This book is the product of the 2004 MSRI (Mathematical Sciences Research Institute, Berkeley) conference “Assessing Students´ Mathematics Learning: Issues, Costs and Benefits”. The conference articulated different purposes of assessment of student performance in mathematics. The book focuses on ethical issues related to assessment, including how assessment interacts with concerns for equity, sensitivity to culture and the severe pressures on urban and high-poverty schools. The book introduces different frameworks, tools and methods for assessment, comparing the kinds of information they offer about a student’s mathematical proficiency. The book describes complexities of assessment when English is not a student’s native language. If a student is not fluent in English, is their failure to solve a problem a result of not understanding the problem or of not understanding the mathematics? The book highlights the kinds of information that different assessments can offer, including many examples of some of the best mathematics assessments worldwide.