational operations to a more general mathematical environment with notation and representation useful across all areas of mathematics. These represent vital, but precarious, passages; students’ transitions into the domain of algebra are often plagued with problems.

Although it has long been considered important, attention



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