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Defining Mathematics Competency in the Service of Cognitively Based Assessment for Grades 6 Through 8

Graf, Edith Aurora
Publication Year:
Report Number:
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Mathematics Assessment Mathematics Cognition Mathematical Competency Mathematics Task Design Evidence-Centered Design (ECD) Cognitively Based Assessment of, for, and as Learning (CBAL)


This report makes recommendations for the development of middle-school assessment in mathematics, based on a synthesis of scientific findings in cognitive psychology and mathematics education. The focus is on background research, rather than test specifications or example tasks. Readers interested in early development and pilot efforts associated with the Cognitively Based Assessment of, for, and as Learning (CBAL) project in mathematics (for which this review helped provide a theoretical foundation) should consult Graf, Harris, Marquez, Fife, and Redman (2009).The organization of the report is motivated by the evidence-centered design (ECD) approach to assessment developed by Mislevy and colleagues (e.g., see Mislevy, Steinberg, & Almond, 2003). The first section consists of a broad literature review that characterizes mathematical competency with respect to both content and process. Subsequent sections discuss: how to model mathematical competency at the middle school level, the kinds of evidence that reflect the level of student competency and support future learning, and how to design tasks that elicit the target evidence.

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