The recent releases of two major international comparative studies that addressed mathematics—the Trends in International Mathematics and Science Study 2003 (TIMSS 2003) and the Program for International Student Assessment 2003 (PISA 2003)—provide opportunities and challenges for mathematics education researchers interested in using the findings, instruments, and conceptual and theoretical perspectives of these studies as catalysts for secondary analysis and additional research. In particular, a number of important questions in mathematics education in the United States can be pursued, using various resources from these studies as a base, by mathematics education researchers and mathematicians collaborating with statisticians and assessment experts. We highlight some of the main findings of TIMSS 2003 and PISA 2003, and suggest how some of the instruments that were used in these studies, as well as the conceptual frameworks and priorities that guided them, might be beneficial in pursuing pressing questions in such areas as the role of curriculum in mathematics performance, the ways in which social contextual variables interact with mathematics learning, and the challenges in measuring the ability to use mathematics in real-world situations.

To investigate mechanisms of failure in mathematics, we adopt the communicational approach to cognition, which describes thinking as an activity of communication and learning mathematics as an initiation to a certain type of discourse. In the search for factors that impede students' participation in arithmetic communication, we examine the arithmetical discourses of two 18-year-old girls with long histories of learning difficulties. The resulting arithmetical discourse profiles of the two students help us substantiate the following two claims: (1) Almost any person may become a skillful participant of arithmetical discourse, provided, first, that a discursive mode is found that makes the best of this person's special strengths and second, that in the process of teaching, the general sociocultural context of learning is taken into account as having a central role in enabling or barring one's access to literate discourses; (2) if the potential for successful participation remains often unrealized, it is mainly because of certain widely practiced abuses of literate mathematical discourse.