ing diverse classes of students, teachers also need to understand better the mathematical resources and difficulties that their students bring from their own environments, as well as how to make productive use of and mediate those (see Moses and Cobb, 2001, for a robust example of designing strong connections between the domain of algebra and students’ out-of-school activities and knowledge use).

RESEARCH AGENDA

There is little agreement at this point on what algebra should be taught or how it should be taught. As in other areas of the curriculum, the questions are in part a matter of valued outcomes for algebra instruction and the instructional time allocation across algebra and other subjects. But a study of the outcomes of different instructional choices can make the decisions far more rational than they can be in the absence of high-quality data.

We propose research and development on four major initiatives in this area:

  1. Alternatives in the teaching and learning of algebra;

  2. Teacher knowledge;

  3. Developing algebra assessments and instruments;

  4. Students’ development over time and the effects of different curricular choices.

Initiative 1: Research and Development on Alternatives in the Teaching and Learning of Algebra

Work supported by the National Science Foundation as well as by private foundations has generated a variety of curriculum materials for schools that constitute different perspectives on algebra, different ideas about what is important for students to learn, and different ideas about how students can most effectively be taught that can be contrasted with the best traditional approaches to teaching algebra. Since these curricula are already developed and in use, they provide an opportunity for understanding the consequences of the choices made.

For example, in some materials a functions approach to algebra is central, while in others, algebra is treated more as generalized arithmetic, and the solving of equations is more



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