This paper discusses higher-order cognitive skills, provides examples of appropriate test item content in various subject areas, and describes higher-level cognitive skills which might be tested by the National Assessment of Educational Progress (NAEP). Higher-order cognitive skills are said to be more difficult to measure than simpler skills; they involve the orchestration and practical use of the simpler skills, which are easier to teach and to assess. Domains of cognitve skill are discussed for mathematics, logic, computer programming, physics, scientific reasoning, reading, writing, history, and biology. Characteristics of human thinking are described; it is stated that test developers should be sensitive to human cognition, as well as to the nature of the skill being tested. It is concluded that there may be some very general higher-order cognitive skills such as problem solving, knowledge acquisition, and self-management and control of cognition. Puzzle problems with low requirements for prior specific knowledge might be considered for testing cognitive skills. Finally, research is seen as a valuable source of assessment techniques. (GDC)