In 1990 the scope of the National Assessment of Educational Progress (NAEP) was broadened by adding the Trial State Assessment (TSA), in which approximately 2,500 eighth graders in 100 schools in 40 states and U.S. territories participated in the mathematics assessment. A major step was training local test administrators to administer the TSA sessions. Members of the NAEP contractor's professional staff were assigned to monitor half of the TSA sessions. A critical question for TSA validity was whether students' performance would differ for monitored and unmonitored sessions. The competence and objectivity of local administrators were issues of great importance. There were small, but reliable differences in the effect of some aspects of the testing environment on the performance of students. When students were cooperative and administrators were proficient, an ideal situation was created for students to demonstrate mathematics proficiency. The differences found were small, but steps should be taken to ensure that the same ideal testing situation is available for all students. Observations of training of TSA administrators confirmed expectations of the highly professional quality of that training. Nevertheless, continued monitoring of state NAEP sessions seems warranted to ensure uniform testing conditions. Nine tables present study data. (SLD)