What Counts as Evidence of Educational Achievement? The Role of Constructs in the Pursuit of Equity in Assessment

what students learned as a result of the instructional practices of teachers were predictable, then all forms of assessment would be unnecessary; student achievement could be determined simply by inventorying their educational experiences. However, because what is learned by students is not related in any simple way to what they have been taught, assessment is a central perhaps even the central process in education. At the very least, assessment is integral to effective instruction. At first sight, it appears that assessment should be relatively uncontested. Everyone parents, teachers, employers, the wider community that supports public education through taxes, and the students themselves just wants to know what it is that students have learned. However, two difficulties emerge immediately. The first is that by its very nature assessment reduces ambiguity. The fifth-grade mathematics standard for many states requires students to be able to compare two fractions to find the larger, but when we assess, we have to decide which pairs of fractions should be included and which should not. This may be done explicitly, through a formal process of construct definition (see below), which lays out clearly what should be included and what should be excluded from the assessment, or more commonly, it may be done through some less formal process, involving a judgment of what is appropriate, given that this standard is intended for fifth-grade students as William Angoff (1974) remarked, lurking behind the criterion-referenced evaluation, perhaps even responsible for it, is the norm-referenced evaluation (p. 4). In fact, the choice of the fractions to be compared makes a huge difference to the rate of student success, even if we restrict the domain to fractions where both numerator and denominator are less than 10. In fifth grade, where the fractions have equal