Section 1. The big picture -- 1. Issues and tensions in the assessment of mathematical proficiency / Alan H. Schoenfeld -- 2. Aims of mathematics education / Judith A. Ramaley -- 3. The No Child Left Behind Act : political context and national goals / Susan Sclafani -- Section 2. Perspectives on mathematical proficiency -- 4. What is mathematical proficiency? / R. James Milgram -- 5. What is mathematical proficiency and how can it be assessed? / Alan H. Schoenfeld -- Section 3. What does assessment assess? : issues and examples -- 6. Mathematical proficiency : what is important? how can it be measured? / Hugh Burkhardt -- 7. Aspects of the art of assessment design / Jan de Lange -- 8. Mathematical proficiency for citizenship / Bernard L. Madison -- 9. Learning from assessment / Richard Askey -- 10. When assessment guides instruction : Silicon Valley's Mathematics Assessment Collaborative / David Foster, Pendred Noyce, and Sara Spiegel -- Section 4. The case of algebra -- 11. Assessing the strands of student proficiency in elementary algebra / William G. McCallum -- 12. Making meaning in algebra : examining students' understandings and misconceptions / David Foster -- 13. Task context and assessment / Ann Shannon -- Section 5. What do assessments assess? : the case of fractions -- 14. Learning about fractions from assessment / Linda Fisher -- 15. Assessing a student's mathematical knowledge by way of interview / Deborah Loewenberg Ball with Brandon Peoples -- 16. Reflections on an assessment interview : what a close look at student understanding can reveal / Alan H. Schoenfeld -- Section 6. The importance of societal context -- 17. Assessment in France / Michèle Artigue -- 18. Assessment to improve learning in mathematics : the BEAR assessment system / Mark Wilson and Claus Carstensen -- 19. English learners and mathematics learning : language issues to consider / Lily Wong Fillmore -- 20. Beyond words to mathematical content : assessing English learners in the mathematics classroom / Judit Moschkovich -- 21. Assessment in the real world : the case of New York City / Elizabeth Taleporos -- 22. Perspectives on state assessments in California : what you release is what teachers get / Elizabeth K. Stage -- Epilogue. What do we need to know? : items for a research agenda.