Education is our means to instruct our youth in the values and accomplishments of our civilization and to prepare them for adult life. For centuries, arguments have been made about what an education means and how to distinguish an educated person from an uneducated one. Two views have contended for our allegiance since the time of the ancient Greeks [Marrou 1956]. One perspective is the rational and humane vision of the Sophists and later the philosopher-teacher Isocrates, for whom the test of an education was its ability to prepare a citizen to engage in public affairs. The other view is that of Plato and Socrates, who taught that education must guide the student toward an uncovering of the Truth and Beauty that underlie our human experience, the universal themes and natural laws that a well schooled mind can discern beneath the surface confusion of life and the awakening of the spirit within, that allow us to care intensely about life and learning.

We cannot clear up some of the controversies about mathematics education and how to assess learning until we deal with two underlying issues. The first is the mindset that underlies our approach to assessment. The other is to articulate and then discuss our often unspoken assumptions about what it means to be well educated.

First, let us consider what drives our current approaches to assessment. In a recent workshop on assessment [NRC 2003], the point was made that the public accountability movement is driving assessment toward increasingly large-scale tests of what students know. These tests “do not easily conform to curricula devised to match state and national standards” [NRC 2003, p. ix]. A basic problem is that testing has been shaped by psychometric questions (How can we measure this?) and used increasingly for political purposes rather than educational questions that can support learning (Is this worth measuring? What do students really need to know and can we measure that knowledge?). We must bridge the gap between what the large-scale tests measure and how the test results are interpreted and used, on the one hand, and what students and teachers are trying to accomplish in the classroom, on the other. To do this, we can profit by studying the NRC workshop report on assessment. It recommends that large-scale assessments and classroom assessments (a) share a common model of student learning, (b) focus on what is most highly valued rather than what is easy to measure, (c) signal to teachers and students what is important for them to teach and learn. The report goes on to offer some helpful technical and design elements that can increase the usefulness of both levels of tests.