Important questions remain unanswered about the knowledge of mathematics needed to teach algebra effectively. As with elementary mathematics, the existence of different curricular approaches and efforts to study them, as outlined above in Initiative 1, provide the opportunity to investigate the demands for teachers in teaching different curricular approaches to algebra. For example, specifically what mathematical demands arise for teachers in teaching approaches to algebra that emphasize symbolic fluency compared with approaches that emphasize modeling and connections to situations? What sort of representational and notational fluency do teachers need? How do teachers need to understand the connections between algebra and other domains of mathematics, and what is demanded of teachers with respect to mathematical reasoning under different approaches to algebra?
The movement of algebra into the elementary school curriculum, as recommended both by the National Council of Teachers of Mathematics’ Principles and Standards for School Mathematics (2000) and Adding It Up (National Research Council, 2001a), creates the opportunity to examine what elementary teachers need to know with respect to algebra. Typically regarded as a secondary school subject, algebra has not played a central role in the preparation of elementary school teachers. Studies of teachers engaged with the new curricula that include elementary school skills and ideas of algebra could provide insight into the kinds of algebra knowledge useful to the teaching of young children. Where and how do ideas and skills of algebra surface in younger children’s learning, and what sorts of knowledge would help teachers address and develop those? As in other areas of the curriculum, it will be particularly important to identify the issues with which teachers struggle most, the conceptions that make effective teaching more difficult.
As in Initiative 1, the study of teacher knowledge requirements would provide the basis for research and development on effective teacher education interventions. The development efforts would be expected to target a variety of teacher learning opportunities, including pre-service education in teaching mathematics, teacher support materials, and in-service education associated with the use of particular curricula.