A separate issue is the assessment over time of the five strands that constitute mathematical proficiency. The past decade has seen the emergence of a spate of new tests and measures. No consensus has emerged, however, on critical measures. While there are some standard and widely used assessment tools to appraise young children’s emergent reading and language skills and competence, no such tools are used on any comparable basis in primary mathematics.

This type of assessment is required to evaluate the effectiveness of a particular curriculum and to make comparisons across curricula. For the most part, we lack sophisticated methods for tracking student learning over time or for examining the contribution of any particular instructional interventions, whether large or small, on students’ learning.

TEACHER KNOWLEDGE

Little is known about what it takes for teachers to use particular instructional approaches effectively, a necessary element of taking any approach to scale. The challenges can be substantial. The curricula mentioned above introduce major changes in approach to teaching mathematics, and effective implementation will require that teachers change their view of mathematics teaching and learning dramatically. In Everyday Mathematics, for example, teachers are expected to introduce topics that will be revisited later in the curriculum. Complete mastery is not expected with the first introduction. This has created some confusion for teachers, who are often unclear about when mastery is sufficient to move on to the next topic (Fuson et al., 2000).

All of the curricula encourage building on students’ own strategies for problem solving and supporting engagement through dialogue about the benefits of alternative strategies. The change required on the part of the teacher to relinquish control of the answer in favor of a dialogue among students has proven difficult when it has been studied (Palincsar et al., 1989). Adequate opportunities to learn and the ongoing supports for an entirely different approach to teaching will be critical to the effectiveness of efforts to scale up the implementation of the curricula. This is clearly an area in need of further study.

One clue regarding teacher knowledge requirements can be found in research pursued for the most part separately from the work on student learning and the design of curriculum ap-



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