Cognitive objectives are designed to increase an individual's knowledge. Many refer to Bloom's taxonomy of cognitive objectives, originated by Benjamin Bloom and collaborators in the 1950's.
Bloom describes several categories of cognitive learning:
Cognitive objectives are designed to increase an individual's knowledge. Cognitive objectives relate to understandings, awareness, insights (e.g., "Given a description of a planet, the student will be able to identify that planet, as demonstrated verbally or in writing, with 100% accuracy." or "The student will be able to evaluate two different theories of the origin of the solar system as demonstrated by his/her ability to compare and discuss verbally or in writing the strengths and weaknesses of each theory."). This includes knowledge or information recall, comprehension or conceptual understanding, the ability to apply knowledge, the ability to analyze a situation, the ability to synthesize information from a given situation, the ability to evaluate a given situation, and the ability to create something new.
Starting with basic factual knowledge, the categories progress through comprehension, application, analysis, synthesis, and evaluation.
In the 1990's, Lorin Anderson, a former student of Bloom, along with David Krathwohl, one of Boom's original partners, worked to revise the original taxonomy. The Anderson and Krathwohl Taxonomy was published in 2001 in the book "A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom's Taxonomy of Educational Objectives."
Note that in the revised taxonomy, synthesis and evaluation are switched. Also, verbs are used in place of nouns to imply the action one takes in each level.
Whether you like the original or revised taxonomy, there are key verbs for each level you can use when writing cognitive objectives.
Anderson, L.W., & Krathwohl (Eds.). (2001). A Taxonomy for Learning, Teaching, and Assessing: A Revision of Bloom's Taxonomy of Educational Objectives. New York: Longman.
Bloom, B.S. and Krathwohl, D. R. (1956). Taxonomy of Educational Objectives: The Classification of Educational Goals, by a committee of college and university examiners. Handbook I: Cognitive Domain. NY, NY: Longmans, Green.