A primary goal of international comparative studies of achievement in mathematics and science is to evaluate the level of performance of students in different countries. An equally important goal is to attempt to understand the bases of differences that emerge. In prior international comparative studies conducted by the International Association for the Evaluation of Educational Achievement (IEA), knowledge of mathematics and science was measured by paper-and-pencil tests, and efforts to understand cross-national differences in achievement were made through questionnaires given to teachers. These methods also constituted the primary means for gathering data for IEA's Third International Mathematics and Science Study (TIMSS). Again, questionnaires were given to teachers and additional data were gathered through questionnaires given to students, parents, and experts in mathematics and science education. As is the case with all methods used for the collection of behavioral and attitudinal data, questionnaires have both strengths and weaknesses. They are the obvious choice when it is necessary to collect large amounts of data on an array of topics at the least expense. But interpretation of data from questionnaires is often more difficult than when there is an opportunity to interact with the respondents and to probe for details or elaboration of answers, as is possible with case studies.