Four topics related to mathematics testing for the National Assessment of Educational Progress (NAEP) are discussed: (1) mathematics achievement; (2) past NAEP approaches; (3) needed changes; and (4) a new conceptual basis for profiling mathematical performance, including recommendations for strengthening current practice. The basic strategy for gathering profile information for students at several age (grade) levels used in the past assessments has been reasonable and has yielded useful information, affecting school mathematics. Current procedures could be improved by discarding content-by-behavior matrices and by adopting a network model, such as conceptual fields. The types of exercises included in the batteries should be expanded to reflect the network model. New contexts should be included so that the construction of knowledge can be assessed. The sampling base can be changed so that data can be gathered for state comparisons. From the rich data such an improved assessment would yield, it should be possible to construct reasonable indicators for use by policymakers. The final four recommendations propose that: (1) work be initiated to identify major conceptual fields in mathematics; (2) future assessments encourage the development of a variety of alternate items and testing formats; (3) the data base be increased so that it reflects current expectations about how students construct mathematical knowledge to build a theoretical model of mathematical performance; and (4) reasonable indicators be constructed from that model for policy purposes. (An extensive list of references is appended.) (GDC)