What can and should we learn from international studies of mathematics achievement?

International studies of mathematics achievement such as Trends in International Mathematics and Science Study and Programme for International Student Assessment have dominated much discussion within the mathematics education community and beyond, but such discussions often do not do justice to the nature of these international studies. In this paper, the espoused purposes of these international studies are examined, and the limitations of large-scale international studies posed by the nature and the methodology of these studies are discussed. It is argued that because of the limitations, only broad-brush pictures about achievements in different countries can be painted, and one such broad-brush picture is the superior performance of East Asian students. Cultural values in these countries are then discussed as possible explanation of student achievement. What should and should not be learned from these international studies are then discussed. Caution is advised against emphasising fine changes in ranking of countries, asserting causal relations between background variables and achievement, drawing conclusions about teacher attributes, and suggesting changes in education policies without due consideration of the nature and limitations of these studies. Instead one should focus on trends in achievement scores (and not rankings), performance in different strands of mathematics, and the attitudes of our students as shown in the questionnaire results.