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Measuring What Counts: A Conceptual Guide for Mathematics Assessment
validity theory can provide much of the technical machinery for determining whether the educational principles are met by a mathematics assessment. One can create a rough correspondence between the content principle and content validity,3 between the learning principle and consequential or systemic validity,4 and between the equity principle and criteria of fairness and accessibility that have been addressed by Silver and Lane.5
Although every mathematics assessment should meet the three principles of content, learning, and equity, that alone cannot guarantee a high-quality assessment. Technical considerations, including generalizability, evidence, and costs, still have a place. The educational principles are primary and essential but they are not sufficient.
The contexts in which assessment tasks are administered and the interpretations students make of them are critical in judging the significance of the content.
What is the mathematical content of the assessment?
What mathematical processes are involved in responding?
Applying the content principle to a mathematics assessment means judging how well it reflects the mathematics that is most important for students to learn. The judgments are similar to early notions of content validity that were limited to asking about the representativeness and relevance of test content. The difference lies in a greater concern today for the quality of the mathematics reflected in the assessment tasks and in the responses to them.
Procedures for evaluating the appropriateness of assessment content are well developed and widely used. Most rely heavily on expert judgment. Judges are asked how well the design of the assessment as a whole captures the content to be measured and how well the individual tasks reflect the design. The two sets of judgments determine whether the tasks sufficiently represent the intended content.
New issues arise when the content principle is applied:
the nature of the important mathematics content leads to some types of tasks that have not been common in educational assessment,
the emphasis on thinking processes leads to new forms of student performance, and