This article addresses the application of the assessment triangle developed by the National Research Council (Pellegrino, Chudowsky, & Glaser, 2001), most specifically the cognition vertex of that triangle, to the unique learning characteristics of students with significant cognitive disabilities in developing and demonstrating academic competence. Given the inclusion of all students, including students with significant cognitive disabilities, in measures of large-scale educational assessment and accountability under the No Child Left Behind Act, it is essential to examine how the primary elements of knowledge representation and competence identified by Pellegrino et al. for all students have special ramifications for students with significant cognitive disabilities. It is only in the development of such a model of competence that it is possible to construct alternate assessments for these students that validly represent what these students know and can do. (Contains 1 note.)