prominent. In some approaches, students are engaged in using the tools of algebra to model situations and problems, while, in others, algebra as an abstract language is stressed. While much controversy surrounds the worth and merit of these different perspectives on the subject, additional debates center on the contribution of calculators and other technology, the structure of lessons, and the role of the teacher. Because curricula have already been developed that represent these different perspectives on the subject and on how it might best be taught, one important initiative of SERP might be to design comparative studies of how these curricula are taught in classrooms and what and how diverse students learn algebra over time.
In this initiative, cohorts of students could be followed longitudinally. Studies could gather information about the instruction they receive, exposure to curriculum, information on the teachers, and their use of the curriculum and other tools. This initiative will depend on the development of effective assessments (see Initiative 3).
As with elementary mathematics, however, knowing why particular curricular interventions produce particular outcomes will require companion controlled experiments at the level of particular program features to test for causality. This kind of research is necessary not only to advance scientific understanding, but also because it provides critical knowledge for teachers who adapt curricula and allows developers to improve curricula or design alternatives that are responsive to research findings.
Simultaneous with this effort, SERP can support curriculum development that extends existing curricula in promising directions. The Algebra Cognitive Tutor, for example, emphasizes highly contextualized problem solving. While many fewer students drop out and students master the material covered more quickly and effectively, the curriculum may not achieve the fluency in symbol manipulation and abstract analysis expected for high-achieving students. The developers suggest that the curriculum could quite easily be strengthened in this respect, and a separate accelerated algebra course is likely to yield even better results for high-achieving students. In studying the set of curricula as they are being implemented, SERP as a third-party entity would be well positioned to identify and support promising areas like this for further development.