The Third International Mathematics and Science Study (TIMSS) is a survey of mathematics and science achievement sponsored by the International Association for the Evaluation of Educational Achievement. With more than 45 participating countries, three target populations, more than thirty languages, 15,000 schools, more than half a million students, TIMSS is the largest and most ambitious international study of educational achievement ever undertaken. Students participating in the assessment were administered one of eight achievement tests that contain items in mathematics and science, using a variety of item formats. As TIMSS is an international study, many audiences will look at the results to make comparisons between the participating countries in terms of their achievement in each of the mathematics and science areas assessed, as well as to answer many other research questions for which the data collected can provide a response. This call for a careful and creative use of psychometric theory so that the results from the assessment can be deemed reliable.