The whole instruction and learning system can be seen as a bridge that is vital in closing the gap between what the standards expect and where assessments show the majority of students to be.

The comprehensive picture that emerges from Webb's alignment document and Black and Wiliam's vision for effective teaching (discussed in Chapter 4) is a rounded picture of the components that are necessary to ensure opportunity to learn for all students. The vision created by these two important recent publications is an exciting one.

In classrooms informed by this vision, students would work on a variety of tasks whose range would extend well beyond the range of tasks that are likely to appear in the on-demand component of the assessment plan. There would be a balance of work on skills, conceptual understanding, and problem solving. Perhaps more students would develop their repertoire of basic mathematical skills as they worked on challenging non-routine problems. There would be fewer instances of tightly sequenced instruction and assessment, and more students who put their mathematics to work in ways that demonstrate an integrated and robust understanding.

In such classrooms, teachers would be freer from the constraints of a fragmented and cluttered curriculum and would be more committed to teach for understanding rather than coverage alone.

In a world informed by this vision, parents might not worry as much about grades and about how well their students compared to other students. Instead, they might worry whether the tests that were administered to their children were aligned to the standards, and whether their children had been given opportunities to learn and to perform.

The primary role of assessment would not be to compare students to one another but to enable students to see how they perform in relation to a balanced, publicly negotiated, and challenging set of standards. Rather than rank or sort, assessment could provide feedback to the students on how well they have learned what they are supposed to learn. As a result, students would have new understandings of what they need to do to learn the mathematics that the standards expect them to learn. It is worth remembering that the main function of alignment is not simply to improve assessment but to use assessment as a means of enhancing student learning.

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