In September 1991, the National Assessment Governing Board (NAGB) announced standards for basic, proficient, and advanced achievement in mathematics and reported that few American students had reached these standards. Expert reviewers noted technical problems with the NAGB approach and questioned its results. In this report, the NAGB standard-setting approach and ability to provide policy guidance to the National Assessment of Education Progress (NAEP) are examined. The NAEP test-score standards set in 1990 were evaluated by examining the adequacy of item-judgment procedures and by studying whether the evidence supported NAGB's interpretation of the NAEP scores selected for each level. The investigation found that the standard-setting approach was procedurally flawed, and that the interpretations of the resulting NAEP scores were of doubtful validity. The NAGB improved its procedures substantially in 1992, but the issue of the validity of interpretation remains. The report concludes that the NAGB approach is unsuited for the NAEP. Alternative approaches are reviewed, but it is apparent that their use will be difficult as the NAEP is currently designed. Specific recommendations are given to help implement these alternative approaches. Six tables and three figures illustrate the discussion. Appendixes include comments from the U.S. Department of Education and from the NAGB, a summary description of the NAEP and other supplementary materials. A four-part bibliography is provided. Contains 44 references. (SLD)