This report is the beginning of a series that will examine the performance of the school children of New Jersey relative to the performance of other children in the United States and worldwide. The measure of performance used was the 1992 National Assessment of Educational Progress (NAEP) mathematics examinations and their linked versions of the 1991 International Assessment. The NAEP is used because it is satisfactory in content and form and because the psychometric model underlying its scoring yields a single scale that allows easy comparison. Students sampled by the NAEP are drawn in a principled way from the populations of interest, supporting the accuracy and honesty of the assessment. Based on unstandardized results of the 1992 mathematics assessment, New Jersey was among the highest performing states. When results were standardized to reflect a single national demographic composition, New Jersey's rank among participating states rose to fourth. The United States, however, finished next-to-last when compared with the other 14 nations. The top 5% of New Jersey students ranked third when compared with the top 5% of members of the Organization for Economic Cooperation and Development. Seven figures illustrate the discussion. (Contains 10 references.) (SLD)