dards Through Classroom Assessment (1998) is used to identify the additional support that teachers must be given if they are to create opportunities for students to learn mathematics in a balanced way. Black and Wiliam urge those interested in raising standards to open up the black box of the classroom. They argue persuasively for the efficacy of formative assessment in raising standards. If formative assessment is to be effective, Black and Wiliam note, it must be integrated into rather than bolted on top of current instructional practices.
Finally, Chapter 5 addresses the issue of aligning instruction and assessment with standards. The presentation here is substantially informed by the recent and comprehensive monograph Criteria for Alignment of Expectations and Assessments in Mathematics and Science Education (Webb, 1997). Webb leaves little doubt that, for assessment to be effective, instruction must be aligned with standards.