In 2003, a trial National Assessment of Educational Progress (NAEP) mathematics assessment was administered in Spanish to public school students at grades 4 and 8 in Puerto Rico. Based on preliminary analyses of the 2003 data, changes were made in administration and translation procedures for the 2005 NAEP administration in Puerto Rico. This report describes the content and administration of the trial NAEP mathematics assessments in Puerto Rico in 2003 and 2005, problems with item misfit in the 2003 data, results of a special validity analysis, and plans to integrate Puerto Rico into the national sample in future administrations. This report is one of a series of three on the administration and results of the 2003 and 2005 trial NAEP mathematics assessments in Puerto Rico: (1) "Mathematics 2003 and 2005 Performance in Puerto Rico: Highlights" [ED495982]; and (2) "Mathematics 2005 Performance in Puerto Rico: Focus on the Content Areas" [ED495981]. This, the third report, focuses on the technical considerations of the trial assessments and plans to include Puerto Rico as part of the national sample in future administrations. (Contains 20 figures and 3 tables.)