To invert Vince Lombardi: context isn't the only thing, it's everything. As the six chapters in this section show, it is sometimes the case that the best way to look inward is to begin by looking outward. Just as fish are said to be unaware of the water in which they swim, those embedded in a cultural context may be unaware of just how much of what they do is socially and culturally determined, and not simply “the way it is” or “the way it must be.”

In Chapter 17, Michèle Artigue takes readers on a tour of mathematics assessments in France. As she does, it becomes clear that some aspects of assessment are universal and that some are very particular to local circumstances. The broad goals of mathematics assessment discussed by Artigue are parallel to those discussed elsewhere in this volume. Assessments should, she writes, reflect our deeply held mathematical values; they should help teachers to know what their students are understanding, in order to enhance diagnosis and remediation; they should provide the government with a general picture of the country based on representative samples of pupils. Note that different assessments in the U.S. serve these functions. For example, the National Assessment of Educational Progress (NAEP) provides some “benchmarking” of American student performance. However, NAEP provides no direct feedback to teachers or students. Numerous high-stakes tests at the state level—in some cases, at every grade from second grade on—are highly consequential for students but have no diagnostic value.