administering classroom assessments. The materials will help administrators provide teachers with the support necessary for enhancing the teaching and learning of mathematics. This chapter begins by defining standards-based assessment and other key terms, and then compares standards-based assessment with traditional norm-referenced tests. The remainder of the chapter describes the organization of the booklet.

In this booklet, experience and research from two assessment development projects, Balanced Assessment and New Standards, will be drawn upon to offer guidance about the development and implementation of assessments. Throughout, four particularly important ideas will be addressed: balance, opportunity to perform, opportunity to learn, and alignment. The intent is not to describe all of the details associated with large-scale assessment development but rather to discuss how these four basic ideas can be used to inform the development and implementation of innovative assessment instruments.

Standards-based assessments

The assessments we are concerned with here are those that are necessary in a standards-based system of education. In such a system, assessments need to be designed to assess whether students meet publicly negotiated and agreed-upon standards. The standards to which an assessment is referenced might be those of a state, a district, or the National Council of Teachers of Mathematics (i.e., NCTM, 1989). It does not necessarily matter what or whose standards are chosen, but in our view what is important is that the selected standards promote a broad and balanced approach to learning mathematics, where conceptual understanding and mathematical skills are both emphasized.

Standards will be more likely to have a positive effect on mathematics learning if assessment, curriculum, and instruction are aligned with them (Webb, 1997). Assessments that are aligned to standards are referred to as standards-based assessments. When curriculum, instruction, and assessment are aligned to the same set of standards, those standards lay out what a student should know and be able to do. Curriculum and instruction provide opportunities for students to learn the mathematics that the standards ask them to learn and to acquire the know-how for them to show what they have learned. Assessments provide opportunities for students to perform and allow inferences to be made about what students know and can do in mathematics.

When instruction and assessment are aligned to standards, the role of the teacher is central. What goes on in the classroom is crucial to the enhancement of learning mathematics (Black &



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